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ckpts/universal/global_step120/zero/18.input_layernorm.weight/exp_avg.pt

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ckpts/universal/global_step120/zero/18.input_layernorm.weight/exp_avg_sq.pt

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ckpts/universal/global_step120/zero/18.input_layernorm.weight/fp32.pt

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venv/lib/python3.10/site-packages/torch/autograd/__init__.py

@@ -0,0 +1,515 @@
+"""
+``torch.autograd`` provides classes and functions implementing automatic
+differentiation of arbitrary scalar valued functions. It requires minimal
+changes to the existing code - you only need to declare :class:`Tensor` s
+for which gradients should be computed with the ``requires_grad=True`` keyword.
+As of now, we only support autograd for floating point :class:`Tensor` types (
+half, float, double and bfloat16) and complex :class:`Tensor` types (cfloat, cdouble).
+"""
+import warnings
+from typing import Any, Callable, cast, List, Optional, Sequence, Tuple, Union
+
+import torch
+
+from torch.types import _size, _TensorOrTensors, _TensorOrTensorsOrGradEdge
+from .. import _vmap_internals
+from ..overrides import handle_torch_function, has_torch_function, is_tensor_like
+from . import forward_ad, functional, graph
+from .anomaly_mode import detect_anomaly, set_detect_anomaly
+from .function import Function, NestedIOFunction
+from .grad_mode import (
+    _force_original_view_tracking,
+    _unsafe_preserve_version_counter,
+    enable_grad,
+    inference_mode,
+    no_grad,
+    set_grad_enabled,
+    set_multithreading_enabled,
+)
+from .gradcheck import gradcheck, gradgradcheck
+from .graph import _engine_run_backward
+
+from .variable import Variable
+
+__all__ = ["Variable", "Function", "backward", "grad_mode"]
+
+_OptionalTensor = Optional[torch.Tensor]
+_ShapeorNestedShape = Union[_size, Sequence[_size], torch.Tensor]
+
+
+def _calculate_shape(
+    output: torch.Tensor, grad: torch.Tensor, is_grads_batched: bool
+) -> Tuple[_ShapeorNestedShape, _ShapeorNestedShape]:
+    # is_same_size ensures that both tensors are either nested or non nested
+    # circular import
+    from torch.nested._internal.nested_tensor import NestedTensor
+
+    if output.is_nested and not isinstance(output, NestedTensor):
+        if is_grads_batched:
+            raise RuntimeError("Batched grads are not supported with Nested Tensor.")
+        out_shape = output._nested_tensor_size()
+        grad_shape = grad._nested_tensor_size()
+
+        return out_shape, grad_shape
+
+    reg_out_shape = output.shape
+    reg_grad_shape = grad.shape if not is_grads_batched else grad.shape[1:]
+    return reg_out_shape, reg_grad_shape
+
+
+def _make_grads(
+    outputs: Sequence[torch.Tensor],
+    grads: Sequence[_OptionalTensor],
+    is_grads_batched: bool,
+) -> Tuple[_OptionalTensor, ...]:
+    new_grads: List[_OptionalTensor] = []
+    for out, grad in zip(outputs, grads):
+        if isinstance(grad, torch.Tensor):
+            from torch.fx.experimental.symbolic_shapes import expect_true, sym_eq
+
+            first_grad = grad if not is_grads_batched else grad[0]
+            # TODO: We can remove this conditional once we uniformly use
+            # singleton int to represent jagged dimension, so that size() call
+            # on nested tensor works
+            if out.is_nested or first_grad.is_nested:
+                shape_matches = torch.is_same_size(out, first_grad)
+            else:
+                # We need to do a regular size check, without going through
+                # the operator, to be able to handle unbacked symints
+                # (expect_true ensures we can deal with unbacked)
+                shape_matches = expect_true(sym_eq(out.size(), first_grad.size()))
+            if not shape_matches:
+                out_shape, grad_shape = _calculate_shape(
+                    out, first_grad, is_grads_batched
+                )
+                if is_grads_batched:
+                    raise RuntimeError(
+                        "If `is_grads_batched=True`, we interpret the first "
+                        "dimension of each grad_output as the batch dimension. "
+                        "The sizes of the remaining dimensions are expected to match "
+                        "the shape of corresponding output, but a mismatch "
+                        "was detected: grad_output["
+                        + str(grads.index(grad))
+                        + "] has a shape of "
+                        + str(grad_shape)
+                        + " and output["
+                        + str(outputs.index(out))
+                        + "] has a shape of "
+                        + str(out_shape)
+                        + ". "
+                        "If you only want some tensors in `grad_output` to be considered "
+                        "batched, consider using vmap."
+                    )
+                else:
+                    raise RuntimeError(
+                        "Mismatch in shape: grad_output["
+                        + str(grads.index(grad))
+                        + "] has a shape of "
+                        + str(grad_shape)
+                        + " and output["
+                        + str(outputs.index(out))
+                        + "] has a shape of "
+                        + str(out_shape)
+                        + "."
+                    )
+            if out.dtype.is_complex != grad.dtype.is_complex:
+                raise RuntimeError(
+                    "For complex Tensors, both grad_output and output"
+                    " are required to have the same dtype."
+                    " Mismatch in dtype: grad_output["
+                    + str(grads.index(grad))
+                    + "] has a dtype of "
+                    + str(grad.dtype)
+                    + " and output["
+                    + str(outputs.index(out))
+                    + "] has a dtype of "
+                    + str(out.dtype)
+                    + "."
+                )
+            new_grads.append(grad)
+        elif grad is None:
+            if out.requires_grad:
+                if out.numel() != 1:
+                    raise RuntimeError(
+                        "grad can be implicitly created only for scalar outputs"
+                    )
+                if not out.dtype.is_floating_point:
+                    msg = (
+                        "grad can be implicitly created only for real scalar outputs"
+                        f" but got {out.dtype}"
+                    )
+                    raise RuntimeError(msg)
+                new_grads.append(
+                    torch.ones_like(out, memory_format=torch.preserve_format)
+                )
+            else:
+                new_grads.append(None)
+        else:
+            raise TypeError(
+                "gradients can be either Tensors or None, but got "
+                + type(grad).__name__
+            )
+    return tuple(new_grads)
+
+
+def _tensor_or_tensors_to_tuple(
+    tensors: Optional[_TensorOrTensors], length: int
+) -> Tuple[_OptionalTensor, ...]:
+    if tensors is None:
+        return (None,) * length
+    if isinstance(tensors, torch.Tensor):
+        return (tensors,)
+    return tuple(tensors)
+
+
+def backward(
+    tensors: _TensorOrTensors,
+    grad_tensors: Optional[_TensorOrTensors] = None,
+    retain_graph: Optional[bool] = None,
+    create_graph: bool = False,
+    grad_variables: Optional[_TensorOrTensors] = None,
+    inputs: Optional[_TensorOrTensorsOrGradEdge] = None,
+) -> None:
+    r"""Computes the sum of gradients of given tensors with respect to graph
+    leaves.
+
+    The graph is differentiated using the chain rule. If any of ``tensors``
+    are non-scalar (i.e. their data has more than one element) and require
+    gradient, then the Jacobian-vector product would be computed, in this
+    case the function additionally requires specifying ``grad_tensors``.
+    It should be a sequence of matching length, that contains the "vector"
+    in the Jacobian-vector product, usually the gradient of the differentiated
+    function w.r.t. corresponding tensors (``None`` is an acceptable value for
+    all tensors that don't need gradient tensors).
+
+    This function accumulates gradients in the leaves - you might need to zero
+    ``.grad`` attributes or set them to ``None`` before calling it.
+    See :ref:`Default gradient layouts<default-grad-layouts>`
+    for details on the memory layout of accumulated gradients.
+
+    .. note::
+        Using this method with ``create_graph=True`` will create a reference cycle
+        between the parameter and its gradient which can cause a memory leak.
+        We recommend using ``autograd.grad`` when creating the graph to avoid this.
+        If you have to use this function, make sure to reset the ``.grad`` fields of your
+        parameters to ``None`` after use to break the cycle and avoid the leak.
+
+    .. note::
+
+        If you run any forward ops, create ``grad_tensors``, and/or call ``backward``
+        in a user-specified CUDA stream context, see
+        :ref:`Stream semantics of backward passes<bwd-cuda-stream-semantics>`.
+
+    .. note::
+
+        When ``inputs`` are provided and a given input is not a leaf,
+        the current implementation will call its grad_fn (even though it is not strictly needed to get this gradients).
+        It is an implementation detail on which the user should not rely.
+        See https://github.com/pytorch/pytorch/pull/60521#issuecomment-867061780 for more details.
+
+    Args:
+        tensors (Sequence[Tensor] or Tensor): Tensors of which the derivative will be
+            computed.
+        grad_tensors (Sequence[Tensor or None] or Tensor, optional): The "vector" in
+            the Jacobian-vector product, usually gradients w.r.t. each element of
+            corresponding tensors. None values can be specified for scalar Tensors or
+            ones that don't require grad. If a None value would be acceptable for all
+            grad_tensors, then this argument is optional.
+        retain_graph (bool, optional): If ``False``, the graph used to compute the grad
+            will be freed. Note that in nearly all cases setting this option to ``True``
+            is not needed and often can be worked around in a much more efficient
+            way. Defaults to the value of ``create_graph``.
+        create_graph (bool, optional): If ``True``, graph of the derivative will
+            be constructed, allowing to compute higher order derivative products.
+            Defaults to ``False``.
+        inputs (Sequence[Tensor] or Tensor or Sequence[GradientEdge], optional): Inputs w.r.t. which the gradient
+            be will accumulated into ``.grad``. All other Tensors will be ignored. If
+            not provided, the gradient is accumulated into all the leaf Tensors that
+            were used to compute the :attr:`tensors`.
+    """
+    if torch._C._are_functorch_transforms_active():
+        raise RuntimeError(
+            "backward() called inside a functorch transform. This is not "
+            "supported, please use functorch.grad or functorch.vjp instead "
+            "or call backward() outside of functorch transforms."
+        )
+
+    if grad_variables is not None:
+        warnings.warn("'grad_variables' is deprecated. Use 'grad_tensors' instead.")
+        if grad_tensors is None:
+            grad_tensors = grad_variables
+        else:
+            raise RuntimeError(
+                "'grad_tensors' and 'grad_variables' (deprecated) "
+                "arguments both passed to backward(). Please only "
+                "use 'grad_tensors'."
+            )
+    if inputs is not None and len(inputs) == 0:
+        raise RuntimeError("'inputs' argument to backward() cannot be empty.")
+
+    tensors = (tensors,) if isinstance(tensors, torch.Tensor) else tuple(tensors)
+    inputs = (
+        (inputs,)
+        if isinstance(inputs, (torch.Tensor, graph.GradientEdge))
+        else tuple(inputs)
+        if inputs is not None
+        else tuple()
+    )
+
+    grad_tensors_ = _tensor_or_tensors_to_tuple(grad_tensors, len(tensors))
+    grad_tensors_ = _make_grads(tensors, grad_tensors_, is_grads_batched=False)
+    if retain_graph is None:
+        retain_graph = create_graph
+
+    # The reason we repeat the same comment below is that
+    # some Python versions print out the first line of a multi-line function
+    # calls in the traceback and some print out the last line
+    _engine_run_backward(
+        tensors,
+        grad_tensors_,
+        retain_graph,
+        create_graph,
+        inputs,
+        allow_unreachable=True,
+        accumulate_grad=True,
+    )
+
+
+def grad(
+    outputs: _TensorOrTensors,
+    inputs: _TensorOrTensorsOrGradEdge,
+    grad_outputs: Optional[_TensorOrTensors] = None,
+    retain_graph: Optional[bool] = None,
+    create_graph: bool = False,
+    only_inputs: bool = True,
+    allow_unused: Optional[bool] = None,
+    is_grads_batched: bool = False,
+    materialize_grads: bool = False,
+) -> Tuple[torch.Tensor, ...]:
+    r"""Computes and returns the sum of gradients of outputs with respect to
+    the inputs.
+
+    ``grad_outputs`` should be a sequence of length matching ``output``
+    containing the "vector" in vector-Jacobian product, usually the pre-computed
+    gradients w.r.t. each of the outputs. If an output doesn't require_grad,
+    then the gradient can be ``None``).
+
+    .. note::
+
+        If you run any forward ops, create ``grad_outputs``, and/or call ``grad``
+        in a user-specified CUDA stream context, see
+        :ref:`Stream semantics of backward passes<bwd-cuda-stream-semantics>`.
+
+    .. note::
+
+        ``only_inputs`` argument is deprecated and is ignored now (defaults to ``True``).
+        To accumulate gradient for other parts of the graph, please use
+        ``torch.autograd.backward``.
+
+    Args:
+        outputs (sequence of Tensor): outputs of the differentiated function.
+        inputs (sequence of Tensor or GradientEdge): Inputs w.r.t. which the gradient will be
+            returned (and not accumulated into ``.grad``).
+        grad_outputs (sequence of Tensor): The "vector" in the vector-Jacobian product.
+            Usually gradients w.r.t. each output. None values can be specified for scalar
+            Tensors or ones that don't require grad. If a None value would be acceptable
+            for all grad_tensors, then this argument is optional. Default: None.
+        retain_graph (bool, optional): If ``False``, the graph used to compute the grad
+            will be freed. Note that in nearly all cases setting this option to ``True``
+            is not needed and often can be worked around in a much more efficient
+            way. Defaults to the value of ``create_graph``.
+        create_graph (bool, optional): If ``True``, graph of the derivative will
+            be constructed, allowing to compute higher order derivative products.
+            Default: ``False``.
+        allow_unused (Optional[bool], optional): If ``False``, specifying inputs
+            that were not used when computing outputs (and therefore their grad is
+            always zero) is an error. Defaults to the value of ``materialize_grads``.
+        is_grads_batched (bool, optional): If ``True``, the first dimension of each
+            tensor in ``grad_outputs`` will be interpreted as the batch dimension.
+            Instead of computing a single vector-Jacobian product, we compute a
+            batch of vector-Jacobian products for each "vector" in the batch.
+            We use the vmap prototype feature as the backend to vectorize calls
+            to the autograd engine so that this computation can be performed in a
+            single call. This should lead to performance improvements when compared
+            to manually looping and performing backward multiple times. Note that
+            due to this feature being experimental, there may be performance
+            cliffs. Please use ``torch._C._debug_only_display_vmap_fallback_warnings(True)``
+            to show any performance warnings and file an issue on github if warnings exist
+            for your use case. Defaults to ``False``.
+        materialize_grads (bool, optional): If ``True``, set the gradient for unused inputs
+            to zero instead of None. This is useful when computing higher-order derivatives.
+            If ``materialize_grads`` is ``True`` and ``allow_unused`` is ``False``, an error
+            will be raised. Defaults to ``False``.
+
+    """
+    if materialize_grads and allow_unused is False:
+        raise ValueError(
+            "Expected allow_unused to be True or not passed when materialize_grads=True, "
+            "but got: allow_unused=False."
+        )
+    if allow_unused is None:
+        allow_unused = materialize_grads
+    t_outputs = cast(
+        Tuple[torch.Tensor, ...],
+        (outputs,) if is_tensor_like(outputs) else tuple(outputs),
+    )
+    if is_tensor_like(inputs) or isinstance(inputs, graph.GradientEdge):
+        inputs = cast(_TensorOrTensorsOrGradEdge, (inputs,))
+    else:
+        inputs = tuple(inputs)
+    t_inputs = tuple(i for i in inputs if is_tensor_like(i))
+    overridable_args = t_outputs + t_inputs
+    if has_torch_function(overridable_args):
+        return handle_torch_function(
+            grad,
+            overridable_args,
+            t_outputs,
+            inputs,
+            grad_outputs=grad_outputs,
+            retain_graph=retain_graph,
+            create_graph=create_graph,
+            only_inputs=only_inputs,
+            allow_unused=allow_unused,
+            is_grads_batched=is_grads_batched,
+            materialize_grads=materialize_grads,
+        )
+
+    if not only_inputs:
+        warnings.warn(
+            "only_inputs argument is deprecated and is ignored now "
+            "(defaults to True). To accumulate gradient for other "
+            "parts of the graph, please use torch.autograd.backward."
+        )
+
+    grad_outputs_ = _tensor_or_tensors_to_tuple(grad_outputs, len(t_outputs))
+    grad_outputs_ = _make_grads(
+        t_outputs, grad_outputs_, is_grads_batched=is_grads_batched
+    )
+
+    if retain_graph is None:
+        retain_graph = create_graph
+
+    # The reason we repeat the same comment several times below is because
+    # some Python versions print out the first line of multi-line function
+    # calls in the traceback and some print out the last line
+    if is_grads_batched:
+
+        def vjp(gO):
+            return _engine_run_backward(
+                t_outputs,
+                gO,
+                retain_graph,
+                create_graph,
+                inputs,
+                allow_unused,
+                accumulate_grad=False,
+            )
+
+        result = _vmap_internals._vmap(vjp, 0, 0, allow_none_pass_through=True)(
+            grad_outputs_
+        )
+    else:
+        result = _engine_run_backward(
+            t_outputs,
+            grad_outputs_,
+            retain_graph,
+            create_graph,
+            inputs,
+            allow_unused,
+            accumulate_grad=False,
+        )
+    if materialize_grads:
+        if any(
+            result[i] is None and not is_tensor_like(inputs[i])
+            for i in range(len(inputs))
+        ):
+            raise RuntimeError(
+                "materialize_grads cannot be used when the given input is a GradientEdge"
+            )
+        result = tuple(
+            output
+            if output is not None
+            else torch.zeros_like(input, requires_grad=True)
+            for (output, input) in zip(result, inputs)
+        )
+    return result
+
+
+# This function applies in case of gradient checkpointing for memory
+# optimization. Currently, gradient checkpointing is supported only if the
+# execution engine is invoked through torch.autograd.backward() and its
+# inputs argument is not passed. It is not supported for torch.autograd.grad().
+# This is because if inputs are specified, the gradient won't be calculated for
+# anything else e.g. model parameters like weights, bias etc.
+#
+# This function returns whether the checkpointing is valid i.e. torch.autograd.backward
+# or not i.e. torch.autograd.grad. The implementation works by maintaining a thread
+# local variable in torch/csrc/autograd/engine.cpp which looks at the NodeTask
+# in the stack and before a NodeTask is executed in evaluate_function, it
+# checks for whether reentrant backwards is imperative or not.
+# See https://github.com/pytorch/pytorch/pull/4594 for more discussion/context
+def _is_checkpoint_valid():
+    return Variable._execution_engine.is_checkpoint_valid()
+
+
+def variable(*args, **kwargs):
+    raise RuntimeError(
+        "torch.autograd.variable(...) is deprecated, use torch.tensor(...) instead"
+    )
+
+
+# Monkey patching variable.Variable to fix FX codegen. FX generates a call by roughly doing
+# f"{fn.__module__}.{fn.__name__}(...). This yields torch.autograd.variable.Variable(...) in the
+# output of an FX graph.  Unfortunately the module name torch.autograd.variable is shadowed by the
+# deprecated function - variable(...).
+variable.Variable = Variable  # type: ignore[attr-defined]
+
+if not torch._C._autograd_init():
+    raise RuntimeError("autograd initialization failed")
+
+# Import all native method/classes
+from torch._C._autograd import (
+    _add_metadata_json,
+    _disable_profiler,
+    _disable_profiler_legacy,
+    _enable_profiler,
+    _enable_profiler_legacy,
+    _enable_record_function,
+    _get_sequence_nr,
+    _kineto_step,
+    _KinetoEvent,
+    _pop_saved_tensors_default_hooks,
+    _prepare_profiler,
+    _profiler_enabled,
+    _ProfilerResult,
+    _push_saved_tensors_default_hooks,
+    _record_function_with_args_enter,
+    _record_function_with_args_exit,
+    _set_empty_test_observer,
+    _supported_activities,
+    DeviceType,
+    kineto_available,
+    ProfilerEvent,
+    SavedTensor,
+)
+
+from torch._C._profiler import ProfilerActivity, ProfilerConfig, ProfilerState
+
+from . import profiler
+
+
+def _register_py_tensor_class_for_device(device, cls):
+    if not isinstance(cls, type):
+        raise RuntimeError("cls isn't a typeinfo object")
+    torch._C._register_py_class_for_device(device, cls)
+
+
+is_multithreading_enabled = torch._C._is_multithreading_enabled
+torch._C._add_docstr(
+    is_multithreading_enabled, "Returns True if multithreading is currently enabled."
+)
+
+is_view_replay_enabled = torch._C._is_view_replay_enabled
+torch._C._add_docstr(
+    is_view_replay_enabled, "Returns True if view-replay is currently enabled."
+)

venv/lib/python3.10/site-packages/torch/autograd/_functions/__init__.py

@@ -0,0 +1 @@
+from .tensor import *  # noqa: F403

venv/lib/python3.10/site-packages/torch/autograd/_functions/tensor.py

@@ -0,0 +1,63 @@
+import operator
+import warnings
+from functools import reduce
+
+import torch
+import torch._utils
+from ..function import Function
+
+
+class Type(Function):
+    @staticmethod
+    def forward(ctx, i, dest_type):
+        warnings.warn(
+            "torch.autograd._functions.Type is deprecated as of PyTorch 2.1, please use "
+            "torch.tensor.to(dtype=dtype) instead."
+        )
+        ctx.input_type = type(i)
+        ctx.input_device = -1 if not i.is_cuda else i.get_device()
+        return i.type(dest_type)
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        if ctx.input_device == -1:
+            return grad_output.type(ctx.input_type), None
+        else:
+            with torch.cuda.device(ctx.input_device):
+                return grad_output.type(ctx.input_type), None
+
+
+# TODO: deprecate this
+class Resize(Function):
+    @staticmethod
+    def forward(ctx, tensor, sizes):
+        ctx.sizes = sizes
+        ctx.numel = reduce(operator.mul, sizes, 1)
+        if tensor.numel() != ctx.numel:
+            raise RuntimeError(
+                (
+                    "requested resize to {} ({} elements in total), "
+                    "but the given tensor has a size of {} ({} elements). "
+                    "autograd's resize can only change the shape of a given "
+                    "tensor, while preserving the number of elements. "
+                ).format(
+                    "x".join(map(str, sizes)),
+                    ctx.numel,
+                    "x".join(map(str, tensor.size())),
+                    tensor.numel(),
+                )
+            )
+        ctx.input_sizes = tensor.size()
+        if tensor.is_quantized:
+            tensor.copy_(tensor)
+            return tensor.contiguous().view(*sizes)
+        if tensor.is_contiguous():
+            result = tensor.new(tensor).contiguous().view(*sizes)
+            return result
+        else:
+            return tensor.contiguous().view(*sizes)
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        assert grad_output.numel() == ctx.numel
+        return grad_output.contiguous().view(ctx.input_sizes), None

venv/lib/python3.10/site-packages/torch/autograd/_functions/utils.py

@@ -0,0 +1,62 @@
+import operator
+from functools import reduce
+
+
+def maybe_view(tensor, size, check_same_size=True):
+    if check_same_size and tensor.size() == size:
+        return tensor
+    return tensor.contiguous().view(size)
+
+
+def maybe_unexpand(tensor, old_size, check_same_size=True):
+    if check_same_size and tensor.size() == old_size:
+        return tensor
+    num_unsqueezed = tensor.dim() - len(old_size)
+    expanded_dims = [
+        dim
+        for dim, (expanded, original) in enumerate(
+            zip(tensor.size()[num_unsqueezed:], old_size)
+        )
+        if expanded != original
+    ]
+
+    for _ in range(num_unsqueezed):
+        tensor = tensor.sum(0, keepdim=False)
+    for dim in expanded_dims:
+        tensor = tensor.sum(dim, keepdim=True)
+    return tensor
+
+
+# Check whether the op enable broadcasting, and whether it is supported by ONNX.
+# If dims1 and dims2 are different, then broadcast is True.
+# We always assume the combination of dims1 and dims2 is broadcastable.
+# The following types of broadcasting are supported in ONNX:
+#     1) Only one element in dims2, such as dims2 = [1, 1]
+#     2) dims2 is suffix of dims1, such as dims1 = [2, 3, 4], and dims2 = [3, 4]
+# Details can be found here: https://github.com/onnx/onnx/blob/master/docs/Operators.md#Gemm
+def check_onnx_broadcast(dims1, dims2):
+    broadcast = False
+    supported = True
+    len1 = len(dims1)
+    len2 = len(dims2)
+    numel1 = reduce(operator.mul, dims1)
+    numel2 = reduce(operator.mul, dims2)
+    if len1 < len2:
+        broadcast = True
+        if numel2 != 1:
+            supported = False
+    elif len1 > len2:
+        broadcast = True
+        if numel2 != 1 and dims1[len1 - len2 :] != dims2:
+            supported = False
+    else:
+        if dims1 != dims2:
+            broadcast = True
+            if numel2 != 1:
+                supported = False
+
+    if not supported:
+        raise ValueError(
+            f"Numpy style broadcasting is not supported in ONNX. Input dims are: {dims1}, {dims2}"
+        )
+    return broadcast

venv/lib/python3.10/site-packages/torch/autograd/anomaly_mode.py

@@ -0,0 +1,119 @@
+import warnings
+
+import torch
+
+__all__ = ["detect_anomaly", "set_detect_anomaly"]
+
+
+class detect_anomaly:
+    r"""Context-manager that enable anomaly detection for the autograd engine.
+
+    This does two things:
+
+    - Running the forward pass with detection enabled will allow the backward
+      pass to print the traceback of the forward operation that created the failing
+      backward function.
+    - If ``check_nan`` is ``True``, any backward computation that generate "nan"
+      value will raise an error. Default ``True``.
+
+    .. warning::
+        This mode should be enabled only for debugging as the different tests
+        will slow down your program execution.
+
+    Example:
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_ANOMALY)
+        >>> import torch
+        >>> from torch import autograd
+        >>> class MyFunc(autograd.Function):
+        ...     @staticmethod
+        ...     def forward(ctx, inp):
+        ...         return inp.clone()
+        ...     @staticmethod
+        ...     def backward(ctx, gO):
+        ...         # Error during the backward pass
+        ...         raise RuntimeError("Some error in backward")
+        ...         return gO.clone()
+        >>> def run_fn(a):
+        ...     out = MyFunc.apply(a)
+        ...     return out.sum()
+        >>> inp = torch.rand(10, 10, requires_grad=True)
+        >>> out = run_fn(inp)
+        >>> out.backward()
+            Traceback (most recent call last):
+              File "<stdin>", line 1, in <module>
+              File "/your/pytorch/install/torch/_tensor.py", line 93, in backward
+                torch.autograd.backward(self, gradient, retain_graph, create_graph)
+              File "/your/pytorch/install/torch/autograd/__init__.py", line 90, in backward
+                allow_unreachable=True)  # allow_unreachable flag
+              File "/your/pytorch/install/torch/autograd/function.py", line 76, in apply
+                return self._forward_cls.backward(self, *args)
+              File "<stdin>", line 8, in backward
+            RuntimeError: Some error in backward
+        >>> with autograd.detect_anomaly():
+        ...     inp = torch.rand(10, 10, requires_grad=True)
+        ...     out = run_fn(inp)
+        ...     out.backward()
+            Traceback of forward call that caused the error:
+              File "tmp.py", line 53, in <module>
+                out = run_fn(inp)
+              File "tmp.py", line 44, in run_fn
+                out = MyFunc.apply(a)
+            Traceback (most recent call last):
+              File "<stdin>", line 4, in <module>
+              File "/your/pytorch/install/torch/_tensor.py", line 93, in backward
+                torch.autograd.backward(self, gradient, retain_graph, create_graph)
+              File "/your/pytorch/install/torch/autograd/__init__.py", line 90, in backward
+                allow_unreachable=True)  # allow_unreachable flag
+              File "/your/pytorch/install/torch/autograd/function.py", line 76, in apply
+                return self._forward_cls.backward(self, *args)
+              File "<stdin>", line 8, in backward
+            RuntimeError: Some error in backward
+
+    """
+
+    def __init__(self, check_nan=True) -> None:
+        self.prev = torch.is_anomaly_enabled()
+        self.check_nan = check_nan
+        self.prev_check_nan = torch.is_anomaly_check_nan_enabled()
+        warnings.warn(
+            "Anomaly Detection has been enabled. "
+            "This mode will increase the runtime "
+            "and should only be enabled for debugging.",
+            stacklevel=2,
+        )
+
+    def __enter__(self) -> None:
+        torch.set_anomaly_enabled(True, self.check_nan)
+
+    def __exit__(self, *args: object) -> None:
+        torch.set_anomaly_enabled(self.prev, self.prev_check_nan)
+
+
+class set_detect_anomaly:
+    r"""Context-manager that sets the anomaly detection for the autograd engine on or off.
+
+    ``set_detect_anomaly`` will enable or disable the autograd anomaly detection
+    based on its argument :attr:`mode`.
+    It can be used as a context-manager or as a function.
+
+    See ``detect_anomaly`` above for details of the anomaly detection behaviour.
+
+    Args:
+        mode (bool): Flag whether to enable anomaly detection (``True``),
+                     or disable (``False``).
+        check_nan (bool): Flag whether to raise an error when the backward
+                          generate "nan"
+
+    """
+
+    def __init__(self, mode: bool, check_nan: bool = True) -> None:
+        self.prev = torch.is_anomaly_enabled()
+        self.prev_check_nan = torch.is_anomaly_check_nan_enabled()
+        torch.set_anomaly_enabled(mode, check_nan)
+
+    def __enter__(self) -> None:
+        pass
+
+    def __exit__(self, *args: object) -> None:
+        torch.set_anomaly_enabled(self.prev, self.prev_check_nan)

venv/lib/python3.10/site-packages/torch/autograd/forward_ad.py

@@ -0,0 +1,227 @@
+import os
+from collections import namedtuple
+
+from typing import Any
+
+import torch
+from .grad_mode import _DecoratorContextManager
+
+__all__ = [
+    "UnpackedDualTensor",
+    "enter_dual_level",
+    "exit_dual_level",
+    "make_dual",
+    "unpack_dual",
+    "dual_level",
+]
+
+# Global variable used to make the python API simpler to use
+_current_level = -1
+
+
+def enter_dual_level():
+    r"""Enter a new forward grad level.
+
+    This level can be used to make and unpack dual Tensors to compute
+    forward gradients.
+
+    This function also updates the current level that is used by default
+    by the other functions in this API.
+    """
+    global _current_level
+    new_level = torch._C._enter_dual_level()
+    if new_level != _current_level + 1:
+        raise RuntimeError(
+            "Entering a new forward AD level but the current level "
+            "is not valid. Make sure you did not modified it directly."
+        )
+    _current_level = new_level
+    return new_level
+
+
+def exit_dual_level(*, level=None):
+    r"""Exit a forward grad level.
+
+    This function deletes all the gradients associated with this
+    level. Only deleting the latest entered level is allowed.
+
+    This function also updates the current level that is used by default
+    by the other functions in this API.
+    """
+    global _current_level
+    if level is None:
+        level = _current_level
+    if level != _current_level:
+        raise RuntimeError(
+            "Trying to exit a forward AD level that was not the last one "
+            "that was created. This is not supported."
+        )
+    torch._C._exit_dual_level(level=level)
+    _current_level = level - 1
+
+
+def make_dual(tensor, tangent, *, level=None):
+    r"""Associate a tensor value with its tangent to create a "dual tensor" for forward AD gradient computation.
+
+    The result is a new tensor aliased to :attr:`tensor` with :attr:`tangent` embedded
+    as an attribute as-is if it has the same storage layout or copied otherwise.
+    The tangent attribute can be recovered with :func:`unpack_dual`.
+
+    This function is backward differentiable.
+
+    Given a function `f` whose jacobian is `J`, it allows one to compute the Jacobian-vector product (`jvp`)
+    between `J` and a given vector `v` as follows.
+
+    Example::
+
+        >>> # xdoctest: +SKIP("Undefined variables")
+        >>> with dual_level():
+        ...     inp = make_dual(x, v)
+        ...     out = f(inp)
+        ...     y, jvp = unpack_dual(out)
+
+    Please see the `forward-mode AD tutorial <https://pytorch.org/tutorials/intermediate/forward_ad_usage.html>`__
+    for detailed steps on how to use this API.
+
+    """
+    # See NOTE: [forward-mode AD decompositions mechanism]
+    #
+    # Import from torch._decomp import decompositions_for_jvp to register
+    # decompositions for jvp to the jit registry
+    #
+    # FIXME: We specify that __debug__ must be True because
+    # if python is run with -OO or -O flags (i.e., __debug__ is False), we encounter the
+    # following error:
+    #
+    # Return value was annotated as having type Tuple[NoneType, NoneType] but is actually of
+    # type Tuple[Tensor, Tensor]:
+    #   File ".../torch/_decomp/__init__.py", line 1585
+    #     else:
+    #         buffer = z
+    #     return min - torch.log1p(z), buffer
+    #     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ <--- HERE
+    if os.environ.get("PYTORCH_JIT", "1") == "1" and __debug__:
+        from torch._decomp import decompositions_for_jvp  # noqa: F401
+
+    if level is None:
+        level = _current_level
+
+    if level < 0:
+        raise RuntimeError(
+            "Trying to create a dual Tensor for forward AD but no level "
+            "exists, make sure to enter_dual_level() first."
+        )
+    if not (tensor.is_floating_point() or tensor.is_complex()):
+        raise ValueError(
+            f"Expected primal to be floating point or complex, but got: {tensor.dtype}"
+        )
+    if not (tangent.is_floating_point() or tangent.is_complex()):
+        raise ValueError(
+            f"Expected tangent to be floating point or complex, but got: {tangent.dtype}"
+        )
+
+    return torch._VF._make_dual(tensor, tangent, level=level)
+
+
+_UnpackedDualTensor = namedtuple("_UnpackedDualTensor", ["primal", "tangent"])
+
+
+class UnpackedDualTensor(_UnpackedDualTensor):
+    r"""Namedtuple returned by :func:`unpack_dual` containing the primal and tangent components of the dual tensor.
+
+    See :func:`unpack_dual` for more details.
+
+    """
+
+    pass
+
+
+def unpack_dual(tensor, *, level=None):
+    r"""Unpack a "dual tensor" to get both its Tensor value and its forward AD gradient.
+
+    The result is a namedtuple ``(primal, tangent)`` where ``primal`` is a view of
+    :attr:`tensor`'s primal and ``tangent`` is :attr:`tensor`'s tangent as-is.
+    Neither of these tensors can be dual tensor of level :attr:`level`.
+
+    This function is backward differentiable.
+
+    Example::
+
+        >>> # xdoctest: +SKIP("Undefined variables")
+        >>> with dual_level():
+        ...     inp = make_dual(x, x_t)
+        ...     out = f(inp)
+        ...     y, jvp = unpack_dual(out)
+        ...     jvp = unpack_dual(out).tangent
+
+    Please see the `forward-mode AD tutorial <https://pytorch.org/tutorials/intermediate/forward_ad_usage.html>`__
+    for detailed steps on how to use this API.
+    """
+    if level is None:
+        level = _current_level
+
+    if level < 0:
+        return UnpackedDualTensor(tensor, None)
+
+    primal, dual = torch._VF._unpack_dual(tensor, level=level)
+
+    return UnpackedDualTensor(primal, dual)
+
+
+class dual_level(_DecoratorContextManager):
+    r"""Context-manager for forward AD, where all forward AD computation must occur within the ``dual_level`` context.
+
+    .. Note::
+
+        The ``dual_level`` context appropriately enters and exit the dual level to
+        controls the current forward AD level, which is used by default by the other
+        functions in this API.
+
+        We currently don't plan to support nested ``dual_level`` contexts, however, so
+        only a single forward AD level is supported. To compute higher-order
+        forward grads, one can use :func:`torch.func.jvp`.
+
+    Example::
+
+        >>> # xdoctest: +SKIP("Undefined variables")
+        >>> x = torch.tensor([1])
+        >>> x_t = torch.tensor([1])
+        >>> with dual_level():
+        ...     inp = make_dual(x, x_t)
+        ...     # Do computations with inp
+        ...     out = your_fn(inp)
+        ...     _, grad = unpack_dual(out)
+        >>> grad is None
+        False
+        >>> # After exiting the level, the grad is deleted
+        >>> _, grad_after = unpack_dual(out)
+        >>> grad is None
+        True
+
+    Please see the `forward-mode AD tutorial <https://pytorch.org/tutorials/intermediate/forward_ad_usage.html>`__
+    for detailed steps on how to use this API.
+    """
+
+    def __enter__(self):
+        return enter_dual_level()
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any) -> None:
+        exit_dual_level()
+
+
+# Private helper functions
+_is_fwd_grad_enabled = torch._C._is_fwd_grad_enabled
+
+
+# Private helper function to enable or disable fwd grad.
+# If you're a user and want to use this, please file an issue to discuss the use case.
+class _set_fwd_grad_enabled(_DecoratorContextManager):
+    def __init__(self, mode: bool) -> None:
+        self.prev = _is_fwd_grad_enabled()
+        torch._C._set_fwd_grad_enabled(mode)
+
+    def __enter__(self) -> None:
+        pass
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any) -> None:
+        torch._C._set_fwd_grad_enabled(self.prev)

venv/lib/python3.10/site-packages/torch/autograd/function.py

@@ -0,0 +1,883 @@
+import functools
+import inspect
+import itertools
+import warnings
+from collections import OrderedDict
+from typing import Any, List, Optional, Tuple
+
+import torch
+import torch._C as _C
+import torch._functorch as _functorch
+import torch.utils.hooks as hooks
+from torch._C import _functions
+from torch._functorch.autograd_function import custom_function_call
+
+__all__ = [
+    "FunctionCtx",
+    "BackwardCFunction",
+    "FunctionMeta",
+    "Function",
+    "once_differentiable",
+    "traceable",
+    "InplaceFunction",
+    "NestedIOFunction",
+]
+
+# Unique id provider for each class inheriting from Function
+# This is incremented in FunctionMeta during class definition
+AUTOGRAD_FUNCTION_COUNTER = itertools.count()
+
+
+# Formerly known as: _ContextMethodMixin
+class FunctionCtx:
+    def save_for_backward(self, *tensors: torch.Tensor):
+        r"""Save given tensors for a future call to :func:`~Function.backward`.
+
+        ``save_for_backward`` should be called at most once, only from inside the
+        :func:`forward` method, and only with tensors.
+
+        All tensors intended to be used in the backward pass should be saved
+        with ``save_for_backward`` (as opposed to directly on ``ctx``) to prevent
+        incorrect gradients and memory leaks, and enable the application of saved
+        tensor hooks. See :class:`torch.autograd.graph.saved_tensors_hooks`.
+
+        Note that if intermediary tensors, tensors that are neither inputs
+        nor outputs of :func:`forward`, are saved for backward, your custom Function
+        may not support double backward.
+        Custom Functions that do not support double backward should decorate their
+        :func:`backward` method with ``@once_differentiable`` so that performing
+        double backward raises an error. If you'd like to support double backward,
+        you can either recompute intermediaries based on the inputs during backward
+        or return the intermediaries as the outputs of the custom Function. See the
+        `double backward tutorial <https://pytorch.org/tutorials/intermediate/custom_function_double_backward_tutorial.html>`_
+        for more details.
+
+        In :func:`backward`, saved tensors can be accessed through the :attr:`saved_tensors`
+        attribute. Before returning them to the user, a check is made to ensure
+        they weren't used in any in-place operation that modified their content.
+
+        Arguments can also be ``None``. This is a no-op.
+
+        See :ref:`extending-autograd` for more details on how to use this method.
+
+        Example::
+            >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+            >>> class Func(Function):
+            >>>     @staticmethod
+            >>>     def forward(ctx, x: torch.Tensor, y: torch.Tensor, z: int):
+            >>>         w = x * z
+            >>>         out = x * y + y * z + w * y
+            >>>         ctx.save_for_backward(x, y, w, out)
+            >>>         ctx.z = z  # z is not a tensor
+            >>>         return out
+            >>>
+            >>>     @staticmethod
+            >>>     @once_differentiable
+            >>>     def backward(ctx, grad_out):
+            >>>         x, y, w, out = ctx.saved_tensors
+            >>>         z = ctx.z
+            >>>         gx = grad_out * (y + y * z)
+            >>>         gy = grad_out * (x + z + w)
+            >>>         gz = None
+            >>>         return gx, gy, gz
+            >>>
+            >>> a = torch.tensor(1., requires_grad=True, dtype=torch.double)
+            >>> b = torch.tensor(2., requires_grad=True, dtype=torch.double)
+            >>> c = 4
+            >>> d = Func.apply(a, b, c)
+
+        """
+        self.to_save = tensors
+
+    def save_for_forward(self, *tensors: torch.Tensor):
+        r"""Save given tensors for a future call to :func:`~Function.jvp`.
+
+        ``save_for_forward`` should be only called once, from inside the :func:`forward`
+        method, and only be called with tensors.
+
+        In :func:`jvp`, saved objects can be accessed through the :attr:`saved_tensors`
+        attribute.
+
+        Arguments can also be ``None``. This is a no-op.
+
+        See :ref:`extending-autograd` for more details on how to use this method.
+
+        Example::
+            >>> # xdoctest: +SKIP
+            >>> class Func(torch.autograd.Function):
+            >>>     @staticmethod
+            >>>     def forward(ctx, x: torch.Tensor, y: torch.Tensor, z: int):
+            >>>         ctx.save_for_backward(x, y)
+            >>>         ctx.save_for_forward(x, y)
+            >>>         ctx.z = z
+            >>>         return x * y * z
+            >>>
+            >>>     @staticmethod
+            >>>     def jvp(ctx, x_t, y_t, _):
+            >>>         x, y = ctx.saved_tensors
+            >>>         z = ctx.z
+            >>>         return z * (y * x_t + x * y_t)
+            >>>
+            >>>     @staticmethod
+            >>>     def vjp(ctx, grad_out):
+            >>>         x, y = ctx.saved_tensors
+            >>>         z = ctx.z
+            >>>         return z * grad_out * y, z * grad_out * x, None
+            >>>
+            >>>     a = torch.tensor(1., requires_grad=True, dtype=torch.double)
+            >>>     t = torch.tensor(1., dtype=torch.double)
+            >>>     b = torch.tensor(2., requires_grad=True, dtype=torch.double)
+            >>>     c = 4
+            >>>
+            >>>     with fwAD.dual_level():
+            >>>         a_dual = fwAD.make_dual(a, t)
+            >>>         d = Func.apply(a_dual, b, c)
+
+        """
+        for tensor in tensors:
+            assert isinstance(tensor, torch.Tensor) or tensor is None, (
+                "save_for_forward expects all arguments to be tensors; you should "
+                "save non-tensors as attributes on ctx."
+            )
+
+        self.saved_for_forward = tensors
+
+    def mark_dirty(self, *args: torch.Tensor):
+        r"""Mark given tensors as modified in an in-place operation.
+
+        **This should be called at most once, only from inside the**
+        :func:`forward` **method, and all arguments should be inputs.**
+
+        Every tensor that's been modified in-place in a call to :func:`forward`
+        should be given to this function, to ensure correctness of our checks.
+        It doesn't matter whether the function is called before or after
+        modification.
+
+        Examples::
+            >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+            >>> class Inplace(Function):
+            >>>     @staticmethod
+            >>>     def forward(ctx, x):
+            >>>         x_npy = x.numpy() # x_npy shares storage with x
+            >>>         x_npy += 1
+            >>>         ctx.mark_dirty(x)
+            >>>         return x
+            >>>
+            >>>     @staticmethod
+            >>>     @once_differentiable
+            >>>     def backward(ctx, grad_output):
+            >>>         return grad_output
+            >>>
+            >>> a = torch.tensor(1., requires_grad=True, dtype=torch.double).clone()
+            >>> b = a * a
+            >>> Inplace.apply(a)  # This would lead to wrong gradients!
+            >>>                   # but the engine would not know unless we mark_dirty
+            >>> # xdoctest: +SKIP
+            >>> b.backward() # RuntimeError: one of the variables needed for gradient
+            >>>              # computation has been modified by an inplace operation
+
+        """
+        self.dirty_tensors = args
+
+    def mark_shared_storage(self, *pairs):
+        warnings.warn(
+            "mark_shared_storage is deprecated. "
+            "Tensors with shared storages are automatically tracked. Note "
+            "that calls to `set_()` are not tracked"
+        )
+
+    def mark_non_differentiable(self, *args: torch.Tensor):
+        r"""Mark outputs as non-differentiable.
+
+        **This should be called at most once, only from inside the**
+        :func:`forward` **method, and all arguments should be tensor outputs.**
+
+        This will mark outputs as not requiring gradients, increasing the
+        efficiency of backward computation. You still need to accept a gradient
+        for each output in :meth:`~Function.backward`, but it's always going to
+        be a zero tensor with the same shape as the shape of a corresponding
+        output.
+
+        This is used e.g. for indices returned from a sort. See example::
+            >>> class Func(Function):
+            >>>     @staticmethod
+            >>>     def forward(ctx, x):
+            >>>         sorted, idx = x.sort()
+            >>>         ctx.mark_non_differentiable(idx)
+            >>>         ctx.save_for_backward(x, idx)
+            >>>         return sorted, idx
+            >>>
+            >>>     @staticmethod
+            >>>     @once_differentiable
+            >>>     def backward(ctx, g1, g2):  # still need to accept g2
+            >>>         x, idx = ctx.saved_tensors
+            >>>         grad_input = torch.zeros_like(x)
+            >>>         grad_input.index_add_(0, idx, g1)
+            >>>         return grad_input
+
+        """
+        self.non_differentiable = args
+
+    def set_materialize_grads(self, value: bool):
+        r"""Set whether to materialize grad tensors. Default is ``True``.
+
+        **This should be called only from inside the** :func:`forward` **method**
+
+        If ``True``, undefined grad tensors will be expanded to tensors full of zeros
+        prior to calling the :func:`backward` and :func:`jvp` methods.
+
+        Example::
+            >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+            >>> class SimpleFunc(Function):
+            >>>     @staticmethod
+            >>>     def forward(ctx, x):
+            >>>         return x.clone(), x.clone()
+            >>>
+            >>>     @staticmethod
+            >>>     @once_differentiable
+            >>>     def backward(ctx, g1, g2):
+            >>>         return g1 + g2  # No check for None necessary
+            >>>
+            >>> # We modify SimpleFunc to handle non-materialized grad outputs
+            >>> class Func(Function):
+            >>>     @staticmethod
+            >>>     def forward(ctx, x):
+            >>>         ctx.set_materialize_grads(False)
+            >>>         ctx.save_for_backward(x)
+            >>>         return x.clone(), x.clone()
+            >>>
+            >>>     @staticmethod
+            >>>     @once_differentiable
+            >>>     def backward(ctx, g1, g2):
+            >>>         x, = ctx.saved_tensors
+            >>>         grad_input = torch.zeros_like(x)
+            >>>         if g1 is not None:  # We must check for None now
+            >>>             grad_input += g1
+            >>>         if g2 is not None:
+            >>>             grad_input += g2
+            >>>         return grad_input
+            >>>
+            >>> a = torch.tensor(1., requires_grad=True)
+            >>> b, _ = Func.apply(a)  # induces g2 to be undefined
+
+        """
+        self.materialize_grads = value
+
+
+# DO NOT USE: This is only defined to be able to load old serialized models
+_ContextMethodMixin = FunctionCtx
+
+
+class _HookMixin:
+    @staticmethod
+    def _register_hook(backward_hooks, hook):
+        if backward_hooks is None:
+            backward_hooks = OrderedDict()
+        handle = hooks.RemovableHandle(backward_hooks)
+        backward_hooks[handle.id] = hook
+        return backward_hooks, handle
+
+
+class BackwardCFunction(_C._FunctionBase, FunctionCtx, _HookMixin):
+    r"""
+    This class is used for internal autograd work. Do not use.
+    """
+
+    def apply(self, *args):
+        r"""
+        Apply method used when executing this Node during the backward
+        """
+        # _forward_cls is defined by derived class
+        # The user should define either backward or vjp but never both.
+        backward_fn = self._forward_cls.backward  # type: ignore[attr-defined]
+        vjp_fn = self._forward_cls.vjp  # type: ignore[attr-defined]
+        if backward_fn is not Function.backward and vjp_fn is not Function.vjp:
+            raise RuntimeError(
+                "Implementing both 'backward' and 'vjp' for a custom "
+                "Function is not allowed. You should only implement one "
+                "of them."
+            )
+        user_fn = vjp_fn if vjp_fn is not Function.vjp else backward_fn
+        return user_fn(self, *args)
+
+    def apply_jvp(self, *args):
+        r"""
+        Apply method used when executing forward mode AD during the forward
+        """
+        # _forward_cls is defined by derived class
+        return self._forward_cls.jvp(self, *args)  # type: ignore[attr-defined]
+
+    def _compiled_autograd_key(self):
+        return self._forward_cls._compiled_autograd_key(self)  # type: ignore[attr-defined]
+
+
+def _warn_traceable_deprecated():
+    warnings.warn(
+        "The is_traceable field on torch.autograd.Function is deprecated "
+        "and will be removed in PyTorch 2.4.",
+        stacklevel=3,
+    )
+
+
+class FunctionMeta(type):
+    """Function metaclass.
+
+    This metaclass sets up the following properties:
+        _backward_cls: The Function class corresponding to the differentiated
+            version of this function (which is generated on the fly by this
+            metaclass).
+    """
+
+    def __init__(cls, name, bases, attrs):
+        backward_fn = type(
+            name + "Backward", (BackwardCFunction,), {"_forward_cls": cls}
+        )
+        backward_fn._autograd_function_id = next(AUTOGRAD_FUNCTION_COUNTER)  # type: ignore[attr-defined]
+        backward_fn._compiled_autograd_should_lift = attrs.get(  # type: ignore[attr-defined]
+            "_compiled_autograd_should_lift", True
+        )
+        cls._backward_cls = backward_fn
+
+        if "is_traceable" in attrs and attrs["is_traceable"] is True:
+            _warn_traceable_deprecated()
+
+        super().__init__(name, bases, attrs)
+
+    def __getattribute__(cls, name):
+        if name == "is_traceable":
+            _warn_traceable_deprecated()
+        return super().__getattribute__(name)
+
+    def __setattr__(cls, name, value):
+        if name == "is_traceable" and value is True:
+            warnings.warn(
+                "The is_traceable field on torch.autograd.Function is deprecated "
+                "and will be removed in PyTorch 2.4.",
+                stacklevel=2,
+            )
+        return super().__setattr__(name, value)
+
+
+class _SingleLevelFunction(
+    _C._FunctionBase, FunctionCtx, _HookMixin, metaclass=FunctionMeta
+):
+    @staticmethod
+    def forward(ctx: Any, *args: Any, **kwargs: Any) -> Any:
+        r"""Define the forward of the custom autograd Function.
+
+        This function is to be overridden by all subclasses.
+        There are two ways to define forward:
+
+        Usage 1 (Combined forward and ctx)::
+
+            @staticmethod
+            def forward(ctx: Any, *args: Any, **kwargs: Any) -> Any:
+                pass
+
+        - It must accept a context ctx as the first argument, followed by any
+          number of arguments (tensors or other types).
+        - See :ref:`combining-forward-context` for more details
+
+        Usage 2 (Separate forward and ctx)::
+
+            @staticmethod
+            def forward(*args: Any, **kwargs: Any) -> Any:
+                pass
+
+            @staticmethod
+            def setup_context(ctx: Any, inputs: Tuple[Any, ...], output: Any) -> None:
+                pass
+
+        - The forward no longer accepts a ctx argument.
+        - Instead, you must also override the :meth:`torch.autograd.Function.setup_context`
+          staticmethod to handle setting up the ``ctx`` object.
+          ``output`` is the output of the forward, ``inputs`` are a Tuple of inputs
+          to the forward.
+        - See :ref:`extending-autograd` for more details
+
+        The context can be used to store arbitrary data that can be then
+        retrieved during the backward pass. Tensors should not be stored
+        directly on `ctx` (though this is not currently enforced for
+        backward compatibility). Instead, tensors should be saved either with
+        :func:`ctx.save_for_backward` if they are intended to be used in
+        ``backward`` (equivalently, ``vjp``) or :func:`ctx.save_for_forward`
+        if they are intended to be used for in ``jvp``.
+        """
+        raise NotImplementedError(
+            "You must implement the forward function for custom autograd.Function."
+        )
+
+    @staticmethod
+    def setup_context(ctx: Any, inputs: Tuple[Any, ...], output: Any) -> Any:
+        r"""There are two ways to define the forward pass of an autograd.Function.
+
+        Either:
+
+        1. Override forward with the signature ``forward(ctx, *args, **kwargs)``.
+           ``setup_context`` is not overridden. Setting up the ctx for backward
+           happens inside the ``forward``.
+        2. Override forward with the signature ``forward(*args, **kwargs)`` and
+           override ``setup_context``. Setting up the ctx for backward happens
+           inside ``setup_context`` (as opposed to inside the ``forward``)
+
+        See :meth:`torch.autograd.Function.forward` and :ref:`extending-autograd` for more details.
+        """
+        raise NotImplementedError("setup_context is not implemented.")
+
+    @staticmethod
+    def backward(ctx: Any, *grad_outputs: Any) -> Any:
+        r"""Define a formula for differentiating the operation with backward mode automatic differentiation.
+
+        This function is to be overridden by all subclasses.
+        (Defining this function is equivalent to defining the ``vjp`` function.)
+
+        It must accept a context :attr:`ctx` as the first argument, followed by
+        as many outputs as the :func:`forward` returned (None will be passed in
+        for non tensor outputs of the forward function),
+        and it should return as many tensors, as there were inputs to
+        :func:`forward`. Each argument is the gradient w.r.t the given output,
+        and each returned value should be the gradient w.r.t. the
+        corresponding input. If an input is not a Tensor or is a Tensor not
+        requiring grads, you can just pass None as a gradient for that input.
+
+        The context can be used to retrieve tensors saved during the forward
+        pass. It also has an attribute :attr:`ctx.needs_input_grad` as a tuple
+        of booleans representing whether each input needs gradient. E.g.,
+        :func:`backward` will have ``ctx.needs_input_grad[0] = True`` if the
+        first input to :func:`forward` needs gradient computed w.r.t. the
+        output.
+        """
+        raise NotImplementedError(
+            "You must implement either the backward or vjp method for "
+            "your custom autograd.Function to use it with backward "
+            "mode AD."
+        )
+
+    # vjp and backward are alias of each other
+    vjp = backward
+
+    @staticmethod
+    def jvp(ctx: Any, *grad_inputs: Any) -> Any:
+        r"""Define a formula for differentiating the operation with forward mode automatic differentiation.
+
+        This function is to be overridden by all subclasses.
+        It must accept a context :attr:`ctx` as the first argument, followed by
+        as many inputs as the :func:`forward` got (None will be passed in
+        for non tensor inputs of the forward function),
+        and it should return as many tensors as there were outputs to
+        :func:`forward`. Each argument is the gradient w.r.t the given input,
+        and each returned value should be the gradient w.r.t. the
+        corresponding output. If an output is not a Tensor or the function is not
+        differentiable with respect to that output, you can just pass None as a
+        gradient for that input.
+
+        You can use the :attr:`ctx` object to pass any value from the forward to this
+        functions.
+        """
+        raise NotImplementedError(
+            "You must implement the jvp function for custom "
+            "autograd.Function to use it with forward mode AD."
+        )
+
+
+class Function(_SingleLevelFunction):
+    r"""Base class to create custom `autograd.Function`.
+
+    To create a custom `autograd.Function`, subclass this class and implement
+    the :meth:`forward` and :meth:`backward` static methods. Then, to use your custom
+    op in the forward pass, call the class method ``apply``. Do not call
+    :meth:`forward` directly.
+
+    To ensure correctness and best performance, make sure you are calling the
+    correct methods on ``ctx`` and validating your backward function using
+    :func:`torch.autograd.gradcheck`.
+
+    See :ref:`extending-autograd` for more details on how to use this class.
+
+    Examples::
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> class Exp(Function):
+        >>>     @staticmethod
+        >>>     def forward(ctx, i):
+        >>>         result = i.exp()
+        >>>         ctx.save_for_backward(result)
+        >>>         return result
+        >>>
+        >>>     @staticmethod
+        >>>     def backward(ctx, grad_output):
+        >>>         result, = ctx.saved_tensors
+        >>>         return grad_output * result
+        >>>
+        >>> # Use it by calling the apply method:
+        >>> # xdoctest: +SKIP
+        >>> output = Exp.apply(input)
+    """
+
+    def __init__(self, *args, **kwargs):
+        cls = self.__class__
+        warnings.warn(
+            f"{cls} should not be instantiated. Methods on autograd functions"
+            "are all static, so you should invoke them on the class itself. "
+            "Instantiating an autograd function will raise an "
+            "error in a future version of PyTorch.",
+            DeprecationWarning,
+            stacklevel=2,
+        )
+
+    def __call__(self, *args, **kwargs):
+        raise RuntimeError(
+            "Legacy autograd function with non-static forward method is deprecated. "
+            "Please use new-style autograd function with static forward method. "
+            "(Example: https://pytorch.org/docs/stable/autograd.html#torch.autograd.Function)"
+        )
+
+    # for the tracer
+    is_traceable = False
+
+    """
+    Bool that specifies if PyTorch should attempt to autogenerate
+    :func:`torch.vmap` support for this autograd.Function. You may set this to
+    True only if this autograd.Function's forward, backward, and jvp (if they
+    exist) are written using PyTorch operations; otherwise, please override
+    :meth:`torch.autograd.Function.vmap` to add support for :func:`torch.vmap`.
+
+    Please see :ref:`func-autograd-function` for more details.
+    """
+    generate_vmap_rule = False
+
+    @staticmethod
+    def vmap(info, in_dims, *args):
+        r"""Define the behavior for this autograd.Function underneath :func:`torch.vmap`.
+
+        For a :func:`torch.autograd.Function` to support
+        :func:`torch.vmap`, you must either override this static method, or set
+        ``generate_vmap_rule`` to ``True`` (you may not do both).
+
+        If you choose to override this staticmethod: it must accept
+
+        - an ``info`` object as the first argument. ``info.batch_size``
+          specifies the size of the dimension being vmapped over,
+          while ``info.randomness`` is the randomness option passed to
+          :func:`torch.vmap`.
+        - an ``in_dims`` tuple as the second argument.
+          For each arg in ``args``, ``in_dims`` has a corresponding
+          ``Optional[int]``. It is ``None`` if the arg is not a Tensor or if
+          the arg is not being vmapped over, otherwise, it is an integer
+          specifying what dimension of the Tensor is being vmapped over.
+        - ``*args``, which is the same as the args to :meth:`~Function.forward`.
+
+        The return of the vmap staticmethod is a tuple of ``(output, out_dims)``.
+        Similar to ``in_dims``, ``out_dims`` should be of the same structure as
+        ``output`` and contain one ``out_dim`` per output that specifies if the
+        output has the vmapped dimension and what index it is in.
+
+        Please see :ref:`func-autograd-function` for more details.
+        """
+        raise NotImplementedError(
+            "To use autograd.Function with vmap, you must either override the "
+            "vmap staticmethod or set generate_vmap_rule=True."
+        )
+
+    @classmethod
+    def apply(cls, *args, **kwargs):
+        def bind_default_args(func, *args, **kwargs):
+            signature = inspect.signature(func)
+            bound_args = signature.bind(*args, **kwargs)
+            bound_args.apply_defaults()
+
+            return bound_args.args
+
+        is_setup_ctx_defined = cls.setup_context != _SingleLevelFunction.setup_context
+        if is_setup_ctx_defined:
+            args = bind_default_args(cls.forward, *args, **kwargs)
+
+        if not torch._C._are_functorch_transforms_active():
+            # See NOTE: [functorch vjp and autograd interaction]
+            args = _functorch.utils.unwrap_dead_wrappers(args)
+            return super().apply(*args, **kwargs)  # type: ignore[misc]
+
+        if not is_setup_ctx_defined:
+            raise RuntimeError(
+                "In order to use an autograd.Function with functorch transforms "
+                "(vmap, grad, jvp, jacrev, ...), it must override the setup_context "
+                "staticmethod. For more details, please see "
+                "https://pytorch.org/docs/master/notes/extending.func.html"
+            )
+
+        return custom_function_call(cls, *args, **kwargs)
+
+    @staticmethod
+    def _compiled_autograd_key(ctx):
+        return (ctx._autograd_function_id,)
+
+
+def once_differentiable(fn):
+    @functools.wraps(fn)
+    def wrapper(ctx, *args):
+        with torch.no_grad():
+            outputs = fn(ctx, *args)
+
+        if not torch.is_grad_enabled():
+            return outputs
+
+        # If any of the inputs have requires_grad=True, we force the outputs
+        # to have requires_grad=True but point to a grad_fn which throws an
+        # error message during (double) back-propagation.
+        # XXX: this is only an approximation of requires_grad - there's no way
+        # to figure out if fn didn't use ctx.saved_tensors and as a result
+        # some Tensors might require grad, even if no args do.
+        # Unfortunately, this leads to unexpected error messages ("no nodes
+        # require computing gradients"), but I don't have a better idea.
+        # These functions would raise an error in backward anyway.
+        requires_grad = any(
+            isinstance(arg, torch.Tensor) and arg.requires_grad for arg in args
+        )
+        if not requires_grad:
+            return outputs
+
+        if not isinstance(outputs, tuple):
+            outputs = (outputs,)
+
+        err_fn = _functions.DelayedError(
+            b"trying to differentiate twice a function that was marked "
+            b"with @once_differentiable",
+            len(outputs),
+        )
+
+        # Create aliases of each output that has requires_grad=True. We need
+        # at least one of the inputs to err_fn to require grad so that the
+        # output will have a grad_fn.
+        def fake_requires_grad(var):
+            if var is not None:
+                var = var.detach()
+                var.requires_grad = True
+            return var
+
+        return err_fn(*[fake_requires_grad(v) for v in outputs])
+
+    return wrapper
+
+
+def traceable(fn_cls):
+    r"""Mark Function as traceable for the JIT.
+
+    Traceable functions have additional restrictions - they can't pass any
+    data-dependent values to backward (e.g. Prod passes the output, which makes
+    it non-traceable), and their backward should be implemented entirely in terms
+    of operations on autograd Tensors in all cases.
+
+    DON'T USE THIS DECORATOR. IT IS FOR INTERNAL USE ONLY AND SHOULD BE HANDLED WITH
+    CARE (or can give incorrect results otherwise).
+    """
+    warnings.warn(
+        "torch.autograd.function.traceable is deprecated "
+        "and will be removed in PyTorch 2.4.",
+        stacklevel=2,
+    )
+    fn_cls.is_traceable = True
+    return fn_cls
+
+
+class InplaceFunction(Function):
+    r"""
+    This class is here only for backward compatibility reasons.
+    Use :class:`Function` instead of this for any new use case.
+    """
+
+    def __init__(self, inplace=False):
+        super().__init__()
+        self.inplace = inplace
+
+
+def _nested_map(condition, fn, condition_msg=None):
+    def _map(obj):
+        if condition(obj):
+            return fn(obj)
+        elif obj is None:
+            return None
+        elif isinstance(obj, (list, tuple)):
+            mapped = (_map(x) for x in obj)
+            if hasattr(obj, "_fields"):
+                # obj is namedtuple
+                return type(obj)(*mapped)
+            return type(obj)(mapped)
+        elif isinstance(obj, dict):
+            return {x: _map(obj[x]) for x in obj}
+        else:
+            raise ValueError(
+                "Auto nesting doesn't know how to process "
+                "an input object of type "
+                + torch.typename(obj)
+                + (
+                    ". Accepted types: " + condition_msg + ", or lists/tuples of them"
+                    if condition_msg
+                    else ""
+                )
+            )
+
+    return _map
+
+
+def _jit_unwrap_structured(obj):
+    if hasattr(obj, "_jit_unwrap"):
+        return obj._jit_unwrap()
+    return obj
+
+
+def _iter_filter(condition, allow_unknown=False, condition_msg=None, conversion=None):
+    def _iter(obj):
+        if conversion is not None:
+            obj = conversion(obj)
+        if condition(obj):
+            yield obj
+        elif obj is None:
+            return
+        elif isinstance(obj, (list, tuple)):
+            for o in obj:
+                yield from _iter(o)
+        elif isinstance(obj, dict):
+            # We only accept primitive key types, so we needn't inspect them
+            for o in obj.values():
+                yield from _iter(o)
+        elif allow_unknown:
+            yield obj
+        else:
+            raise ValueError(
+                "Auto nesting doesn't know how to process "
+                "an input object of type "
+                + torch.typename(obj)
+                + (
+                    ". Accepted types: " + condition_msg + ", or lists/tuples of them"
+                    if condition_msg
+                    else ""
+                )
+            )
+
+    return _iter
+
+
+def _unflatten(input, proto):
+    # unflatten a list or tuple input into a nested list/tuple structure
+    # specified by proto
+    def unflatten_helper(input, proto):
+        res: List[Optional[torch.Tensor]] = []
+        if hasattr(proto, "_jit_wrap"):
+            return proto._jit_wrap(input)
+        if not isinstance(proto, (list, tuple)):
+            return input[0], input[1:]
+        for e in proto:
+            if e is None:
+                res.append(e)
+            else:
+                res_e, input = unflatten_helper(input, e)
+                res.append(res_e)
+        return type(proto)(res), input
+
+    return unflatten_helper(input, proto)[0]
+
+
+_iter_jit_values = _iter_filter(
+    lambda o: o is None or isinstance(o, torch._C.Value),
+    condition_msg="jit's Values or None",
+)
+_iter_tensors = _iter_filter(
+    lambda x: isinstance(x, torch.Tensor),
+    condition_msg="Tensors",
+    conversion=_jit_unwrap_structured,
+)
+_iter_tensors_permissive = _iter_filter(
+    lambda x: isinstance(x, torch.Tensor),
+    allow_unknown=True,
+    condition_msg="Tensors (permissive)",
+)
+_iter_None_tensors = _iter_filter(
+    lambda o: o is None or isinstance(o, torch.Tensor), condition_msg="Tensors or None"
+)
+_map_tensor_data = _nested_map(
+    lambda x: isinstance(x, torch.Tensor), lambda o: o.data, condition_msg="Tensors"
+)
+
+
+class NestedIOFunction(Function):
+    r"""
+    This class is here only for backward compatibility reasons.
+    Use :class:`Function` instead of this for any new use case.
+    """
+    # The 'type: ignore' statements are needed here because these functions are declared as '@staticmethod' in the
+    # superclass (Function) but are instance methods here, which mypy reports as incompatible.
+
+    def _do_forward(self, *input):
+        self._nested_input = input
+        flat_input = tuple(_iter_tensors(input))
+        flat_output = super()._do_forward(*flat_input)  # type: ignore[misc]
+        nested_output = self._nested_output
+        nested_tensors = _unflatten(flat_output, self._nested_output)
+        return nested_tensors
+
+    def _do_backward(self, gradients, retain_variables):
+        self.retain_variables = retain_variables
+        result = super()._do_backward(gradients, retain_variables)  # type: ignore[misc]
+        if not retain_variables:
+            del self._nested_output
+            del self._to_save_nested
+        return result
+
+    def backward(self, *gradients: Any) -> Any:  # type: ignore[override]
+        r"""
+        Shared backward utility.
+        """
+        nested_gradients = _unflatten(gradients, self._nested_output)
+        result = self.backward_extended(*nested_gradients)  # type: ignore[func-returns-value]
+        return tuple(_iter_None_tensors(result))
+
+    __call__ = _do_forward
+
+    def forward(self, *args: Any) -> Any:  # type: ignore[override]
+        r"""
+        Shared forward utility.
+        """
+        nested_tensors = _map_tensor_data(self._nested_input)
+        result = self.forward_extended(*nested_tensors)  # type: ignore[func-returns-value]
+        del self._nested_input
+        self._nested_output = result
+        return tuple(_iter_tensors(result))
+
+    def save_for_backward(self, *args: Any) -> None:
+        r"""
+        See :meth:`Function.save_for_backward`.
+        """
+        self.to_save = tuple(_iter_tensors(args))
+        self._to_save_nested = args
+
+    @property
+    def saved_tensors(self):
+        r"""
+        See :meth:`Function.saved_tensors`.
+        """
+        flat_tensors = super().saved_tensors  # type: ignore[misc]
+        return _unflatten(flat_tensors, self._to_save_nested)
+
+    def mark_dirty(self, *args: Any, **kwargs: Any) -> None:
+        r"""
+        See :meth:`Function.mark_dirty`.
+        """
+        self.dirty_tensors = tuple(_iter_tensors((args, kwargs)))
+
+    def mark_non_differentiable(self, *args: Any, **kwargs: Any) -> None:
+        r"""
+        See :meth:`Function.mark_non_differentiable`.
+        """
+        self.non_differentiable = tuple(_iter_tensors((args, kwargs)))
+
+    def forward_extended(self, *input: Any) -> None:
+        r"""
+        User defined forward.
+        """
+        raise NotImplementedError
+
+    def backward_extended(self, *grad_output: Any) -> None:
+        r"""
+        User defined backward.
+        """
+        raise NotImplementedError

venv/lib/python3.10/site-packages/torch/autograd/functional.py

@@ -0,0 +1,1182 @@
+from typing import List, Tuple
+
+import torch
+from torch._vmap_internals import _vmap
+from . import forward_ad as fwAD
+
+__all__ = ["vjp", "jvp", "jacobian", "hessian", "hvp", "vhp"]
+
+# Utility functions
+
+
+def _as_tuple_nocheck(x):
+    if isinstance(x, tuple):
+        return x
+    elif isinstance(x, list):
+        return tuple(x)
+    else:
+        return (x,)
+
+
+def _as_tuple(inp, arg_name=None, fn_name=None):
+    # Ensures that inp is a tuple of Tensors
+    # Returns whether or not the original inp was a tuple and the tupled version of the input
+    if arg_name is None and fn_name is None:
+        return _as_tuple_nocheck(inp)
+
+    is_inp_tuple = True
+    if not isinstance(inp, tuple):
+        inp = (inp,)
+        is_inp_tuple = False
+
+    for i, el in enumerate(inp):
+        if not isinstance(el, torch.Tensor):
+            if is_inp_tuple:
+                raise TypeError(
+                    f"The {arg_name} given to {fn_name} must be either a Tensor or a tuple of Tensors but the"
+                    f" value at index {i} has type {type(el)}."
+                )
+            else:
+                raise TypeError(
+                    f"The {arg_name} given to {fn_name} must be either a Tensor or a tuple of Tensors but the"
+                    f" given {arg_name} has type {type(el)}."
+                )
+
+    return is_inp_tuple, inp
+
+
+def _tuple_postprocess(res, to_unpack):
+    # Unpacks a potentially nested tuple of Tensors
+    # to_unpack should be a single boolean or a tuple of two booleans.
+    # It is used to:
+    # - invert _as_tuple when res should match the inp given to _as_tuple
+    # - optionally remove nesting of two tuples created by multiple calls to _as_tuple
+    if isinstance(to_unpack, tuple):
+        assert len(to_unpack) == 2
+        if not to_unpack[1]:
+            res = tuple(el[0] for el in res)
+        if not to_unpack[0]:
+            res = res[0]
+    else:
+        if not to_unpack:
+            res = res[0]
+    return res
+
+
+def _grad_preprocess(inputs, create_graph, need_graph):
+    # Preprocess the inputs to make sure they require gradient
+    # inputs is a tuple of Tensors to preprocess
+    # create_graph specifies if the user wants gradients to flow back to the Tensors in inputs
+    # need_graph specifies if we internally want gradients to flow back to the Tensors in res
+    # Note that we *always* create a new Tensor object to be able to see the difference between
+    # inputs given as arguments and the same Tensors automatically captured by the user function.
+    # Check this issue for more details on how that can happen: https://github.com/pytorch/pytorch/issues/32576
+    res = []
+    for inp in inputs:
+        if create_graph and inp.requires_grad:
+            # Create at least a new Tensor object in a differentiable way
+            if not inp.is_sparse:
+                # Use .view_as() to get a shallow copy
+                res.append(inp.view_as(inp))
+            else:
+                # We cannot use view for sparse Tensors so we clone
+                res.append(inp.clone())
+        else:
+            res.append(inp.detach().requires_grad_(need_graph))
+    return tuple(res)
+
+
+def _grad_postprocess(inputs, create_graph):
+    # Postprocess the generated Tensors to avoid returning Tensors with history when the user did not
+    # request it.
+    if isinstance(inputs[0], torch.Tensor):
+        if not create_graph:
+            return tuple(inp.detach() for inp in inputs)
+        else:
+            return inputs
+    else:
+        return tuple(_grad_postprocess(inp, create_graph) for inp in inputs)
+
+
+def _validate_v(v, other, is_other_tuple):
+    # This assumes that other is the correct shape, and v should match
+    # Both are assumed to be tuples of Tensors
+    if len(other) != len(v):
+        if is_other_tuple:
+            raise RuntimeError(
+                f"v is a tuple of invalid length: should be {len(other)} but got {len(v)}."
+            )
+        else:
+            raise RuntimeError("The given v should contain a single Tensor.")
+
+    for idx, (el_v, el_other) in enumerate(zip(v, other)):
+        if el_v.size() != el_other.size():
+            prepend = ""
+            if is_other_tuple:
+                prepend = f"Entry {idx} in "
+            raise RuntimeError(
+                f"{prepend}v has invalid size: should be {el_other.size()} but got {el_v.size()}."
+            )
+
+
+def _check_requires_grad(inputs, input_type, strict):
+    # Used to make all the necessary checks to raise nice errors in strict mode.
+    if not strict:
+        return
+
+    if input_type not in ["outputs", "grad_inputs", "jacobian", "hessian"]:
+        raise RuntimeError("Invalid input_type to _check_requires_grad")
+    for i, inp in enumerate(inputs):
+        if inp is None:
+            # This can only be reached for grad_inputs.
+            raise RuntimeError(
+                f"The output of the user-provided function is independent of input {i}."
+                " This is not allowed in strict mode."
+            )
+        if not inp.requires_grad:
+            if input_type == "hessian":
+                raise RuntimeError(
+                    f"The hessian of the user-provided function with respect to input {i}"
+                    " is independent of the input. This is not allowed in strict mode."
+                    " You should ensure that your function is thrice differentiable and that"
+                    " the hessian depends on the inputs."
+                )
+            elif input_type == "jacobian":
+                raise RuntimeError(
+                    "While computing the hessian, found that the jacobian of the user-provided"
+                    f" function with respect to input {i} is independent of the input. This is not"
+                    " allowed in strict mode. You should ensure that your function is twice"
+                    " differentiable and that the jacobian depends on the inputs (this would be"
+                    " violated by a linear function for example)."
+                )
+            elif input_type == "grad_inputs":
+                raise RuntimeError(
+                    f"The gradient with respect to input {i} is independent of the inputs of the"
+                    " user-provided function. This is not allowed in strict mode."
+                )
+            else:
+                raise RuntimeError(
+                    f"Output {i} of the user-provided function does not require gradients."
+                    " The outputs must be computed in a differentiable manner from the input"
+                    " when running in strict mode."
+                )
+
+
+def _autograd_grad(
+    outputs,
+    inputs,
+    grad_outputs=None,
+    create_graph=False,
+    retain_graph=None,
+    is_grads_batched=False,
+):
+    # Version of autograd.grad that accepts `None` in outputs and do not compute gradients for them.
+    # This has the extra constraint that inputs has to be a tuple
+    assert isinstance(outputs, tuple)
+    if grad_outputs is None:
+        grad_outputs = (None,) * len(outputs)
+    assert isinstance(grad_outputs, tuple)
+    assert len(outputs) == len(grad_outputs)
+
+    new_outputs: Tuple[torch.Tensor, ...] = tuple()
+    new_grad_outputs: Tuple[torch.Tensor, ...] = tuple()
+    for out, grad_out in zip(outputs, grad_outputs):
+        if out is not None and out.requires_grad:
+            new_outputs += (out,)
+            new_grad_outputs += (grad_out,)
+
+    if len(new_outputs) == 0:
+        # No differentiable output, we don't need to call the autograd engine
+        return (None,) * len(inputs)
+    else:
+        return torch.autograd.grad(
+            new_outputs,
+            inputs,
+            new_grad_outputs,
+            allow_unused=True,
+            create_graph=create_graph,
+            retain_graph=retain_graph,
+            is_grads_batched=is_grads_batched,
+        )
+
+
+def _fill_in_zeros(grads, refs, strict, create_graph, stage):
+    # Used to detect None in the grads and depending on the flags, either replace them
+    # with Tensors full of 0s of the appropriate size based on the refs or raise an error.
+    # strict and create graph allow us to detect when it is appropriate to raise an error
+    # stage gives us information of which backward call we consider to give good error message
+    if stage not in ["back", "back_trick", "double_back", "double_back_trick"]:
+        raise RuntimeError(f"Invalid stage argument '{stage}' to _fill_in_zeros")
+
+    res: Tuple[torch.Tensor, ...] = tuple()
+    for i, grads_i in enumerate(grads):
+        if grads_i is None:
+            if strict:
+                if stage == "back":
+                    raise RuntimeError(
+                        "The output of the user-provided function is independent of "
+                        f"input {i}. This is not allowed in strict mode."
+                    )
+                elif stage == "back_trick":
+                    raise RuntimeError(
+                        f"The gradient with respect to the input is independent of entry {i}"
+                        " in the grad_outputs when using the double backward trick to compute"
+                        " forward mode gradients. This is not allowed in strict mode."
+                    )
+                elif stage == "double_back":
+                    raise RuntimeError(
+                        "The jacobian of the user-provided function is independent of "
+                        f"input {i}. This is not allowed in strict mode."
+                    )
+                else:
+                    raise RuntimeError(
+                        "The hessian of the user-provided function is independent of "
+                        f"entry {i} in the grad_jacobian. This is not allowed in strict "
+                        "mode as it prevents from using the double backward trick to "
+                        "replace forward mode AD."
+                    )
+
+            grads_i = torch.zeros_like(refs[i])
+        else:
+            if strict and create_graph and not grads_i.requires_grad:
+                if "double" not in stage:
+                    raise RuntimeError(
+                        "The jacobian of the user-provided function is independent of "
+                        f"input {i}. This is not allowed in strict mode when create_graph=True."
+                    )
+                else:
+                    raise RuntimeError(
+                        "The hessian of the user-provided function is independent of "
+                        f"input {i}. This is not allowed in strict mode when create_graph=True."
+                    )
+
+        res += (grads_i,)
+
+    return res
+
+
+# Public API
+
+
+def vjp(func, inputs, v=None, create_graph=False, strict=False):
+    r"""Compute the dot product between a vector ``v`` and the Jacobian of the given function at the point given by the inputs.
+
+    Args:
+        func (function): a Python function that takes Tensor inputs and returns
+            a tuple of Tensors or a Tensor.
+        inputs (tuple of Tensors or Tensor): inputs to the function ``func``.
+        v (tuple of Tensors or Tensor): The vector for which the vector
+            Jacobian product is computed.  Must be the same size as the output
+            of ``func``. This argument is optional when the output of ``func``
+            contains a single element and (if it is not provided) will be set
+            as a Tensor containing a single ``1``.
+        create_graph (bool, optional): If ``True``, both the output and result
+            will be computed in a differentiable way. Note that when ``strict``
+            is ``False``, the result can not require gradients or be
+            disconnected from the inputs.  Defaults to ``False``.
+        strict (bool, optional): If ``True``, an error will be raised when we
+            detect that there exists an input such that all the outputs are
+            independent of it. If ``False``, we return a Tensor of zeros as the
+            vjp for said inputs, which is the expected mathematical value.
+            Defaults to ``False``.
+
+    Returns:
+        output (tuple): tuple with:
+            func_output (tuple of Tensors or Tensor): output of ``func(inputs)``
+
+            vjp (tuple of Tensors or Tensor): result of the dot product with
+            the same shape as the inputs.
+
+    Example:
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> def exp_reducer(x):
+        ...     return x.exp().sum(dim=1)
+        >>> inputs = torch.rand(4, 4)
+        >>> v = torch.ones(4)
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> vjp(exp_reducer, inputs, v)
+        (tensor([5.7817, 7.2458, 5.7830, 6.7782]),
+         tensor([[1.4458, 1.3962, 1.3042, 1.6354],
+                [2.1288, 1.0652, 1.5483, 2.5035],
+                [2.2046, 1.1292, 1.1432, 1.3059],
+                [1.3225, 1.6652, 1.7753, 2.0152]]))
+
+        >>> vjp(exp_reducer, inputs, v, create_graph=True)
+        (tensor([5.7817, 7.2458, 5.7830, 6.7782], grad_fn=<SumBackward1>),
+         tensor([[1.4458, 1.3962, 1.3042, 1.6354],
+                [2.1288, 1.0652, 1.5483, 2.5035],
+                [2.2046, 1.1292, 1.1432, 1.3059],
+                [1.3225, 1.6652, 1.7753, 2.0152]], grad_fn=<MulBackward0>))
+
+        >>> def adder(x, y):
+        ...     return 2 * x + 3 * y
+        >>> inputs = (torch.rand(2), torch.rand(2))
+        >>> v = torch.ones(2)
+        >>> vjp(adder, inputs, v)
+        (tensor([2.4225, 2.3340]),
+         (tensor([2., 2.]), tensor([3., 3.])))
+    """
+    with torch.enable_grad():
+        is_inputs_tuple, inputs = _as_tuple(inputs, "inputs", "vjp")
+        inputs = _grad_preprocess(inputs, create_graph=create_graph, need_graph=True)
+
+        outputs = func(*inputs)
+        is_outputs_tuple, outputs = _as_tuple(
+            outputs, "outputs of the user-provided function", "vjp"
+        )
+        _check_requires_grad(outputs, "outputs", strict=strict)
+
+        if v is not None:
+            _, v = _as_tuple(v, "v", "vjp")
+            v = _grad_preprocess(v, create_graph=create_graph, need_graph=False)
+            _validate_v(v, outputs, is_outputs_tuple)
+        else:
+            if len(outputs) != 1 or outputs[0].nelement() != 1:
+                raise RuntimeError(
+                    "The vector v can only be None if the "
+                    "user-provided function returns "
+                    "a single Tensor with a single element."
+                )
+
+    enable_grad = True if create_graph else torch.is_grad_enabled()
+    with torch.set_grad_enabled(enable_grad):
+        grad_res = _autograd_grad(outputs, inputs, v, create_graph=create_graph)
+        vjp = _fill_in_zeros(grad_res, inputs, strict, create_graph, "back")
+
+    # Cleanup objects and return them to the user
+    outputs = _grad_postprocess(outputs, create_graph)
+    vjp = _grad_postprocess(vjp, create_graph)
+
+    return _tuple_postprocess(outputs, is_outputs_tuple), _tuple_postprocess(
+        vjp, is_inputs_tuple
+    )
+
+
+def jvp(func, inputs, v=None, create_graph=False, strict=False):
+    r"""Compute the dot product between the Jacobian of the given function at the point given by the inputs and a vector ``v``.
+
+    Args:
+        func (function): a Python function that takes Tensor inputs and returns
+            a tuple of Tensors or a Tensor.
+        inputs (tuple of Tensors or Tensor): inputs to the function ``func``.
+        v (tuple of Tensors or Tensor): The vector for which the Jacobian
+            vector product is computed. Must be the same size as the input of
+            ``func``. This argument is optional when the input to ``func``
+            contains a single element and (if it is not provided) will be set
+            as a Tensor containing a single ``1``.
+        create_graph (bool, optional): If ``True``, both the output and result
+            will be computed in a differentiable way. Note that when ``strict``
+            is ``False``, the result can not require gradients or be
+            disconnected from the inputs.  Defaults to ``False``.
+        strict (bool, optional): If ``True``, an error will be raised when we
+            detect that there exists an input such that all the outputs are
+            independent of it. If ``False``, we return a Tensor of zeros as the
+            jvp for said inputs, which is the expected mathematical value.
+            Defaults to ``False``.
+
+    Returns:
+        output (tuple): tuple with:
+            func_output (tuple of Tensors or Tensor): output of ``func(inputs)``
+
+            jvp (tuple of Tensors or Tensor): result of the dot product with
+            the same shape as the output.
+
+    Note:
+        ``autograd.functional.jvp`` computes the jvp by using the backward of
+        the backward (sometimes called the double backwards trick). This is not
+        the most performant way of computing the jvp. Please consider using
+        :func:`torch.func.jvp` or the
+        :ref:`low-level forward-mode AD API <forward-mode-ad>` instead.
+
+    Example:
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> def exp_reducer(x):
+        ...     return x.exp().sum(dim=1)
+        >>> inputs = torch.rand(4, 4)
+        >>> v = torch.ones(4, 4)
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> jvp(exp_reducer, inputs, v)
+        (tensor([6.3090, 4.6742, 7.9114, 8.2106]),
+         tensor([6.3090, 4.6742, 7.9114, 8.2106]))
+
+        >>> jvp(exp_reducer, inputs, v, create_graph=True)
+        (tensor([6.3090, 4.6742, 7.9114, 8.2106], grad_fn=<SumBackward1>),
+         tensor([6.3090, 4.6742, 7.9114, 8.2106], grad_fn=<SqueezeBackward1>))
+
+        >>> def adder(x, y):
+        ...     return 2 * x + 3 * y
+        >>> inputs = (torch.rand(2), torch.rand(2))
+        >>> v = (torch.ones(2), torch.ones(2))
+        >>> jvp(adder, inputs, v)
+        (tensor([2.2399, 2.5005]),
+         tensor([5., 5.]))
+
+    """
+    with torch.enable_grad():
+        is_inputs_tuple, inputs = _as_tuple(inputs, "inputs", "jvp")
+        inputs = _grad_preprocess(inputs, create_graph=create_graph, need_graph=True)
+
+        if v is not None:
+            _, v = _as_tuple(v, "v", "jvp")
+            v = _grad_preprocess(v, create_graph=create_graph, need_graph=False)
+            _validate_v(v, inputs, is_inputs_tuple)
+        else:
+            if len(inputs) != 1 or inputs[0].nelement() != 1:
+                raise RuntimeError(
+                    "The vector v can only be None if the input to "
+                    "the user-provided function is a single Tensor "
+                    "with a single element."
+                )
+
+        outputs = func(*inputs)
+        is_outputs_tuple, outputs = _as_tuple(
+            outputs, "outputs of the user-provided function", "jvp"
+        )
+        _check_requires_grad(outputs, "outputs", strict=strict)
+        # The backward is linear so the value of grad_outputs is not important as
+        # it won't appear in the double backward graph. We only need to ensure that
+        # it does not contain inf or nan.
+        grad_outputs = tuple(
+            torch.zeros_like(out, requires_grad=True) for out in outputs
+        )
+
+        grad_inputs = _autograd_grad(outputs, inputs, grad_outputs, create_graph=True)
+        _check_requires_grad(grad_inputs, "grad_inputs", strict=strict)
+
+    if create_graph:
+        with torch.enable_grad():
+            grad_res = _autograd_grad(
+                grad_inputs, grad_outputs, v, create_graph=create_graph
+            )
+            jvp = _fill_in_zeros(grad_res, outputs, strict, create_graph, "back_trick")
+    else:
+        grad_res = _autograd_grad(
+            grad_inputs, grad_outputs, v, create_graph=create_graph
+        )
+        jvp = _fill_in_zeros(grad_res, outputs, strict, create_graph, "back_trick")
+
+    # Cleanup objects and return them to the user
+    outputs = _grad_postprocess(outputs, create_graph)
+    jvp = _grad_postprocess(jvp, create_graph)
+
+    return _tuple_postprocess(outputs, is_outputs_tuple), _tuple_postprocess(
+        jvp, is_outputs_tuple
+    )
+
+
+def _construct_standard_basis_for(
+    tensors: Tuple[torch.Tensor, ...], tensor_numels: Tuple[int, ...]
+) -> Tuple[torch.Tensor, ...]:
+    # This function:
+    # - constructs a N=sum(tensor_numels) standard basis. i.e. an NxN identity matrix.
+    # - Splits the identity matrix into chunks with each chunk size determined by `tensor_numels`.
+    # - Each chunk corresponds to one tensor. The chunk has the same dtype and
+    #   device as the tensor
+    #
+    # For example, with tensor_numels = [1, 2, 1], this function returns:
+    # ( tensor([[1],     tensor([[0, 0],      tensor([[0],
+    #           [0],             [1, 0],              [0],
+    #           [0],             [0, 1],              [0],
+    #           [0]])  ,         [0, 0]])  ,          [1]])  )
+    #
+    # Precondition: tensor_numels == tuple(tensor.numel() for tensor in tensors)
+    # Precondition: tensors always has at least one element.
+    #
+    # See NOTE: [Computing jacobian with vmap and grad for multiple tensors]
+    # for context behind this function. All the pre-conditions are guarded for
+    # in torch.autograd.functional.jacobian.
+    assert len(tensors) == len(tensor_numels)
+    assert len(tensors) > 0
+    total_numel = sum(tensor_numels)
+    chunks = tuple(
+        tensor.new_zeros(total_numel, tensor_numel)
+        for tensor, tensor_numel in zip(tensors, tensor_numels)
+    )
+    diag_start_idx = 0
+    for chunk, numel in zip(chunks, tensor_numels):
+        chunk.diagonal(diag_start_idx).fill_(1)
+        diag_start_idx -= numel
+    return chunks
+
+
+def _jacfwd(func, inputs, strict=False, vectorize=False):
+    if strict:
+        raise RuntimeError(
+            "torch.autograd.functional.jacobian: `strict=True` "
+            'and `strategy="forward-mode"` are not supported together (yet). '
+            "Please either set `strict=False` or "
+            '`strategy="reverse-mode"`.'
+        )
+    is_inputs_tuple, inputs = _as_tuple(inputs, "inputs", "jacobian")
+    output_info = []
+
+    if vectorize:
+        # See NOTE: [Computing jacobian with vmap and grad for multiple outputs]
+        input_numels = tuple(input.numel() for input in inputs)
+
+        # Step 1: Prepare tangents
+        tangents = _construct_standard_basis_for(inputs, input_numels)
+
+        # Step 2: Compute vmap over computation with dual tensors
+        def jvp(tangents):
+            with fwAD.dual_level():
+                dual_inputs = tuple(
+                    fwAD.make_dual(input, tangent.view_as(input))
+                    for input, tangent in zip(inputs, tangents)
+                )
+                _is_outputs_tuple, dual_outputs = _as_tuple(
+                    func(*dual_inputs), "outputs"
+                )
+                output_info.append(_is_outputs_tuple)
+                jv = []
+                primal_outs = []
+                for dual_out in dual_outputs:
+                    primal, tangent = fwAD.unpack_dual(dual_out)
+                    primal_outs.append(primal)
+                    if tangent is not None:
+                        jv.append(tangent)
+                    else:
+                        jv.append(torch.zeros_like(primal))
+                output_info.append(primal_outs)
+                return tuple(jv)
+
+        outputs_before_split = _vmap(jvp)(tangents)
+        is_outputs_tuple, outputs = output_info
+        # Step 3: for each of the output tangents, split along dim 0
+        jacobian_input_output = []
+        for jac_output_i, output_i in zip(outputs_before_split, outputs):
+            jacobian_output_i_output = []
+            for jac, input_j in zip(jac_output_i.split(input_numels, dim=0), inputs):
+                # We need to transpose the Jacobian because in forward AD, the
+                # batch dimension represents that of the inputs
+                jacobian_input_i_output_j = jac.permute(*range(1, jac.ndim), 0).reshape(
+                    (*output_i.shape, *input_j.shape)
+                )  # noqa: C409
+
+                jacobian_output_i_output.append(jacobian_input_i_output_j)
+            jacobian_input_output.append(jacobian_output_i_output)
+
+        # Omit [Step 4] because everything is already transposed w/ forward AD
+        return _tuple_postprocess(
+            jacobian_input_output, (is_outputs_tuple, is_inputs_tuple)
+        )
+    else:
+        raise NotImplementedError(
+            "Computing Jacobian using forward-AD or forward-over-reverse Hessian is"
+            "only implemented for `vectorize=True`."
+        )
+
+
+def jacobian(
+    func,
+    inputs,
+    create_graph=False,
+    strict=False,
+    vectorize=False,
+    strategy="reverse-mode",
+):
+    r"""Compute the Jacobian of a given function.
+
+    Args:
+        func (function): a Python function that takes Tensor inputs and returns
+            a tuple of Tensors or a Tensor.
+        inputs (tuple of Tensors or Tensor): inputs to the function ``func``.
+        create_graph (bool, optional): If ``True``, the Jacobian will be
+            computed in a differentiable manner. Note that when ``strict`` is
+            ``False``, the result can not require gradients or be disconnected
+            from the inputs.  Defaults to ``False``.
+        strict (bool, optional): If ``True``, an error will be raised when we
+            detect that there exists an input such that all the outputs are
+            independent of it. If ``False``, we return a Tensor of zeros as the
+            jacobian for said inputs, which is the expected mathematical value.
+            Defaults to ``False``.
+        vectorize (bool, optional): This feature is experimental.
+            Please consider using :func:`torch.func.jacrev` or
+            :func:`torch.func.jacfwd` instead if you are looking for something
+            less experimental and more performant.
+            When computing the jacobian, usually we invoke
+            ``autograd.grad`` once per row of the jacobian. If this flag is
+            ``True``, we perform only a single ``autograd.grad`` call with
+            ``batched_grad=True`` which uses the vmap prototype feature.
+            Though this should lead to performance improvements in many cases,
+            because this feature is still experimental, there may be performance
+            cliffs. See :func:`torch.autograd.grad`'s ``batched_grad`` parameter for
+            more information.
+        strategy (str, optional): Set to ``"forward-mode"`` or ``"reverse-mode"`` to
+            determine whether the Jacobian will be computed with forward or reverse
+            mode AD. Currently, ``"forward-mode"`` requires ``vectorized=True``.
+            Defaults to ``"reverse-mode"``. If ``func`` has more outputs than
+            inputs, ``"forward-mode"`` tends to be more performant. Otherwise,
+            prefer to use ``"reverse-mode"``.
+
+    Returns:
+        Jacobian (Tensor or nested tuple of Tensors): if there is a single
+        input and output, this will be a single Tensor containing the
+        Jacobian for the linearized inputs and output. If one of the two is
+        a tuple, then the Jacobian will be a tuple of Tensors. If both of
+        them are tuples, then the Jacobian will be a tuple of tuple of
+        Tensors where ``Jacobian[i][j]`` will contain the Jacobian of the
+        ``i``\th output and ``j``\th input and will have as size the
+        concatenation of the sizes of the corresponding output and the
+        corresponding input and will have same dtype and device as the
+        corresponding input. If strategy is ``forward-mode``, the dtype will be
+        that of the output; otherwise, the input.
+
+    Example:
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> def exp_reducer(x):
+        ...     return x.exp().sum(dim=1)
+        >>> inputs = torch.rand(2, 2)
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> jacobian(exp_reducer, inputs)
+        tensor([[[1.4917, 2.4352],
+                 [0.0000, 0.0000]],
+                [[0.0000, 0.0000],
+                 [2.4369, 2.3799]]])
+
+        >>> jacobian(exp_reducer, inputs, create_graph=True)
+        tensor([[[1.4917, 2.4352],
+                 [0.0000, 0.0000]],
+                [[0.0000, 0.0000],
+                 [2.4369, 2.3799]]], grad_fn=<ViewBackward>)
+
+        >>> def exp_adder(x, y):
+        ...     return 2 * x.exp() + 3 * y
+        >>> inputs = (torch.rand(2), torch.rand(2))
+        >>> jacobian(exp_adder, inputs)
+        (tensor([[2.8052, 0.0000],
+                [0.0000, 3.3963]]),
+         tensor([[3., 0.],
+                 [0., 3.]]))
+    """
+    assert strategy in ("forward-mode", "reverse-mode"), (
+        'Expected strategy to be either "forward-mode" or "reverse-mode". Hint: If your '
+        'function has more outputs than inputs, "forward-mode" tends to be more performant. '
+        'Otherwise, prefer to use "reverse-mode".'
+    )
+    if strategy == "forward-mode":
+        if create_graph:
+            raise NotImplementedError(
+                "torch.autograd.functional.jacobian: `create_graph=True` "
+                'and `strategy="forward-mode"` are not supported together (yet). '
+                "Please either set `create_graph=False` or "
+                '`strategy="reverse-mode"`.'
+            )
+        return _jacfwd(func, inputs, strict, vectorize)
+
+    with torch.enable_grad():
+        is_inputs_tuple, inputs = _as_tuple(inputs, "inputs", "jacobian")
+        inputs = _grad_preprocess(inputs, create_graph=create_graph, need_graph=True)
+
+        outputs = func(*inputs)
+        is_outputs_tuple, outputs = _as_tuple(
+            outputs, "outputs of the user-provided function", "jacobian"
+        )
+        _check_requires_grad(outputs, "outputs", strict=strict)
+
+        if vectorize:
+            if strict:
+                raise RuntimeError(
+                    "torch.autograd.functional.jacobian: `strict=True` "
+                    "and `vectorized=True` are not supported together. "
+                    "Please either set `strict=False` or "
+                    "`vectorize=False`."
+                )
+            # NOTE: [Computing jacobian with vmap and grad for multiple outputs]
+            #
+            # Let's consider f(x) = (x**2, x.sum()) and let x = torch.randn(3).
+            # It turns out we can compute the jacobian of this function with a single
+            # call to autograd.grad by using vmap over the correct grad_outputs.
+            #
+            # Firstly, one way to compute the jacobian is to stack x**2 and x.sum()
+            # into a 4D vector. E.g., use g(x) = torch.stack([x**2, x.sum()])
+            #
+            # To get the first row of the jacobian, we call
+            # >>> autograd.grad(g(x), x, grad_outputs=torch.tensor([1, 0, 0, 0]))
+            # To get the 2nd row of the jacobian, we call
+            # >>> autograd.grad(g(x), x, grad_outputs=torch.tensor([0, 1, 0, 0]))
+            # and so on.
+            #
+            # Using vmap, we can vectorize all 4 of these computations into one by
+            # passing the standard basis for R^4 as the grad_output.
+            # vmap(partial(autograd.grad, g(x), x))(torch.eye(4)).
+            #
+            # Now, how do we compute the jacobian *without stacking the output*?
+            # We can just split the standard basis across the outputs. So to
+            # compute the jacobian of f(x), we'd use
+            # >>> autograd.grad(f(x), x, grad_outputs=_construct_standard_basis_for(...))
+            # The grad_outputs looks like the following:
+            # ( torch.tensor([[1, 0, 0],
+            #                 [0, 1, 0],
+            #                 [0, 0, 1],
+            #                 [0, 0, 0]]),
+            #   torch.tensor([[0],
+            #                 [0],
+            #                 [0],
+            #                 [1]]) )
+            #
+            # But we're not done yet!
+            # >>> vmap(partial(autograd.grad(f(x), x, grad_outputs=...)))
+            # returns a Tensor of shape [4, 3]. We have to remember to split the
+            # jacobian of shape [4, 3] into two:
+            # - one of shape [3, 3] for the first output
+            # - one of shape [   3] for the second output
+
+            # Step 1: Construct grad_outputs by splitting the standard basis
+            output_numels = tuple(output.numel() for output in outputs)
+            grad_outputs = _construct_standard_basis_for(outputs, output_numels)
+            flat_outputs = tuple(output.reshape(-1) for output in outputs)
+
+            # Step 2: Call vmap + autograd.grad
+            def vjp(grad_output):
+                vj = list(
+                    _autograd_grad(
+                        flat_outputs,
+                        inputs,
+                        grad_output,
+                        create_graph=create_graph,
+                        is_grads_batched=True,
+                    )
+                )
+                for el_idx, vj_el in enumerate(vj):
+                    if vj_el is not None:
+                        continue
+                    vj[el_idx] = torch.zeros_like(inputs[el_idx]).expand(
+                        (sum(output_numels),) + inputs[el_idx].shape
+                    )
+                return tuple(vj)
+
+            jacobians_of_flat_output = vjp(grad_outputs)
+
+            # Step 3: The returned jacobian is one big tensor per input. In this step,
+            # we split each Tensor by output.
+            jacobian_input_output = []
+            for jac_input_i, input_i in zip(jacobians_of_flat_output, inputs):
+                jacobian_input_i_output = []
+                for jac, output_j in zip(
+                    jac_input_i.split(output_numels, dim=0), outputs
+                ):
+                    jacobian_input_i_output_j = jac.view(output_j.shape + input_i.shape)
+                    jacobian_input_i_output.append(jacobian_input_i_output_j)
+                jacobian_input_output.append(jacobian_input_i_output)
+
+            # Step 4: Right now, `jacobian` is a List[List[Tensor]].
+            # The outer List corresponds to the number of inputs,
+            # the inner List corresponds to the number of outputs.
+            # We need to exchange the order of these and convert to tuples
+            # before returning.
+            jacobian_output_input = tuple(zip(*jacobian_input_output))
+
+            jacobian_output_input = _grad_postprocess(
+                jacobian_output_input, create_graph
+            )
+            return _tuple_postprocess(
+                jacobian_output_input, (is_outputs_tuple, is_inputs_tuple)
+            )
+
+        jacobian: Tuple[torch.Tensor, ...] = tuple()
+
+        for i, out in enumerate(outputs):
+            # mypy complains that expression and variable have different types due to the empty list
+            jac_i: Tuple[List[torch.Tensor]] = tuple([] for _ in range(len(inputs)))  # type: ignore[assignment]
+            for j in range(out.nelement()):
+                vj = _autograd_grad(
+                    (out.reshape(-1)[j],),
+                    inputs,
+                    retain_graph=True,
+                    create_graph=create_graph,
+                )
+
+                for el_idx, (jac_i_el, vj_el, inp_el) in enumerate(
+                    zip(jac_i, vj, inputs)
+                ):
+                    if vj_el is not None:
+                        if strict and create_graph and not vj_el.requires_grad:
+                            msg = (
+                                "The jacobian of the user-provided function is "
+                                f"independent of input {i}. This is not allowed in "
+                                "strict mode when create_graph=True."
+                            )
+                            raise RuntimeError(msg)
+                        jac_i_el.append(vj_el)
+                    else:
+                        if strict:
+                            msg = (
+                                f"Output {i} of the user-provided function is "
+                                f"independent of input {el_idx}. This is not allowed in "
+                                "strict mode."
+                            )
+                            raise RuntimeError(msg)
+                        jac_i_el.append(torch.zeros_like(inp_el))
+
+            jacobian += (
+                tuple(
+                    torch.stack(jac_i_el, dim=0).view(
+                        out.size() + inputs[el_idx].size()  # type: ignore[operator]
+                    )
+                    for (el_idx, jac_i_el) in enumerate(jac_i)
+                ),
+            )
+
+        jacobian = _grad_postprocess(jacobian, create_graph)
+
+        return _tuple_postprocess(jacobian, (is_outputs_tuple, is_inputs_tuple))
+
+
+def hessian(
+    func,
+    inputs,
+    create_graph=False,
+    strict=False,
+    vectorize=False,
+    outer_jacobian_strategy="reverse-mode",
+):
+    r"""Compute the Hessian of a given scalar function.
+
+    Args:
+        func (function): a Python function that takes Tensor inputs and returns
+            a Tensor with a single element.
+        inputs (tuple of Tensors or Tensor): inputs to the function ``func``.
+        create_graph (bool, optional): If ``True``, the Hessian will be computed in
+            a differentiable manner. Note that when ``strict`` is ``False``, the result can not
+            require gradients or be disconnected from the inputs.
+            Defaults to ``False``.
+        strict (bool, optional): If ``True``, an error will be raised when we detect that there exists an input
+            such that all the outputs are independent of it. If ``False``, we return a Tensor of zeros as the
+            hessian for said inputs, which is the expected mathematical value.
+            Defaults to ``False``.
+        vectorize (bool, optional): This feature is experimental.
+            Please consider using :func:`torch.func.hessian`
+            instead if you are looking for something less experimental and more performant.
+            When computing the hessian, usually we invoke
+            ``autograd.grad`` once per row of the hessian. If this flag is
+            ``True``, we use the vmap prototype feature as the backend to
+            vectorize calls to ``autograd.grad`` so we only invoke it once
+            instead of once per row. This should lead to performance
+            improvements in many use cases, however, due to this feature
+            being incomplete, there may be performance cliffs. Please
+            use `torch._C._debug_only_display_vmap_fallback_warnings(True)`
+            to show any performance warnings and file us issues if
+            warnings exist for your use case. Defaults to ``False``.
+        outer_jacobian_strategy (str, optional): The Hessian is computed by
+            computing the Jacobian of a Jacobian. The inner Jacobian is always
+            computed in reverse-mode AD. Setting strategy to ``"forward-mode"``
+            or ``"reverse-mode"`` determines whether the outer Jacobian will be
+            computed with forward or reverse mode AD. Currently, computing the outer
+            Jacobian in ``"forward-mode"`` requires ``vectorized=True``. Defaults
+            to ``"reverse-mode"``.
+
+    Returns:
+        Hessian (Tensor or a tuple of tuple of Tensors): if there is a single input,
+        this will be a single Tensor containing the Hessian for the input.
+        If it is a tuple, then the Hessian will be a tuple of tuples where
+        ``Hessian[i][j]`` will contain the Hessian of the ``i``\th input
+        and ``j``\th input with size the sum of the size of the ``i``\th input plus
+        the size of the ``j``\th input. ``Hessian[i][j]`` will have the same
+        dtype and device as the corresponding ``i``\th input.
+
+    Example:
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> def pow_reducer(x):
+        ...     return x.pow(3).sum()
+        >>> inputs = torch.rand(2, 2)
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> hessian(pow_reducer, inputs)
+        tensor([[[[5.2265, 0.0000],
+                  [0.0000, 0.0000]],
+                 [[0.0000, 4.8221],
+                  [0.0000, 0.0000]]],
+                [[[0.0000, 0.0000],
+                  [1.9456, 0.0000]],
+                 [[0.0000, 0.0000],
+                  [0.0000, 3.2550]]]])
+
+        >>> hessian(pow_reducer, inputs, create_graph=True)
+        tensor([[[[5.2265, 0.0000],
+                  [0.0000, 0.0000]],
+                 [[0.0000, 4.8221],
+                  [0.0000, 0.0000]]],
+                [[[0.0000, 0.0000],
+                  [1.9456, 0.0000]],
+                 [[0.0000, 0.0000],
+                  [0.0000, 3.2550]]]], grad_fn=<ViewBackward>)
+
+
+        >>> def pow_adder_reducer(x, y):
+        ...     return (2 * x.pow(2) + 3 * y.pow(2)).sum()
+        >>> inputs = (torch.rand(2), torch.rand(2))
+        >>> hessian(pow_adder_reducer, inputs)
+        ((tensor([[4., 0.],
+                  [0., 4.]]),
+          tensor([[0., 0.],
+                  [0., 0.]])),
+         (tensor([[0., 0.],
+                  [0., 0.]]),
+          tensor([[6., 0.],
+                  [0., 6.]])))
+    """
+    is_inputs_tuple, inputs = _as_tuple(inputs, "inputs", "hessian")
+    assert outer_jacobian_strategy in (
+        "forward-mode",
+        "reverse-mode",
+    ), 'Expected strategy to be either "forward-mode" or "reverse-mode".'
+
+    def ensure_single_output_function(*inp):
+        out = func(*inp)
+        is_out_tuple, t_out = _as_tuple(
+            out, "outputs of the user-provided function", "hessian"
+        )
+        _check_requires_grad(t_out, "outputs", strict=strict)
+
+        if is_out_tuple or not isinstance(out, torch.Tensor):
+            raise RuntimeError(
+                "The function given to hessian should return a single Tensor"
+            )
+
+        if out.nelement() != 1:
+            raise RuntimeError(
+                "The Tensor returned by the function given to hessian should contain a single element"
+            )
+
+        return out.squeeze()
+
+    def jac_func(*inp):
+        if outer_jacobian_strategy == "forward-mode":
+            # _grad_preprocess requires create_graph=True and input to require_grad
+            # or else the input will be detached
+            inp = tuple(t.requires_grad_(True) for t in inp)
+        jac = jacobian(ensure_single_output_function, inp, create_graph=True)
+        _check_requires_grad(jac, "jacobian", strict=strict)
+        return jac
+
+    res = jacobian(
+        jac_func,
+        inputs,
+        create_graph=create_graph,
+        strict=strict,
+        vectorize=vectorize,
+        strategy=outer_jacobian_strategy,
+    )
+    return _tuple_postprocess(res, (is_inputs_tuple, is_inputs_tuple))
+
+
+def vhp(func, inputs, v=None, create_graph=False, strict=False):
+    r"""Compute the dot product between vector ``v`` and Hessian of a  given scalar function at a specified point.
+
+    Args:
+        func (function): a Python function that takes Tensor inputs and returns
+            a Tensor with a single element.
+        inputs (tuple of Tensors or Tensor): inputs to the function ``func``.
+        v (tuple of Tensors or Tensor): The vector for which the vector Hessian
+            product is computed. Must be the same size as the input of
+            ``func``. This argument is optional when ``func``'s input contains
+            a single element and (if it is not provided) will be set as a
+            Tensor containing a single ``1``.
+        create_graph (bool, optional): If ``True``, both the output and result
+            will be computed in a differentiable way. Note that when ``strict``
+            is ``False``, the result can not require gradients or be
+            disconnected from the inputs.
+            Defaults to ``False``.
+        strict (bool, optional): If ``True``, an error will be raised when we
+            detect that there exists an input such that all the outputs are
+            independent of it. If ``False``, we return a Tensor of zeros as the
+            vhp for said inputs, which is the expected mathematical value.
+            Defaults to ``False``.
+
+    Returns:
+        output (tuple): tuple with:
+            func_output (tuple of Tensors or Tensor): output of ``func(inputs)``
+
+            vhp (tuple of Tensors or Tensor): result of the dot product with the
+            same shape as the inputs.
+
+    Example:
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> def pow_reducer(x):
+        ...     return x.pow(3).sum()
+        >>> inputs = torch.rand(2, 2)
+        >>> v = torch.ones(2, 2)
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> vhp(pow_reducer, inputs, v)
+        (tensor(0.5591),
+         tensor([[1.0689, 1.2431],
+                 [3.0989, 4.4456]]))
+        >>> vhp(pow_reducer, inputs, v, create_graph=True)
+        (tensor(0.5591, grad_fn=<SumBackward0>),
+         tensor([[1.0689, 1.2431],
+                 [3.0989, 4.4456]], grad_fn=<MulBackward0>))
+        >>> def pow_adder_reducer(x, y):
+        ...     return (2 * x.pow(2) + 3 * y.pow(2)).sum()
+        >>> inputs = (torch.rand(2), torch.rand(2))
+        >>> v = (torch.zeros(2), torch.ones(2))
+        >>> vhp(pow_adder_reducer, inputs, v)
+        (tensor(4.8053),
+         (tensor([0., 0.]),
+          tensor([6., 6.])))
+    """
+    with torch.enable_grad():
+        is_inputs_tuple, inputs = _as_tuple(inputs, "inputs", "vhp")
+        inputs = _grad_preprocess(inputs, create_graph=create_graph, need_graph=True)
+
+        if v is not None:
+            _, v = _as_tuple(v, "v", "vhp")
+            v = _grad_preprocess(v, create_graph=create_graph, need_graph=False)
+            _validate_v(v, inputs, is_inputs_tuple)
+        else:
+            if len(inputs) != 1 or inputs[0].nelement() != 1:
+                raise RuntimeError(
+                    "The vector v can only be None if the input to the user-provided function "
+                    "is a single Tensor with a single element."
+                )
+        outputs = func(*inputs)
+        is_outputs_tuple, outputs = _as_tuple(
+            outputs, "outputs of the user-provided function", "vhp"
+        )
+        _check_requires_grad(outputs, "outputs", strict=strict)
+
+        if is_outputs_tuple or not isinstance(outputs[0], torch.Tensor):
+            raise RuntimeError(
+                "The function given to vhp should return a single Tensor"
+            )
+
+        if outputs[0].nelement() != 1:
+            raise RuntimeError(
+                "The Tensor returned by the function given to vhp should contain a single element"
+            )
+
+        jac = _autograd_grad(outputs, inputs, create_graph=True)
+        _check_requires_grad(jac, "jacobian", strict=strict)
+
+    enable_grad = True if create_graph else torch.is_grad_enabled()
+    with torch.set_grad_enabled(enable_grad):
+        grad_res = _autograd_grad(jac, inputs, v, create_graph=create_graph)
+        vhp = _fill_in_zeros(grad_res, inputs, strict, create_graph, "double_back")
+
+    outputs = _grad_postprocess(outputs, create_graph)
+    vhp = _grad_postprocess(vhp, create_graph)
+
+    return _tuple_postprocess(outputs, is_outputs_tuple), _tuple_postprocess(
+        vhp, is_inputs_tuple
+    )
+
+
+def hvp(func, inputs, v=None, create_graph=False, strict=False):
+    r"""Compute the dot product between the scalar function's Hessian and a vector ``v`` at a specified point.
+
+    Args:
+        func (function): a Python function that takes Tensor inputs and returns
+            a Tensor with a single element.
+        inputs (tuple of Tensors or Tensor): inputs to the function ``func``.
+        v (tuple of Tensors or Tensor): The vector for which the Hessian vector
+            product is computed. Must be the same size as the input of
+            ``func``. This argument is optional when ``func``'s input contains
+            a single element and (if it is not provided) will be set as a
+            Tensor containing a single ``1``.
+        create_graph (bool, optional): If ``True``, both the output and result will be
+            computed in a differentiable way. Note that when ``strict`` is
+            ``False``, the result can not require gradients or be disconnected
+            from the inputs.  Defaults to ``False``.
+        strict (bool, optional): If ``True``, an error will be raised when we
+            detect that there exists an input such that all the outputs are
+            independent of it. If ``False``, we return a Tensor of zeros as the
+            hvp for said inputs, which is the expected mathematical value.
+            Defaults to ``False``.
+    Returns:
+        output (tuple): tuple with:
+            func_output (tuple of Tensors or Tensor): output of ``func(inputs)``
+
+            hvp (tuple of Tensors or Tensor): result of the dot product with
+            the same shape as the inputs.
+
+    Example:
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> def pow_reducer(x):
+        ...     return x.pow(3).sum()
+        >>> inputs = torch.rand(2, 2)
+        >>> v = torch.ones(2, 2)
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> hvp(pow_reducer, inputs, v)
+        (tensor(0.1448),
+         tensor([[2.0239, 1.6456],
+                 [2.4988, 1.4310]]))
+
+        >>> hvp(pow_reducer, inputs, v, create_graph=True)
+        (tensor(0.1448, grad_fn=<SumBackward0>),
+         tensor([[2.0239, 1.6456],
+                 [2.4988, 1.4310]], grad_fn=<MulBackward0>))
+
+
+        >>> def pow_adder_reducer(x, y):
+        ...     return (2 * x.pow(2) + 3 * y.pow(2)).sum()
+        >>> inputs = (torch.rand(2), torch.rand(2))
+        >>> v = (torch.zeros(2), torch.ones(2))
+        >>> hvp(pow_adder_reducer, inputs, v)
+        (tensor(2.3030),
+         (tensor([0., 0.]),
+          tensor([6., 6.])))
+
+    Note:
+
+        This function is significantly slower than `vhp` due to backward mode AD constraints.
+        If your functions is twice continuously differentiable, then hvp = vhp.t(). So if you
+        know that your function satisfies this condition, you should use vhp instead that is
+        much faster with the current implementation.
+
+    """
+    with torch.enable_grad():
+        is_inputs_tuple, inputs = _as_tuple(inputs, "inputs", "hvp")
+        inputs = _grad_preprocess(inputs, create_graph=create_graph, need_graph=True)
+
+        if v is not None:
+            _, v = _as_tuple(v, "v", "hvp")
+            v = _grad_preprocess(v, create_graph=create_graph, need_graph=False)
+            _validate_v(v, inputs, is_inputs_tuple)
+        else:
+            if len(inputs) != 1 or inputs[0].nelement() != 1:
+                raise RuntimeError(
+                    "The vector v can only be None if the input to the user-provided function "
+                    "is a single Tensor with a single element."
+                )
+        outputs = func(*inputs)
+        is_outputs_tuple, outputs = _as_tuple(
+            outputs, "outputs of the user-provided function", "hvp"
+        )
+        _check_requires_grad(outputs, "outputs", strict=strict)
+
+        if is_outputs_tuple or not isinstance(outputs[0], torch.Tensor):
+            raise RuntimeError(
+                "The function given to hvp should return a single Tensor"
+            )
+
+        if outputs[0].nelement() != 1:
+            raise RuntimeError(
+                "The Tensor returned by the function given to hvp should contain a single element"
+            )
+
+        jac = _autograd_grad(outputs, inputs, create_graph=True)
+        _check_requires_grad(jac, "jacobian", strict=strict)
+
+        grad_jac = tuple(torch.zeros_like(inp, requires_grad=True) for inp in inputs)
+
+        double_back = _autograd_grad(jac, inputs, grad_jac, create_graph=True)
+        _check_requires_grad(jac, "hessian", strict=strict)
+
+    enable_grad = True if create_graph else torch.is_grad_enabled()
+    with torch.set_grad_enabled(enable_grad):
+        grad_res = _autograd_grad(double_back, grad_jac, v, create_graph=create_graph)
+        hvp = _fill_in_zeros(
+            grad_res, inputs, strict, create_graph, "double_back_trick"
+        )
+
+    outputs = _grad_postprocess(outputs, create_graph)
+    hvp = _grad_postprocess(hvp, create_graph)
+
+    return _tuple_postprocess(outputs, is_outputs_tuple), _tuple_postprocess(
+        hvp, is_inputs_tuple
+    )

venv/lib/python3.10/site-packages/torch/autograd/grad_mode.py

@@ -0,0 +1,396 @@
+from typing import Any
+
+import torch
+
+from torch.utils._contextlib import (
+    _DecoratorContextManager,
+    _NoParamDecoratorContextManager,
+    F,
+)
+
+__all__ = [
+    "no_grad",
+    "enable_grad",
+    "set_grad_enabled",
+    "inference_mode",
+    "set_multithreading_enabled",
+]
+
+
+class no_grad(_NoParamDecoratorContextManager):
+    r"""Context-manager that disables gradient calculation.
+
+    Disabling gradient calculation is useful for inference, when you are sure
+    that you will not call :meth:`Tensor.backward()`. It will reduce memory
+    consumption for computations that would otherwise have `requires_grad=True`.
+
+    In this mode, the result of every computation will have
+    `requires_grad=False`, even when the inputs have `requires_grad=True`.
+    There is an exception! All factory functions, or functions that create
+    a new Tensor and take a requires_grad kwarg, will NOT be affected by
+    this mode.
+
+    This context manager is thread local; it will not affect computation
+    in other threads.
+
+    Also functions as a decorator.
+
+    .. note::
+        No-grad is one of several mechanisms that can enable or
+        disable gradients locally see :ref:`locally-disable-grad-doc` for
+        more information on how they compare.
+
+    .. note::
+        This API does not apply to :ref:`forward-mode AD <forward-mode-ad>`.
+        If you want to disable forward AD for a computation, you can unpack
+        your dual tensors.
+
+    Example::
+        >>> # xdoctest: +SKIP
+        >>> x = torch.tensor([1.], requires_grad=True)
+        >>> with torch.no_grad():
+        ...     y = x * 2
+        >>> y.requires_grad
+        False
+        >>> @torch.no_grad()
+        ... def doubler(x):
+        ...     return x * 2
+        >>> z = doubler(x)
+        >>> z.requires_grad
+        False
+        >>> @torch.no_grad
+        ... def tripler(x):
+        ...     return x * 3
+        >>> z = tripler(x)
+        >>> z.requires_grad
+        False
+        >>> # factory function exception
+        >>> with torch.no_grad():
+        ...     a = torch.nn.Parameter(torch.rand(10))
+        >>> a.requires_grad
+        True
+    """
+
+    def __init__(self) -> None:
+        if not torch._jit_internal.is_scripting():
+            super().__init__()
+        self.prev = False
+
+    def __enter__(self) -> None:
+        self.prev = torch.is_grad_enabled()
+        torch.set_grad_enabled(False)
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any) -> None:
+        torch.set_grad_enabled(self.prev)
+
+
+class enable_grad(_NoParamDecoratorContextManager):
+    r"""Context-manager that enables gradient calculation.
+
+    Enables gradient calculation, if it has been disabled via :class:`~no_grad`
+    or :class:`~set_grad_enabled`.
+
+    This context manager is thread local; it will not affect computation
+    in other threads.
+
+    Also functions as a decorator.
+
+    .. note::
+        enable_grad is one of several mechanisms that can enable or
+        disable gradients locally see :ref:`locally-disable-grad-doc` for
+        more information on how they compare.
+
+    .. note::
+        This API does not apply to :ref:`forward-mode AD <forward-mode-ad>`.
+
+    Example::
+        >>> # xdoctest: +SKIP
+        >>> x = torch.tensor([1.], requires_grad=True)
+        >>> with torch.no_grad():
+        ...     with torch.enable_grad():
+        ...         y = x * 2
+        >>> y.requires_grad
+        True
+        >>> y.backward()
+        >>> x.grad
+        tensor([2.])
+        >>> @torch.enable_grad()
+        ... def doubler(x):
+        ...     return x * 2
+        >>> with torch.no_grad():
+        ...     z = doubler(x)
+        >>> z.requires_grad
+        True
+        >>> @torch.enable_grad
+        ... def tripler(x):
+        ...     return x * 3
+        >>> with torch.no_grad():
+        ...     z = tripler(x)
+        >>> z.requires_grad
+        True
+
+    """
+
+    def __enter__(self) -> None:
+        self.prev = torch.is_grad_enabled()
+        torch._C._set_grad_enabled(True)
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any) -> None:
+        torch._C._set_grad_enabled(self.prev)
+
+
+class set_grad_enabled(_DecoratorContextManager):
+    r"""Context-manager that sets gradient calculation on or off.
+
+    ``set_grad_enabled`` will enable or disable grads based on its argument :attr:`mode`.
+    It can be used as a context-manager or as a function.
+
+    This context manager is thread local; it will not affect computation
+    in other threads.
+
+    Args:
+        mode (bool): Flag whether to enable grad (``True``), or disable
+                     (``False``). This can be used to conditionally enable
+                     gradients.
+
+    .. note::
+        set_grad_enabled is one of several mechanisms that can enable or
+        disable gradients locally see :ref:`locally-disable-grad-doc` for
+        more information on how they compare.
+
+    .. note::
+        This API does not apply to :ref:`forward-mode AD <forward-mode-ad>`.
+
+    Example::
+        >>> # xdoctest: +SKIP
+        >>> x = torch.tensor([1.], requires_grad=True)
+        >>> is_train = False
+        >>> with torch.set_grad_enabled(is_train):
+        ...     y = x * 2
+        >>> y.requires_grad
+        False
+        >>> _ = torch.set_grad_enabled(True)
+        >>> y = x * 2
+        >>> y.requires_grad
+        True
+        >>> _ = torch.set_grad_enabled(False)
+        >>> y = x * 2
+        >>> y.requires_grad
+        False
+
+    """
+
+    def __init__(self, mode: bool) -> None:
+        self.prev = torch.is_grad_enabled()
+        self.mode = mode
+        torch._C._set_grad_enabled(mode)
+
+    def __call__(self, orig_func: F) -> F:
+        torch._C._set_grad_enabled(self.prev)
+        return super().__call__(orig_func)
+
+    def __enter__(self) -> None:
+        torch._C._set_grad_enabled(self.mode)
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any) -> None:
+        torch._C._set_grad_enabled(self.prev)
+
+    def clone(self) -> "set_grad_enabled":
+        r"""
+        Create a copy of this class
+        """
+        return self.__class__(self.mode)
+
+
+class inference_mode(_DecoratorContextManager):
+    r"""Context-manager that enables or disables inference mode.
+
+    InferenceMode is a new context manager analogous to :class:`~no_grad`
+    to be used when you are certain your operations will have no interactions
+    with autograd (e.g., model training). Code run under this mode gets better
+    performance by disabling view tracking and version counter bumps. Note that
+    unlike some other mechanisms that locally enable or disable grad,
+    entering inference_mode also disables to :ref:`forward-mode AD <forward-mode-ad>`.
+
+    This context manager is thread local; it will not affect computation
+    in other threads.
+
+    Also functions as a decorator.
+
+    .. note::
+        Inference mode is one of several mechanisms that can enable or
+        disable gradients locally see :ref:`locally-disable-grad-doc` for
+        more information on how they compare.
+
+    Args:
+        mode (bool or function): Either a boolean flag whether to enable or
+            disable inference mode or a Python function to decorate with
+            inference mode enabled
+
+    Example::
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> import torch
+        >>> x = torch.ones(1, 2, 3, requires_grad=True)
+        >>> with torch.inference_mode():
+        ...     y = x * x
+        >>> y.requires_grad
+        False
+        >>> # xdoctest: +SKIP("want string isnt quite right")
+        >>> y._version
+        Traceback (most recent call last):
+        File "<stdin>", line 1, in <module>
+        RuntimeError: Inference tensors do not track version counter.
+        >>> @torch.inference_mode()
+        ... def func(x):
+        ...     return x * x
+        >>> out = func(x)
+        >>> out.requires_grad
+        False
+        >>> @torch.inference_mode
+        ... def doubler(x):
+        ...     return x * 2
+        >>> out = doubler(x)
+        >>> out.requires_grad
+        False
+
+    """
+
+    def __init__(self, mode: bool = True) -> None:
+        if not torch._jit_internal.is_scripting():
+            super().__init__()
+        self.mode = mode
+
+    def __new__(cls, mode=True):
+        if isinstance(mode, bool):
+            return super().__new__(cls)
+        return cls()(mode)
+
+    def __enter__(self) -> None:
+        self._inference_mode_context = torch._C._InferenceMode(self.mode)
+        self._inference_mode_context.__enter__()
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any) -> None:
+        self._inference_mode_context.__exit__(exc_type, exc_value, traceback)
+
+    def clone(self) -> "inference_mode":
+        r"""
+        Create a copy of this class
+        """
+        return self.__class__(self.mode)
+
+
+def _enter_inference_mode(mode):
+    mode_context = torch._C._InferenceMode(mode)
+    mode_context.__enter__()
+    return mode_context
+
+
+def _exit_inference_mode(mode):
+    mode.__exit__(None, None, None)
+
+
+class set_multithreading_enabled(_DecoratorContextManager):
+    r"""Context-manager that sets multithreaded backwards on or off.
+
+    ``set_multithreading_enabled`` will enable or disable multithreaded backwards based on its argument :attr:`mode`.
+    It can be used as a context-manager or as a function.
+
+    This context manager is thread local; it will not affect computation
+    in other threads.
+
+    Args:
+        mode (bool): Flag whether to enable multithreaded backwards (``True``), or disable
+                     (``False``).
+
+    .. note::
+        This API does not apply to :ref:`forward-mode AD <forward-mode-ad>`.
+
+    """
+
+    def __init__(self, mode: bool) -> None:
+        self.prev = torch._C._is_multithreading_enabled()
+        torch._C._set_multithreading_enabled(mode)
+        self.mode = mode
+
+    def __enter__(self) -> None:
+        pass
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any) -> None:
+        torch._C._set_multithreading_enabled(self.prev)
+
+    def clone(self) -> "set_multithreading_enabled":
+        r"""
+        Create a copy of this class
+        """
+        return self.__class__(self.mode)
+
+
+class _force_original_view_tracking(_DecoratorContextManager):
+    r"""Context-manager that sets whether or not to always enable view-replay in autograd.
+
+    ``set_view_replay_enabled`` will enable or disable view-replay based on its argument :attr:`mode`.
+    It can be used as a context-manager or as a function.
+
+    This context manager is thread local; it will not affect computation
+    in other threads.
+
+    When a tensor view is mutated, the autograd engine needs to decide whether or not
+    to regenerate the "updated view" by either replaying the chain of views from the updated base,
+    or with a single call to as_strided.
+
+    If set_view_replay_enabled is set to True, then autograd will always use view replay.
+    Otherwise, it will fall back to its existing logic.
+
+    Args:
+        mode (bool): Flag whether to enable view-replay (``True``), or disable
+                     (``False``).
+
+    """
+
+    def __init__(self, mode: bool) -> None:
+        self.prev = torch._C._is_view_replay_enabled()
+        torch._C._set_view_replay_enabled(mode)
+        self.mode = mode
+
+    def __enter__(self) -> None:
+        pass
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any) -> None:
+        torch._C._set_view_replay_enabled(self.prev)
+
+    def clone(self):
+        return self.__class__(self.mode)
+
+
+class _unsafe_preserve_version_counter(_DecoratorContextManager):
+    r"""DO NOT USE THIS UNLESS YOU KNOW EXACTLY WHAT YOU'RE DOING.
+
+    This context manager can lead to arbitrary silent-correctness issues in any other part of your code
+    (even the ones not touched directly by the context manager)!
+
+    Ordinarily, autograd will track mutations to tensors by incrementing it's `._version` attribute.
+    This is generally important for correctness, as for example, mutating a tensor that autograd has saved
+    for the backwards pass can result in incorrect gradients, and autograd uses the version counter to detect
+    and error out in this situation.
+
+    However, there are rare instances where it might be useful to hide mutations from autograd. For example:
+    if a tensor is very large, and you'd like to free its memory by storing it elsewhere, and re-populate
+    the tensor right before it is needed by autograd.
+
+    Args:
+        tensor (torch.Tensor): the tensor in question, that you would like to preserve the version counter of.
+
+    .. note::
+        This API does not apply to :ref:`forward-mode AD <forward-mode-ad>`.
+
+    """
+
+    def __init__(self, tensor: torch.Tensor) -> None:
+        self.tensor = tensor
+        self.prev_version = tensor._version
+
+    def __enter__(self) -> None:
+        pass
+
+    def __exit__(self, *args) -> None:
+        torch._C._autograd._unsafe_set_version_counter(self.tensor, self.prev_version)

venv/lib/python3.10/site-packages/torch/autograd/gradcheck.py

@@ -0,0 +1,2266 @@
+import collections
+import functools
+import warnings
+from itertools import product
+from typing import Callable, Dict, Iterable, List, Optional, Tuple, Union
+
+import torch
+import torch.testing
+from torch._vmap_internals import _vmap, vmap
+from torch.overrides import is_tensor_like
+from torch.types import _TensorOrTensors
+
+# Note: `get_*_jacobian` functions are added here even though we didn't intend to make them public
+# since they have been exposed from before we added `__all__`  and we already maintain BC for them
+# We should eventually deprecate them and remove them from `__all__`
+__all__ = [
+    "gradcheck",
+    "gradgradcheck",
+    "GradcheckError",
+    "get_numerical_jacobian",
+    "get_analytical_jacobian",
+    "get_numerical_jacobian_wrt_specific_input",
+]
+
+
+class GradcheckError(RuntimeError):
+    r"""Error raised by :func:`gradcheck` and :func:`gradgradcheck`."""
+
+    pass
+
+
+def _is_sparse_compressed_tensor(obj: torch.Tensor):
+    return obj.layout in {
+        torch.sparse_csr,
+        torch.sparse_csc,
+        torch.sparse_bsr,
+        torch.sparse_bsc,
+    }
+
+
+def _is_sparse_any_tensor(obj: torch.Tensor):
+    return _is_sparse_compressed_tensor(obj) or obj.layout is torch.sparse_coo
+
+
+def _is_float_or_complex_tensor(obj):
+    return is_tensor_like(obj) and (obj.is_floating_point() or obj.is_complex())
+
+
+def _allocate_jacobians_with_inputs(
+    input_tensors: Tuple, numel_output
+) -> Tuple[torch.Tensor, ...]:
+    # Makes zero-filled tensors from inputs. If `numel_output` is not None, for
+    # each tensor in `input_tensors`, returns a new zero-filled tensor with height
+    # of `t.numel` and width of `numel_output`. Otherwise, for each tensor, returns
+    # a 1-d tensor with size `(t.numel,)`. Each new tensor will be strided and have
+    # the same dtype and device as those of the corresponding input.
+    out: List[torch.Tensor] = []
+    for t in input_tensors:
+        if _is_float_or_complex_tensor(t) and t.requires_grad:
+            out.append(t.new_zeros((t.numel(), numel_output), layout=torch.strided))
+    return tuple(out)
+
+
+def _allocate_jacobians_with_outputs(
+    output_tensors: Tuple, numel_input, dtype=None, device=None
+) -> Tuple[torch.Tensor, ...]:
+    # Makes zero-filled tensors from outputs. If `dim` is not None, for each tensor
+    # in `output_tensors`, returns a new zero-filled tensor with height of `dim` and
+    # width of `t.numel`. Otherwise, for each tensor, returns a 1-d tensor with size
+    # (t.numel,).
+    out: List[torch.Tensor] = []
+    options = {"dtype": dtype, "device": device, "layout": torch.strided}
+    for t in output_tensors:
+        if _is_float_or_complex_tensor(t):
+            out.append(t.new_zeros((numel_input, t.numel()), **options))
+    return tuple(out)
+
+
+def _iter_tensors(
+    x: Union[torch.Tensor, Iterable[torch.Tensor]], only_requiring_grad: bool = False
+) -> Iterable[torch.Tensor]:
+    if is_tensor_like(x):
+        # mypy doesn't narrow type of `x` to torch.Tensor
+        if x.requires_grad or not only_requiring_grad:  # type: ignore[union-attr]
+            yield x  # type: ignore[misc]
+    elif isinstance(x, collections.abc.Iterable) and not isinstance(x, str):
+        for elem in x:
+            yield from _iter_tensors(elem, only_requiring_grad)
+
+
+def _densify(x):
+    # return a copy of sparse x with all unspecified elements
+    # "replaced" with zero-valued elements
+    if isinstance(x, (list, tuple)):
+        return type(x)(map(_densify, x))
+    elif not is_tensor_like(x) or x.layout in {torch.strided, torch._mkldnn}:  # type: ignore[attr-defined] # no attr _mkldnn
+        return x
+    elif x.layout is torch.sparse_coo:
+        device = x.device
+        indices_dtype = x._indices().dtype
+        tmp = torch.ones(x.shape[: x.sparse_dim()], dtype=torch.int8, device=device)
+        indices = tmp.nonzero().t().to(dtype=indices_dtype)
+        values = torch.zeros(
+            (tmp.numel(), *x.shape[x.sparse_dim() :]), dtype=x.dtype, device=device
+        )
+        x_coalesced = x.detach().coalesce()
+        if x_coalesced.numel() > 0:
+            stride = tmp.stride()
+            flat_indices = (
+                x_coalesced.indices()
+                .mul(
+                    torch.tensor(stride, dtype=indices_dtype, device=device).unsqueeze(
+                        1
+                    )
+                )
+                .sum(0)
+            )
+            values[flat_indices] = x_coalesced.values()
+        return (
+            torch.sparse_coo_tensor(indices, values, x.shape)
+            ._coalesced_(True)
+            .requires_grad_(x.requires_grad)
+        )
+    elif _is_sparse_compressed_tensor(x):
+        blocksize = (
+            x.values().shape[1:3]
+            if x.layout in {torch.sparse_bsr, torch.sparse_bsc}
+            else None
+        )
+        compressed_indices = (
+            x.crow_indices()
+            if x.layout in {torch.sparse_csr, torch.sparse_bsr}
+            else x.ccol_indices()
+        )
+        # We'll use intermediate sparse COO for simplicity
+        r = _densify(x.detach().to_sparse(layout=torch.sparse_coo)).to_sparse(
+            layout=x.layout, blocksize=blocksize
+        )
+        # Check that all elements are specified also after `to_sparse` op:
+        dense_numel = r.values().numel() // max(1, r.values().shape[0])
+        batch_numel = compressed_indices.numel() // compressed_indices.shape[-1]
+        sparse_numel = r.numel() // max(1, dense_numel * batch_numel)
+        if sparse_numel != r._nnz():
+            raise AssertionError(
+                f"{x.layout} densify failed: expected nnz={sparse_numel} but got {r._nnz()}"
+            )
+        return r.requires_grad_(x.requires_grad)
+    elif _is_sparse_any_tensor(x):
+        raise NotImplementedError(x.layout)
+    return x
+
+
+def _iter_tensor(x_tensor):
+    # (Only used for slow gradcheck) Returns a generator that yields the following
+    # elements at each iteration:
+    #  1) a tensor: the same tensor is returned across all iterations. The tensor
+    #     is not the same as the original x_tensor as given as input - it is
+    #     prepared so that it can be modified in-place. Depending on whether the
+    #     input tensor is strided, sparse, or dense, the returned tensor may or may
+    #     not share storage with x_tensor.
+    #  2) a tuple of indices that can be used with advanced indexing (yielded in
+    #     dictionary order)
+    #  3) flattened index that will be used to index into the Jacobian tensor
+    #
+    # For a tensor t with size (2, 2), _iter_tensor yields:
+    #     `x, (0, 0), 0`, `x, (0, 1), 1`, `x, (1, 0), 2`, `x, (1, 1), 3`
+    #
+    # where x is the t.data of the original tensor. Perturbing the entry of x
+    # at index (1, 1) yields the 3rd column of the overall Jacobian matrix.
+    if _is_sparse_any_tensor(x_tensor):
+
+        def get_stride(size):
+            dim = len(size)
+            tmp = 1
+            stride = [0] * dim
+            for i in reversed(range(dim)):
+                stride[i] = tmp
+                tmp *= size[i]
+            return stride
+
+        x_nnz = x_tensor._nnz()
+        x_size = list(x_tensor.size())
+        if x_tensor.layout is torch.sparse_coo:
+            x_indices = x_tensor._indices().t()
+            x_values = x_tensor._values()
+        elif x_tensor.layout is torch.sparse_csr:
+            x_indices = torch._convert_indices_from_csr_to_coo(
+                x_tensor.crow_indices(), x_tensor.col_indices()
+            ).t()
+            x_values = x_tensor.values()
+        elif x_tensor.layout is torch.sparse_csc:
+            x_indices = torch._convert_indices_from_csr_to_coo(
+                x_tensor.ccol_indices(), x_tensor.row_indices(), transpose=True
+            ).t()
+            x_values = x_tensor.values()
+        elif x_tensor.layout is torch.sparse_bsr:
+            x_block_values = x_tensor.values()
+            x_blocksize = x_block_values.size()[1:3]
+            x_indices = (
+                torch._convert_indices_from_csr_to_coo(
+                    x_tensor.crow_indices(), x_tensor.col_indices()
+                )
+                .repeat_interleave(x_blocksize[0] * x_blocksize[1], 1)
+                .mul_(torch.tensor(x_blocksize, device=x_tensor.device).reshape(2, 1))
+                .add_(
+                    torch.stack(
+                        torch.where(torch.ones(x_blocksize, device=x_tensor.device))
+                    ).repeat(1, x_nnz)
+                )
+                .t()
+            )
+            x_values = x_block_values.flatten(0, 2)
+            x_nnz = x_values.size(0)
+        elif x_tensor.layout is torch.sparse_bsc:
+            x_block_values = x_tensor.values()
+            x_blocksize = x_block_values.size()[1:3]
+            x_indices = (
+                torch._convert_indices_from_csr_to_coo(
+                    x_tensor.ccol_indices(), x_tensor.row_indices(), transpose=True
+                )
+                .repeat_interleave(x_blocksize[0] * x_blocksize[1], 1)
+                .mul_(torch.tensor(x_blocksize, device=x_tensor.device).reshape(2, 1))
+                .add_(
+                    torch.stack(
+                        torch.where(torch.ones(x_blocksize, device=x_tensor.device))
+                    ).repeat(1, x_nnz)
+                )
+                .t()
+            )
+            x_values = x_block_values.flatten(0, 2)
+            x_nnz = x_values.size(0)
+        else:
+            raise NotImplementedError(f"_iter_tensor for {x_tensor.layout} input")
+        x_stride = get_stride(x_size)
+        # Use .data here to get around the version check
+        x_values = x_values.data
+        for i in range(x_nnz):
+            x_value = x_values[i]
+            for x_idx in product(*[range(m) for m in x_values.size()[1:]]):
+                indices = x_indices[i].tolist() + list(x_idx)
+                d_idx = sum(indices[k] * x_stride[k] for k in range(len(x_size)))
+                yield x_value, x_idx, d_idx
+    elif x_tensor.layout == torch._mkldnn:  # type: ignore[attr-defined]
+        for d_idx, x_idx in enumerate(product(*[range(m) for m in x_tensor.size()])):
+            # this is really inefficient, but without indexing implemented, there's
+            # not really a better way than converting back and forth
+            x_tensor_dense = x_tensor.to_dense()
+            yield x_tensor_dense, x_idx, d_idx
+    else:
+        # Use .data here to get around the version check
+        x_tensor = x_tensor.data
+        for d_idx, x_idx in enumerate(product(*[range(m) for m in x_tensor.size()])):
+            yield x_tensor, x_idx, d_idx
+
+
+def _get_numerical_jacobian(
+    fn, inputs, outputs=None, target=None, eps=1e-3, is_forward_ad=False
+) -> List[Tuple[torch.Tensor, ...]]:
+    """Compute the numerical Jacobian of `fn(inputs)` with respect to `target`.
+
+    If not specified, targets are the input. Returns M * N Jacobians where N is the
+    number of tensors in target that require grad and M is the number of non-integral
+    outputs.
+
+    Args:
+        fn: the function to compute the jacobian for
+        inputs: inputs to `fn`
+        outputs: provide precomputed outputs to avoid one extra invocation of fn
+        target: the Tensors wrt whom Jacobians are calculated (default=`inputs`)
+        eps: the magnitude of the perturbation during finite differencing
+             (default=`1e-3`)
+        is_forward_ad: if this numerical jacobian is computed to be checked wrt
+                       forward AD gradients (this is used for error checking only)
+
+    Returns:
+        A list of M N-tuples of tensors
+
+    Note that `target` may not even be part of `input` to `fn`, so please be
+    **very careful** in this to not clone `target`.
+    """
+    jacobians: List[Tuple[torch.Tensor, ...]] = []
+    if outputs is None:
+        outputs = _as_tuple(fn(*_as_tuple(inputs)))
+    if not is_forward_ad and any(o.is_complex() for o in outputs):
+        raise ValueError(
+            "Expected output to be non-complex. get_numerical_jacobian no "
+            "longer supports functions that return complex outputs."
+        )
+    if target is None:
+        target = inputs
+    inp_indices = [
+        i for i, a in enumerate(target) if is_tensor_like(a) and a.requires_grad
+    ]
+    for i, (inp, inp_idx) in enumerate(zip(_iter_tensors(target, True), inp_indices)):
+        jacobians += [
+            get_numerical_jacobian_wrt_specific_input(
+                fn,
+                inp_idx,
+                inputs,
+                outputs,
+                eps,
+                input=inp,
+                is_forward_ad=is_forward_ad,
+            )
+        ]
+    return jacobians
+
+
+def get_numerical_jacobian(fn, inputs, target=None, eps=1e-3, grad_out=1.0):
+    """Compute the numerical Jacobian for a given fn and its inputs.
+
+    This is a Deprecated API.
+
+    Args:
+        fn: the function to compute the Jacobian for (must take inputs as a tuple)
+        input: input to `fn`
+        target: the Tensors wrt whom Jacobians are calculated (default=`input`)
+        eps: the magnitude of the perturbation during finite differencing
+             (default=`1e-3`)
+
+    Returns:
+        A list of Jacobians of `fn` (restricted to its first output) with respect to
+        each input or target, if provided.
+
+    Note that `target` may not even be part of `input` to `fn`, so please be
+    **very careful** in this to not clone `target`.
+    """
+    warnings.warn(
+        "get_numerical_jacobian was part of PyTorch's private API and not "
+        "meant to be exposed. We are deprecating it and it will be removed "
+        "in a future version of PyTorch. If you have a specific use for "
+        "this or feature request for this to be a stable API, please file "
+        "us an issue at https://github.com/pytorch/pytorch/issues/new"
+    )
+    if (
+        grad_out != 1.0
+    ):  # grad_out param is only kept for backward compatibility reasons
+        raise ValueError(
+            "Expected grad_out to be 1.0. get_numerical_jacobian no longer "
+            "supports values of grad_out != 1.0."
+        )
+
+    def fn_pack_inps(*inps):
+        return fn(inps)
+
+    jacobians = _get_numerical_jacobian(fn_pack_inps, inputs, None, target, eps)
+
+    return tuple(jacobian_for_each_output[0] for jacobian_for_each_output in jacobians)
+
+
+def _compute_numerical_gradient(fn, entry, v, norm_v, nbhd_checks_fn):
+    # Computes numerical directional derivative as finite difference
+    # of function `fn` at input `entry`, perturbed by vector `v`.
+    if _is_sparse_compressed_tensor(entry):
+        # sparse compressed tensors don't implement sub/add/copy_
+        # yet. However, in non-masked semantics context entry and v
+        # have the same sparse indices ...
+        assert entry.layout == v.layout, (entry.layout, v.layout)
+        assert entry._nnz() == v._nnz(), (entry._nnz(), v._nnz(), entry.shape)
+        # ... the finite differencing can be performed on values only:
+        entry = entry.values()
+        v = v.values()
+        # we'll detach to avoid backward computations that sparse
+        # tensors have limited support for.
+        entry = entry.detach()
+
+    orig = entry.clone()
+    entry.copy_(orig - v)
+    outa = fn()
+    entry.copy_(orig + v)
+    outb = fn()
+    entry.copy_(orig)
+
+    def compute(a, b):
+        nbhd_checks_fn(a, b)
+        ret = (b - a) / (2 * norm_v)  # use central difference approx
+        return ret.detach().reshape(-1)
+
+    return tuple(compute(a, b) for (a, b) in zip(outa, outb))
+
+
+def _compute_numerical_jvps_wrt_specific_input(
+    jvp_fn, delta, input_is_complex, is_forward_ad=False
+) -> List[torch.Tensor]:
+    # Computing the jacobian only works for real delta
+    # For details on the algorithm used here, refer:
+    # Section 3.5.3 https://arxiv.org/pdf/1701.00392.pdf
+    # s = fn(z) where z = x for real valued input
+    # and z = x + yj for complex valued input
+    jvps: List[torch.Tensor] = []
+    ds_dx_tup = jvp_fn(delta[0] if isinstance(delta, tuple) else delta)
+
+    if input_is_complex:  # C -> R
+        ds_dy_tup = (
+            jvp_fn(delta[1] * 1j) if isinstance(delta, tuple) else jvp_fn(delta * 1j)
+        )
+        for ds_dx, ds_dy in zip(ds_dx_tup, ds_dy_tup):
+            assert not ds_dx.is_complex()
+            # conjugate wirtinger derivative
+            conj_w_d = ds_dx + ds_dy * 1j
+            jvps.append(conj_w_d)
+    else:
+        for ds_dx in ds_dx_tup:  # R -> R or (R -> C for the forward AD case)
+            assert is_forward_ad or not ds_dx.is_complex()
+            jvps.append(ds_dx)
+    return jvps
+
+
+def _combine_jacobian_cols(
+    jacobians_cols: Dict[int, List[torch.Tensor]], outputs, input, numel
+) -> Tuple[torch.Tensor, ...]:
+    # jacobian_cols maps column_idx -> output_idx -> single column of jacobian Tensor
+    # we return a list that maps output_idx -> full jacobian Tensor
+    jacobians = _allocate_jacobians_with_outputs(
+        outputs, numel, dtype=input.dtype if input.dtype.is_complex else None
+    )
+    for i, jacobian in enumerate(jacobians):
+        for k, v in jacobians_cols.items():
+            jacobian[k] = v[i]
+    return jacobians
+
+
+def _prepare_input(
+    input: torch.Tensor, maybe_perturbed_input: Optional[torch.Tensor], fast_mode=False
+) -> torch.Tensor:
+    # Prepares the inputs to be passed into the function while including the new
+    # modified input.
+    if input.layout == torch._mkldnn:  # type: ignore[attr-defined] # no attr _mkldnn
+        # Convert back to mkldnn
+        if maybe_perturbed_input is not None:
+            return maybe_perturbed_input.to_mkldnn()
+        else:
+            return input
+    elif _is_sparse_any_tensor(input):
+        if fast_mode and maybe_perturbed_input is not None:
+            # entry is already a "cloned" version of the original tensor
+            # thus changes to entry are not reflected in the input
+            return maybe_perturbed_input
+        else:
+            return input
+    else:
+        # We cannot use entry (input.data) if we want gradgrad to work because
+        # fn (in the gradgrad case) needs to compute grad wrt input
+        return input
+
+
+def _check_outputs_same_dtype_and_shape(output1, output2, eps, idx=None) -> None:
+    # Check that the returned outputs don't have different dtype or shape when you
+    # perturb the input
+    on_index = "on index {idx} " if idx is not None else ""
+    assert output1.shape == output2.shape, (
+        f"Expected `func` to return outputs with the same shape"
+        f" when inputs are perturbed {on_index}by {eps}, but got:"
+        f" shapes {output1.shape} and {output2.shape}."
+    )
+    assert output1.dtype == output2.dtype, (
+        f"Expected `func` to return outputs with the same dtype"
+        f" when inputs are perturbed {on_index}by {eps}, but got:"
+        f" dtypes {output1.dtype} and {output2.dtype}."
+    )
+
+
+def get_numerical_jacobian_wrt_specific_input(
+    fn, input_idx, inputs, outputs, eps, input=None, is_forward_ad=False
+) -> Tuple[torch.Tensor, ...]:
+    # Computes the numerical jacobians wrt to a single input. Returns N jacobian
+    # tensors, where N is the number of outputs. We use a dictionary for
+    # jacobian_cols because indices aren't necessarily consecutive for sparse inputs
+    # When we perturb only a single element of the input tensor at a time, the jvp
+    # is equivalent to a single col of the Jacobian matrix of fn.
+    jacobian_cols: Dict[int, List[torch.Tensor]] = {}
+    input = inputs[input_idx] if input is None else input
+    assert input.requires_grad
+    for x, idx, d_idx in _iter_tensor(input):
+        wrapped_fn = _with_prepare_inputs(fn, inputs, input_idx, x)
+        input_to_perturb = x[idx]
+        nbhd_checks_fn = functools.partial(
+            _check_outputs_same_dtype_and_shape, idx=idx, eps=eps
+        )
+        jvp_fn = _get_numerical_jvp_fn(
+            wrapped_fn, input_to_perturb, eps, nbhd_checks_fn
+        )
+        jacobian_cols[d_idx] = _compute_numerical_jvps_wrt_specific_input(
+            jvp_fn, eps, x.is_complex(), is_forward_ad
+        )
+    return _combine_jacobian_cols(jacobian_cols, outputs, input, input.numel())
+
+
+def _get_analytical_jacobian_forward_ad(
+    fn, inputs, outputs, *, check_grad_dtypes=False, all_u=None
+) -> Tuple[Tuple[torch.Tensor, ...], ...]:
+    """Compute the analytical Jacobian using forward mode AD of `fn(inputs)` using forward mode AD with respect to `target`.
+
+    Return N * M Jacobians where N is the number of tensors in target that require grad and
+    M is the number of non-integral outputs.
+    Contrary to other functions here, this function requires "inputs" to actually be used by the function.
+    The computed value is expected to be wrong if the function captures the inputs by side effect instead of
+    using the passed ones (many torch.nn tests do this).
+
+    Args:
+        fn: the function to compute the jacobian for
+        inputs: inputs to `fn`
+        outputs: provide precomputed outputs to avoid one extra invocation of fn
+        check_grad_dtypes: if True, will check that the gradient dtype are valid
+        all_u (optional): if provided, the Jacobian will be right multiplied with this vector
+
+    Returns:
+        A tuple of M N-tuples of tensors
+    """
+    # To avoid early import issues
+    fwAD = torch.autograd.forward_ad
+
+    tensor_inputs = tuple(i for i in inputs if is_tensor_like(i) and i.requires_grad)
+
+    if any(i.is_complex() for i in tensor_inputs):
+        raise ValueError(
+            "Expected inputs to be non-complex for _get_analytical_jacobian_forward_ad."
+        )
+
+    if all_u:
+        jacobians = tuple(
+            _allocate_jacobians_with_outputs(outputs, 1) for i in tensor_inputs
+        )
+    else:
+        jacobians = tuple(
+            _allocate_jacobians_with_outputs(outputs, i.numel()) for i in tensor_inputs
+        )
+
+    with fwAD.dual_level():
+        fw_grads = []
+        dual_inputs = []
+        for i, inp in enumerate(inputs):
+            if is_tensor_like(inp) and inp.requires_grad:
+                if inp.layout == torch._mkldnn:  # type: ignore[attr-defined]
+                    raise ValueError(
+                        "MKLDNN inputs are not support for forward AD gradcheck."
+                    )
+
+                inp = fwAD.make_dual(inp.detach(), torch.zeros_like(inp))
+                # If inp is a differentiable view, the dual might not be the tangent given to
+                # make_dual, so read it explicitly from the dual tensor
+                fw_grads.append(fwAD.unpack_dual(inp)[1])
+            dual_inputs.append(inp)
+
+        if all_u:
+            # Do the full reduction in one pass
+            # To be consistent with numerical evaluation, we actually compute one reduction per input
+            for i, (fw_grad, u) in enumerate(zip(fw_grads, all_u)):
+                fw_grad.copy_(u.view_as(fw_grad))
+                raw_outputs = _as_tuple(fn(*dual_inputs))
+                dual_outputs = filter(_is_float_or_complex_tensor, raw_outputs)
+                for index_o, d_o in enumerate(dual_outputs):
+                    val, res = fwAD.unpack_dual(d_o)
+                    if (
+                        check_grad_dtypes
+                        and res is not None
+                        and val.is_complex() != res.is_complex()
+                    ):
+                        raise GradcheckError("Forward AD gradient has dtype mismatch.")
+
+                    # Remove extra dimension of size 1 corresponding to the reduced input
+                    jacobians[i][index_o].squeeze_(0)
+                    if res is None:
+                        jacobians[i][index_o].zero_()
+                    else:
+                        jacobians[i][index_o].copy_(res.reshape(-1))
+                fw_grad.zero_()
+        else:
+            # Reconstruct the full Jacobian column by column
+            for i, fw_grad in enumerate(fw_grads):
+                for lin_idx, grad_idx in enumerate(
+                    product(*[range(m) for m in fw_grad.size()])
+                ):
+                    fw_grad[grad_idx] = 1.0
+                    raw_outputs = _as_tuple(fn(*dual_inputs))
+                    dual_outputs = filter(_is_float_or_complex_tensor, raw_outputs)
+                    for index_o, d_o in enumerate(dual_outputs):
+                        val, res = fwAD.unpack_dual(d_o)
+                        if (
+                            check_grad_dtypes
+                            and res is not None
+                            and val.is_complex() != res.is_complex()
+                        ):
+                            raise GradcheckError(
+                                "Forward AD gradient has dtype mismatch."
+                            )
+
+                        if res is None:
+                            jacobians[i][index_o][lin_idx].zero_()
+                        else:
+                            jacobians[i][index_o][lin_idx].copy_(res.reshape(-1))
+                    fw_grad[grad_idx] = 0.0
+
+    return jacobians
+
+
+def _get_input_to_perturb(input):
+    # Prepare the input so that it can be modified in-place and do certain
+    # operations that require the tensor to have strides. If fast_mode=False,
+    # _iter_tensor would handle the below cases:
+    if input.layout == torch._mkldnn:  # type: ignore[attr-defined] # no attr _mkldnn
+        # Convert to dense so we can perform operations that require strided tensors
+        input_to_perturb = input.to_dense()
+    elif _is_sparse_any_tensor(input):
+        # Clone because input may require grad, and copy_ calls resize_,
+        # which is not allowed for .data
+        input_to_perturb = input.clone()
+    else:
+        input_to_perturb = input.data
+    return input_to_perturb
+
+
+def _with_prepare_inputs(fn, inputs, input_idx, input_to_perturb, fast_mode=False):
+    # Wraps `fn` so that its inputs are already supplied
+    def wrapped_fn():
+        inp = tuple(
+            _prepare_input(a, input_to_perturb if i == input_idx else None, fast_mode)
+            if is_tensor_like(a)
+            else a
+            for i, a in enumerate(_as_tuple(inputs))
+        )
+        return tuple(a.clone() for a in _as_tuple(fn(*inp)))
+
+    return wrapped_fn
+
+
+def _get_numerical_jvp_fn(wrapped_fn, input_to_perturb, eps, nbhd_checks_fn):
+    # Wraps jvp_fn so that certain arguments are already supplied
+    def jvp_fn(delta):
+        return _compute_numerical_gradient(
+            wrapped_fn, input_to_perturb, delta, eps, nbhd_checks_fn
+        )
+
+    return jvp_fn
+
+
+def _reshape_tensor_or_tuple(u, shape):
+    # We don't need to reshape when input corresponding to u is sparse
+    if isinstance(u, tuple):
+        if not _is_sparse_any_tensor(u[0]):
+            return (u[0].reshape(shape), u[1].reshape(shape))
+    else:
+        if not _is_sparse_any_tensor(u):
+            return u.reshape(shape)
+    return u
+
+
+def _mul_tensor_or_tuple(u, k):
+    if isinstance(u, tuple):
+        return (k * u[0], k * u[1])
+    else:
+        return k * u
+
+
+def _get_numerical_jvp_wrt_specific_input(
+    fn, input_idx, inputs, u, eps, is_forward_ad=False
+) -> List[torch.Tensor]:
+    input = inputs[input_idx]
+    input_to_perturb = _get_input_to_perturb(input)
+    wrapped_fn = _with_prepare_inputs(fn, inputs, input_idx, input_to_perturb, True)
+    nbhd_checks_fn = functools.partial(_check_outputs_same_dtype_and_shape, eps=eps)
+    jvp_fn = _get_numerical_jvp_fn(wrapped_fn, input_to_perturb, eps, nbhd_checks_fn)
+    u = _reshape_tensor_or_tuple(u, input_to_perturb.shape)
+    u = _mul_tensor_or_tuple(u, eps)
+    return _compute_numerical_jvps_wrt_specific_input(
+        jvp_fn, u, input.is_complex(), is_forward_ad
+    )
+
+
+def _get_numerical_vJu(
+    fn, inputs, inp_indices, func_out, all_u, all_v, eps, is_forward_ad
+):
+    # Note that all_v can also be None, in that case, this function only computes Ju.
+    reduced_jacobians: List[List[torch.Tensor]] = []
+    for i, (inp_idx, u) in enumerate(zip(inp_indices, all_u)):
+        all_Ju = _get_numerical_jvp_wrt_specific_input(
+            fn, inp_idx, inputs, u, eps, is_forward_ad
+        )
+        # Filter out the Ju for non floating point outputs
+        filtered_Ju = []
+        func_out = _as_tuple(func_out)
+        assert len(all_Ju) == len(func_out)
+        for Ju, output in zip(all_Ju, func_out):
+            if _is_float_or_complex_tensor(output):
+                filtered_Ju.append(Ju)
+            else:
+                # TODO: handle the other Ju
+                pass
+        if all_v is not None:
+            jacobian_scalars: List[torch.Tensor] = []
+            for v, Ju in zip(all_v, filtered_Ju):
+                jacobian_scalars.append(_dot_with_type_promotion(v, Ju))
+            reduced_jacobians.append(jacobian_scalars)
+        else:
+            reduced_jacobians.append(filtered_Ju)
+    return reduced_jacobians
+
+
+def _check_jacobians_equal(j1, j2, atol):
+    # Check whether the max difference between two Jacobian tensors are within some
+    # tolerance `atol`.
+    for j1_x, j2_x in zip(j1, j2):
+        if j1_x.numel() != 0 and (j1_x - j2_x).abs().max() > atol:
+            return False
+    return True
+
+
+def _stack_and_check_tensors(
+    list_of_list_of_tensors, inputs, numel_outputs
+) -> Tuple[Tuple[torch.Tensor, ...], bool, bool]:
+    # For the ith tensor in the inner list checks whether it has the same size and
+    # dtype as the ith differentiable input.
+    out_jacobians = _allocate_jacobians_with_inputs(inputs, numel_outputs)
+    diff_input_list = list(_iter_tensors(inputs, True))
+    correct_grad_sizes = True
+    correct_grad_types = True
+    for i, tensor_list in enumerate(list_of_list_of_tensors):
+        inp = diff_input_list[i]
+        out_jacobian = out_jacobians[i]
+        for j, tensor in enumerate(tensor_list):
+            if tensor is not None and tensor.size() != inp.size():
+                correct_grad_sizes = False
+            elif tensor is not None and tensor.dtype != inp.dtype:
+                correct_grad_types = False
+            if tensor is None:
+                out_jacobian[:, j].zero_()
+            else:
+                dense = (
+                    tensor.to_dense() if not tensor.layout == torch.strided else tensor
+                )
+                assert out_jacobian[:, j].numel() == dense.numel()
+                out_jacobian[:, j] = dense.reshape(-1)
+    return out_jacobians, correct_grad_sizes, correct_grad_types
+
+
+FAILED_NONDET_MSG = """\n
+NOTE: If your op relies on non-deterministic operations i.e., it is listed here:
+https://pytorch.org/docs/stable/generated/torch.use_deterministic_algorithms.html
+this failure might be expected.
+
+If you are adding a new operator, please file an issue and then use one of the
+workarounds. The workaround depends on how your test invokes gradcheck/gradgradcheck.
+If the test
+- manually invokes gradcheck/gradgradcheck, then call gradcheck/gradgradcheck
+  with `nondet_tol=<tol>` as a keyword argument.
+- is OpInfo-based (e.g., in test_ops_gradients.py), then modify the OpInfo for the test
+  to have `gradcheck_nondet_tol=<tol>`.
+- is a Module test (e.g., in common_nn.py), then modify the corresponding
+  module_test entry to have `gradcheck_nondet_tol=<tol>`
+"""
+
+
+def _check_analytical_jacobian_attributes(
+    inputs, output, nondet_tol, check_grad_dtypes, fast_mode=False, v=None
+) -> Tuple[torch.Tensor, ...]:
+    # This is used by both fast and slow mode:
+    #  - For slow mode, vjps[i][j] is the jth row of the Jacobian wrt the ith
+    #    input.
+    #  - For fast mode, vjps[i][0] is a linear combination of the rows
+    #    of the Jacobian wrt the ith input
+    diff_input_list = list(_iter_tensors(inputs, True))
+
+    def vjp_fn(grad_output):
+        return torch.autograd.grad(
+            output, diff_input_list, grad_output, retain_graph=True, allow_unused=True
+        )
+
+    # Compute everything twice to check for nondeterminism (which we call reentrancy)
+    if fast_mode:
+        vjps1 = _get_analytical_vjps_wrt_specific_output(vjp_fn, output.clone(), v)
+        vjps2 = _get_analytical_vjps_wrt_specific_output(vjp_fn, output.clone(), v)
+    else:
+        vjps1 = _compute_analytical_jacobian_rows(vjp_fn, output.clone())
+        vjps2 = _compute_analytical_jacobian_rows(vjp_fn, output.clone())
+
+    output_numel = output.numel() if not fast_mode else 1
+    jacobians1, types_ok, sizes_ok = _stack_and_check_tensors(
+        vjps1, inputs, output_numel
+    )
+    jacobians2, _, _ = _stack_and_check_tensors(vjps2, inputs, output_numel)
+    reentrant = _check_jacobians_equal(jacobians1, jacobians2, nondet_tol)
+
+    if not types_ok and check_grad_dtypes:
+        raise GradcheckError("Gradient has dtype mismatch")
+    if not sizes_ok:
+        raise GradcheckError("Analytical gradient has incorrect size")
+    if not reentrant:
+        raise GradcheckError(
+            "Backward is not reentrant, i.e., running backward with "
+            "same input and grad_output multiple times gives different values, "
+            "although analytical gradient matches numerical gradient."
+            f"The tolerance for nondeterminism was {nondet_tol}." + FAILED_NONDET_MSG
+        )
+    return jacobians1
+
+
+def _get_analytical_vJu_backward_mode(
+    inputs, outputs, nondet_tol, check_grad_dtypes, all_v, all_u
+):
+    reduced_jacobians: List[List[torch.Tensor]] = []
+    for output, v in zip(outputs, all_v):
+        all_vJ = _check_analytical_jacobian_attributes(
+            inputs, output, nondet_tol, check_grad_dtypes, fast_mode=True, v=v
+        )
+        jacobian_scalars: List[torch.Tensor] = []
+        for vJ, u in zip(all_vJ, all_u):
+            # Why do we need squeeze here? vJ is a 2-d tensor so that we can reuse
+            # the error checking logic from slow mode
+            vJ = vJ.T.squeeze(0)
+            if vJ.is_complex():  # C -> R
+                tv = torch.view_as_real(vJ.resolve_conj())
+                tr = tv.select(-1, 0)
+                ti = tv.select(-1, 1)
+                jacobian_scalars.append(tr.dot(u[0]) + 1j * ti.dot(u[1]))
+            else:  # R -> R
+                jacobian_scalars.append(vJ.dot(u))
+        reduced_jacobians.append(jacobian_scalars)
+    return reduced_jacobians
+
+
+def get_analytical_jacobian(inputs, output, nondet_tol=0.0, grad_out=1.0):
+    # Replicates the behavior of the old get_analytical_jacobian before the refactor
+    # This shares much of its code with _check_analytical_jacobian_attributes
+    warnings.warn(
+        "get_analytical_jacobian was part of PyTorch's private API and not "
+        "meant to be exposed. We are deprecating it and it will be removed "
+        "in a future version of PyTorch. If you have a specific use for "
+        "this or feature request for this to be a stable API, please file "
+        "us an issue at https://github.com/pytorch/pytorch/issues/new"
+    )
+    if (
+        grad_out != 1.0
+    ):  # grad_out param is only kept for backward compatibility reasons
+        raise ValueError(
+            "Expected grad_out to be 1.0. get_analytical_jacobian no longer "
+            "supports values of grad_out != 1.0."
+        )
+    if output.is_complex():
+        raise ValueError(
+            "Expected output to be non-complex. get_analytical_jacobian no "
+            "longer supports functions that return complex outputs."
+        )
+    diff_input_list = list(_iter_tensors(inputs, True))
+
+    def vjp_fn(grad_output):
+        return torch.autograd.grad(
+            output, diff_input_list, grad_output, retain_graph=True, allow_unused=True
+        )
+
+    # Compute everything twice to check for nondeterminism (which we call reentrancy)
+    vjps1 = _compute_analytical_jacobian_rows(vjp_fn, output.clone())
+    vjps2 = _compute_analytical_jacobian_rows(vjp_fn, output.clone())
+
+    output_numel = output.numel()
+    jacobians1, types_ok, sizes_ok = _stack_and_check_tensors(
+        vjps1, inputs, output_numel
+    )
+    jacobians2, _, _ = _stack_and_check_tensors(vjps2, inputs, output_numel)
+    reentrant = _check_jacobians_equal(jacobians1, jacobians2, nondet_tol)
+
+    return jacobians1, reentrant, sizes_ok, types_ok
+
+
+def _get_analytical_jacobian(inputs, outputs, input_idx, output_idx):
+    # Computes the analytical Jacobian in slow mode for a single input-output pair.
+    # Forgoes performing checks on dtype, shape, and reentrancy.
+    jacobians = _check_analytical_jacobian_attributes(
+        inputs, outputs[output_idx], nondet_tol=float("inf"), check_grad_dtypes=False
+    )
+    return jacobians[input_idx]
+
+
+def _compute_analytical_jacobian_rows(
+    vjp_fn, sample_output
+) -> List[List[Optional[torch.Tensor]]]:
+    # Computes Jacobian row-by-row by projecting `vjp_fn` = v^T J on standard basis
+    # vectors: vjp_fn(e) = e^T J is a corresponding row of the Jacobian.
+    # NB: this function does not assume vjp_fn(v) to return tensors with the same
+    # number of elements for different v. This is checked when we later combine the
+    # rows into a single tensor.
+    grad_out_base = torch.zeros_like(
+        sample_output, memory_format=torch.legacy_contiguous_format
+    )
+    flat_grad_out = grad_out_base.view(-1)
+    # jacobians_rows[i][j] is the Jacobian jth row for the ith input
+    jacobians_rows: List[List[Optional[torch.Tensor]]] = []
+    for j in range(flat_grad_out.numel()):
+        flat_grad_out.zero_()
+        flat_grad_out[j] = 1.0  # projection for jth row of Jacobian
+        grad_inputs = vjp_fn(grad_out_base)
+        for i, d_x in enumerate(grad_inputs):
+            if j == 0:
+                jacobians_rows.append([])
+            jacobians_rows[i] += [
+                d_x.clone() if isinstance(d_x, torch.Tensor) else None
+            ]
+    return jacobians_rows
+
+
+def _get_analytical_vjps_wrt_specific_output(
+    vjp_fn, sample_output, v
+) -> List[List[Optional[torch.Tensor]]]:
+    vjps: List[List[Optional[torch.Tensor]]] = []
+    grad_inputs = vjp_fn(v.reshape(sample_output.shape))
+    for vjp in grad_inputs:
+        vjps.append([vjp.clone() if isinstance(vjp, torch.Tensor) else None])
+    return vjps
+
+
+def _check_inputs(tupled_inputs) -> bool:
+    # Make sure that gradients are saved for at least one input
+    any_input_requiring_grad = False
+    for idx, inp in enumerate(tupled_inputs):
+        if is_tensor_like(inp) and inp.requires_grad:
+            if not (inp.dtype == torch.float64 or inp.dtype == torch.complex128):
+                warnings.warn(
+                    f"Input #{idx} requires gradient and "
+                    "is not a double precision floating point or complex. "
+                    "This check will likely fail if all the inputs are "
+                    "not of double precision floating point or complex. "
+                )
+            if inp.is_sparse:
+                content = inp._values()
+            elif _is_sparse_compressed_tensor(inp):
+                content = inp.values()
+            else:
+                content = inp
+            # TODO: To cover more problematic cases, replace stride = 0 check with
+            # "any overlap in memory" once we have a proper function to check it.
+            if content.layout is not torch._mkldnn:  # type: ignore[attr-defined]
+                if not all(
+                    st > 0 or sz <= 1
+                    for st, sz in zip(content.stride(), content.size())
+                ):
+                    raise RuntimeError(
+                        f"The {idx}th input has a dimension with stride 0. gradcheck only "
+                        "supports inputs that are non-overlapping to be able to "
+                        "compute the numerical gradients correctly. You should call "
+                        ".contiguous on the input before passing it to gradcheck."
+                    )
+            any_input_requiring_grad = True
+
+    if not any_input_requiring_grad:
+        raise ValueError(
+            "gradcheck expects at least one input tensor to require gradient, "
+            "but none of the them have requires_grad=True."
+        )
+    return True
+
+
+def _check_outputs(outputs) -> None:
+    if any(_is_sparse_any_tensor(t) for t in outputs if isinstance(t, torch.Tensor)):
+        # it is easier to call to_dense() on the sparse output than
+        # to modify analytical jacobian
+        raise ValueError(
+            "Sparse output is not supported at gradcheck yet. "
+            "Please call to_dense(masked_grad=...) on the output of fn for gradcheck."
+        )
+    if any(t.layout == torch._mkldnn for t in outputs if isinstance(t, torch.Tensor)):  # type: ignore[attr-defined]
+        raise ValueError(
+            "MKLDNN output is not supported at gradcheck yet. "
+            "Please call to_dense(masked_grad=...) on the output of fn for gradcheck."
+        )
+
+
+def _check_no_differentiable_outputs(
+    func, inputs, func_out, eps, *, is_forward_ad
+) -> bool:
+    # When there are no differentiable outputs, numerical gradient for a function is
+    # expected to be zero.
+    jacobians_all_inputs_outputs = _get_numerical_jacobian(
+        func, inputs, func_out, eps=eps, is_forward_ad=is_forward_ad
+    )
+    for jacobians_all_outputs_and_fixed_input in jacobians_all_inputs_outputs:
+        for jacobian in jacobians_all_outputs_and_fixed_input:
+            if torch.ne(jacobian, 0).sum() > 0:
+                raise GradcheckError(
+                    "Numerical gradient for function expected to be zero"
+                )
+    return True
+
+
+def _check_no_differentiable_outputs_fast(
+    func, func_out, all_inputs, inputs_indices, all_u, eps, nondet_tol
+):
+    for inp_idx, u in zip(inputs_indices, all_u):
+        jvps = _get_numerical_jvp_wrt_specific_input(func, inp_idx, all_inputs, u, eps)
+        for jvp in jvps:
+            if jvp.numel() == 0:
+                continue
+            if (jvp - torch.zeros_like(jvp)).abs().max() > nondet_tol:
+                raise GradcheckError(
+                    "Numerical gradient for function expected to be zero"
+                )
+    return True
+
+
+FAILED_BATCHED_GRAD_MSG = """
+gradcheck or gradgradcheck failed while testing batched gradient computation.
+This could have been invoked in a number of ways (via a test that calls
+gradcheck/gradgradcheck directly or via an autogenerated test).
+
+If you are adding a new operator, please file an issue and then use one of the
+workarounds. The workaround depends on how your test invokes gradcheck/gradgradcheck.
+If the test
+- manually invokes gradcheck/gradgradcheck, then call gradcheck/gradgradcheck
+  with `check_batched_grad=False` as a keyword argument.
+- is OpInfo-based (e.g., in test_ops_gradients.py), then modify the OpInfo for the test
+  to have `check_batched_grad=False` and/or `check_batched_gradgrad=False`.
+
+If you're modifying an existing operator that supports batched grad computation,
+or wish to make a new operator work with batched grad computation, please read
+the following.
+
+To compute batched grads (e.g., jacobians, hessians), we vmap over the backward
+computation. The most common failure case is if there is a 'vmap-incompatible
+operation' in the backward pass. Please see
+NOTE: [How to write vmap-compatible backward formulas]
+in the codebase for an explanation of how to fix this.
+""".strip()
+
+FAILED_BATCHED_GRAD_MSG_FWD_AD = """
+gradcheck failed while testing batched gradient computation with forward-mode AD.
+This test is enabled automatically when both `check_batched_grad=True`
+and `check_forward_ad=True`, but can be disabled in the following ways
+dependong on how the test was invoked (via a test that calls gradcheck
+directly or via an autogenerated test).
+
+If you are adding a new operator, please file an issue and then use one of the
+workarounds. The workaround depends on how your test invokes gradcheck/gradgradcheck.
+If the test
+- manually invokes gradcheck/gradgradcheck, then call gradcheck/gradgradcheck
+  with `check_batched_forward_grad=False` as a keyword argument.
+- is OpInfo-based (e.g., in test_ops_gradients.py), then modify the OpInfo for the test
+  to have `check_batched_forward_grad=False`
+"""
+
+
+def _get_failed_batched_grad_test_msg(
+    output_idx, input_idx, res, exp, is_forward_ad=False
+):
+    return f"""
+For output {output_idx} and input {input_idx}:
+
+{FAILED_BATCHED_GRAD_MSG_FWD_AD if is_forward_ad else FAILED_BATCHED_GRAD_MSG}
+
+Got:
+{res}
+
+Expected:
+{exp}
+""".strip()
+
+
+def _test_batched_grad_forward_ad(func, inputs) -> bool:
+    fwAD = torch.autograd.forward_ad  # To avoid early import issues (do we need this?)
+    assert isinstance(inputs, tuple)
+
+    for input_idx, current_input in enumerate(inputs):
+        if not (is_tensor_like(current_input) and current_input.requires_grad):
+            continue
+
+        def jvp(tangent: torch.Tensor):
+            with fwAD.dual_level():
+                dual = fwAD.make_dual(current_input.detach(), tangent)
+                inputs_with_dual = tuple(
+                    dual
+                    if idx == input_idx
+                    else (inp.detach() if is_tensor_like(inp) else inp)
+                    for idx, inp in enumerate(inputs)
+                )
+                dual_outputs = _as_tuple(func(*inputs_with_dual))
+                ret = []
+                for dual_output in dual_outputs:
+                    if dual_output is None:
+                        continue
+                    primal_out, tangent_out = fwAD.unpack_dual(dual_output)
+                    if tangent_out is not None:
+                        ret.append(tangent_out)
+                    else:
+                        ret.append(
+                            torch.zeros(
+                                [], dtype=primal_out.dtype, device=primal_out.device
+                            ).expand(primal_out.shape)
+                        )
+                return tuple(ret)
+
+        if not _is_float_or_complex_tensor(current_input):
+            continue
+
+        tangents = [torch.randn_like(current_input) for _ in range(2)]
+        expected = [jvp(t) for t in tangents]
+        expected = [torch.stack(shards) for shards in zip(*expected)]
+
+        try:
+            result = _vmap(jvp)(torch.stack(tangents))
+        except RuntimeError as ex:
+            # Rethrow to provide a better error message
+            raise GradcheckError(
+                f"While computing batched gradients, got: {ex}\n\n{FAILED_BATCHED_GRAD_MSG_FWD_AD}"
+            ) from ex
+
+        for input_idx, (res, exp) in enumerate(zip(result, expected)):
+            if torch.allclose(res, exp):
+                continue
+            raise GradcheckError(
+                _get_failed_batched_grad_test_msg(
+                    input_idx, input_idx, res, exp, is_forward_ad=True
+                )
+            )
+    return True
+
+
+def _test_batched_grad(input, output, output_idx) -> bool:
+    # NB: _test_batched_grad compares two autograd.grad invocations with a single
+    # vmap(autograd.grad) invocation. It's not exactly a "gradcheck" in the
+    # sense that we're not comparing an analytical jacobian with a numeric one,
+    # but it is morally similar (we could have computed a full analytic jac
+    # via vmap, but that is potentially slow)
+    diff_input_list = list(_iter_tensors(input, True))
+    grad = functools.partial(
+        torch.autograd.grad,
+        output,
+        diff_input_list,
+        retain_graph=True,
+        allow_unused=True,
+    )
+
+    def vjp(v):
+        results = grad(v)
+        results = tuple(
+            grad
+            if grad is not None
+            else torch.zeros([], dtype=inp.dtype, device=inp.device).expand(inp.shape)
+            for grad, inp in zip(results, diff_input_list)
+        )
+        return results
+
+    grad_outputs = [torch.randn_like(output) for _ in range(2)]
+
+    expected = [vjp(gO) for gO in grad_outputs]
+    expected = [torch.stack(shards) for shards in zip(*expected)]
+
+    # Squash warnings since these are expected to happen in most cases
+    # NB: this doesn't work for CUDA tests: https://github.com/pytorch/pytorch/issues/50209
+    with warnings.catch_warnings():
+        warnings.filterwarnings("ignore", message="There is a performance drop")
+        warnings.filterwarnings("ignore", message="Please use torch.vmap")
+        try:
+            result = vmap(vjp)(torch.stack(grad_outputs))
+        except RuntimeError as ex:
+            # It's OK that we're not raising the error at the correct callsite.
+            # That's because the callsite is always going to inside the Python
+            # autograd.grad instead of the C++ traceback of what line in the
+            # backward formula
+            raise GradcheckError(
+                f"While computing batched gradients, got: {ex}\n\n{FAILED_BATCHED_GRAD_MSG}"
+            ) from ex
+
+    for input_idx, (res, exp) in enumerate(zip(result, expected)):
+        if torch.allclose(res, exp):
+            continue
+        raise GradcheckError(
+            _get_failed_batched_grad_test_msg(output_idx, input_idx, res, exp)
+        )
+    return True
+
+
+def _test_backward_mul_by_grad_output(outputs, inputs, masked) -> bool:
+    # Tests that backward is multiplied by grad_output
+    diff_input_list: List[torch.Tensor] = list(_iter_tensors(inputs, True))
+    if not diff_input_list:
+        raise GradcheckError("no Tensors requiring grad found in input")
+    grads_input = torch.autograd.grad(
+        outputs,
+        diff_input_list,
+        [
+            torch.zeros_like(o, memory_format=torch.legacy_contiguous_format)
+            for o in outputs
+        ],
+        allow_unused=True,
+    )
+    for gi, di in zip(grads_input, diff_input_list):
+        if gi is None:
+            continue
+        if isinstance(gi, torch.Tensor) and gi.layout != torch.strided:
+            if gi.layout != di.layout:
+                raise GradcheckError(
+                    "grad is incorrect layout ("
+                    + str(gi.layout)
+                    + " is not "
+                    + str(di.layout)
+                    + ")"
+                )
+            if _is_sparse_any_tensor(gi):
+                sparse_kind = str(gi.layout).replace("torch.", "").replace("_coo", "")
+                if gi.sparse_dim() != di.sparse_dim():
+                    raise GradcheckError(
+                        f"grad is {sparse_kind} tensor, but has incorrect sparse_dim"
+                        f" {gi.sparse_dim()}, expected {di.sparse_dim()}"
+                    )
+                if gi.dense_dim() != di.dense_dim():
+                    raise GradcheckError(
+                        f"grad is {sparse_kind} tensor, but has incorrect dense_dim"
+                        f" {gi.dense_dim()}, expected {di.dense_dim()}"
+                    )
+            gi = gi.to_dense()
+            di = di.to_dense()
+        if masked:
+            if not torch.allclose(gi, torch.zeros_like(gi)):
+                raise GradcheckError("backward not multiplied by grad_output")
+        elif not gi.eq(0).all():
+            raise GradcheckError("backward not multiplied by grad_output")
+        if gi.dtype != di.dtype:
+            raise GradcheckError("grad is incorrect type")
+        if gi.device != di.device:
+            raise GradcheckError("grad is incorrect device")
+        if gi.size() != di.size():
+            raise GradcheckError("grad is incorrect size")
+    return True
+
+
+def _test_undefined_forward_mode(func, outputs, inputs):
+    fwAD = torch.autograd.forward_ad
+
+    inp_tensors_idx, inp_tensors = _get_inp_tensors(inputs)
+    all_v, all_u, all_u_dense = _make_vectors(inp_tensors, outputs, use_forward_ad=True)
+
+    tensor_inputs = tuple(i for i in inputs if is_tensor_like(i) and i.requires_grad)
+
+    with fwAD.dual_level():
+        fw_grads = []
+        dual_inputs = []
+        tensor_indices = set()
+        for i, inp in enumerate(inputs):
+            if is_tensor_like(inp) and inp.requires_grad:
+                if inp.layout == torch._mkldnn:  # type: ignore[attr-defined]
+                    raise ValueError(
+                        "MKLDNN inputs are not support for forward AD gradcheck."
+                    )
+
+                inp = fwAD.make_dual(inp.detach(), torch.zeros_like(inp))
+                # If inp is a differentiable view, the dual might not be the tangent given to
+                # make_dual, so read it explicitly from the dual tensor
+                fw_grads.append(fwAD.unpack_dual(inp)[1])
+                tensor_indices.add(i)
+            dual_inputs.append(inp)
+
+        for i, (fw_grad, u) in enumerate(zip(fw_grads, all_u)):
+            fw_grad.copy_(u.view_as(fw_grad))
+
+        for idx, inp in enumerate(inputs):
+            if idx not in tensor_indices:
+                continue
+            dual_inp_obj = dual_inputs[idx]
+
+            # case 1 (Materialized Zero Tensor Tangent)
+            dual_inputs[idx] = fwAD.make_dual(inp.detach(), torch.zeros_like(inp))
+            raw_outputs = _as_tuple(func(*dual_inputs))
+            dual_outputs1 = filter(_is_float_or_complex_tensor, raw_outputs)
+
+            # case 2 (Efficient Zero Tensor Tangent since we don't make a dual object and pass a regular tensor)
+            dual_inputs[idx] = inp.detach()
+            raw_outputs = _as_tuple(func(*dual_inputs))
+            dual_outputs2 = filter(_is_float_or_complex_tensor, raw_outputs)
+
+            # reset
+            dual_inputs[idx] = dual_inp_obj
+
+            for index_o, (d_o1, d_o2) in enumerate(zip(dual_outputs1, dual_outputs2)):
+                val1, res1 = fwAD.unpack_dual(d_o1)
+                val2, res2 = fwAD.unpack_dual(d_o2)
+
+                if not (res1 is None or res2 is None):
+                    if not torch.allclose(res1, res2):
+                        raise GradcheckError(
+                            "Mismatch in tangent values for output with index: ",
+                            index_o,
+                            " when input: ",
+                            inp,
+                            " has an undefined tangent value. ",
+                            " Got: ",
+                            res1,
+                            " but expected: ",
+                            res2,
+                        )
+    return True
+
+
+def _test_undefined_backward_mode(func, outputs, inputs) -> bool:
+    diff_input_list: List[torch.Tensor] = list(_iter_tensors(inputs, True))
+    if not diff_input_list:
+        raise GradcheckError("no Tensors requiring grad found in input")
+
+    def warn_bc_breaking():
+        warnings.warn(
+            "Backwards compatibility: New undefined gradient support checking "
+            "feature is enabled by default, but it may break existing callers "
+            "of this function. If this is true for you, you can call this "
+            'function with "check_undefined_grad=False" to disable the feature'
+        )
+
+    def check_undefined_grad_support(output_to_check):
+        grads_output = [
+            torch.zeros_like(o, memory_format=torch.legacy_contiguous_format)
+            for o in output_to_check
+        ]
+        try:
+            grads_input = torch.autograd.grad(
+                output_to_check, diff_input_list, grads_output, allow_unused=True
+            )
+        except RuntimeError as e:
+            warn_bc_breaking()
+            raise GradcheckError(
+                "Expected backward function to handle undefined output grads. "
+                'Please look at "Notes about undefined output gradients" in '
+                '"tools/autograd/derivatives.yaml"'
+            ) from e
+
+        for gi, i in zip(grads_input, diff_input_list):
+            if (gi is not None) and (not gi.eq(0).all()):
+                warn_bc_breaking()
+                raise GradcheckError(
+                    "Expected all input grads to be undefined or zero when all output grads are undefined "
+                    'or zero. Please look at "Notes about undefined output gradients" in '
+                    '"tools/autograd/derivatives.yaml"'
+                )
+        return True
+
+    # All backward functions must work properly if all output grads are undefined
+    outputs_to_check = [
+        [
+            torch._C._functions.UndefinedGrad()(o)
+            for o in _differentiable_outputs(func(*inputs))
+            # This check filters out Tensor-likes that aren't instances of Tensor.
+            if isinstance(o, torch.Tensor)
+        ]
+    ]
+
+    # If there are multiple output grads, we should be able to undef one at a time without error
+    if len(outputs_to_check[0]) > 1:
+        for undef_grad_idx in range(len(outputs)):
+            output_to_check = _differentiable_outputs(func(*inputs))
+            outputs_to_check.append(
+                [
+                    torch._C._functions.UndefinedGrad()(o)
+                    if idx == undef_grad_idx
+                    else o
+                    for idx, o in enumerate(output_to_check)
+                ]
+            )
+
+    return all(check_undefined_grad_support(output) for output in outputs_to_check)
+
+
+def _as_tuple(x):
+    if isinstance(x, tuple):
+        return x
+    elif isinstance(x, list):
+        return tuple(x)
+    else:
+        return (x,)
+
+
+def _differentiable_outputs(x):
+    return tuple(o for o in _as_tuple(x) if o.requires_grad)
+
+
+def _get_notallclose_msg(
+    analytical,
+    numerical,
+    output_idx,
+    input_idx,
+    complex_indices,
+    test_imag=False,
+    is_forward_ad=False,
+) -> str:
+    out_is_complex = (
+        (not is_forward_ad) and complex_indices and output_idx in complex_indices
+    )
+    inp_is_complex = is_forward_ad and complex_indices and input_idx in complex_indices
+    part = "imaginary" if test_imag else "real"
+    element = "inputs" if is_forward_ad else "outputs"
+    prefix = (
+        ""
+        if not (out_is_complex or inp_is_complex)
+        else f"While considering the {part} part of complex {element} only, "
+    )
+    mode = "computed with forward mode " if is_forward_ad else ""
+    return (
+        prefix + "Jacobian %smismatch for output %d with respect to input %d,\n"
+        "numerical:%s\nanalytical:%s\n"
+        % (mode, output_idx, input_idx, numerical, analytical)
+    )
+
+
+def _transpose(matrix_of_tensors):
+    # returns list of tuples
+    return list(zip(*matrix_of_tensors))
+
+
+def _real_and_imag_output(fn):
+    # returns new functions real(fn), and imag(fn) where real(fn) and imag(fn) behave the same as
+    # the original fn, except torch.real or torch.imag are applied to the complex outputs
+    def apply_to_c_outs(fn, fn_to_apply):
+        def wrapped_fn(*inputs):
+            outs = _as_tuple(fn(*inputs))
+            return tuple(fn_to_apply(o) if o.is_complex() else o for o in outs)
+
+        return wrapped_fn
+
+    return apply_to_c_outs(fn, torch.real), apply_to_c_outs(fn, torch.imag)
+
+
+def _real_and_imag_input(fn, complex_inp_indices, tupled_inputs):
+    # returns new functions that take real inputs instead of complex inputs as
+    # (x, y) -> fn(x + y * 1j). And it computes: inp -> fn(inp + y * 1j) and inp -> fn(x + inp * 1j).
+    # In each case, the other part is considered constant.
+    # We do not use 0 for the constant here to make sure we always call the user function with a valid input.
+    def apply_to_c_inps(fn, fn_to_apply):
+        def wrapped_fn(*inputs):
+            new_inputs = list(inputs)
+            for should_be_complex in complex_inp_indices:
+                new_inputs[should_be_complex] = fn_to_apply(
+                    new_inputs[should_be_complex], tupled_inputs[should_be_complex]
+                )
+            return _as_tuple(fn(*new_inputs))
+
+        return wrapped_fn
+
+    real_fn = apply_to_c_inps(fn, lambda inp, orig: inp + orig.imag * 1j)
+    imag_fn = apply_to_c_inps(fn, lambda inp, orig: orig.real + inp * 1j)
+    return real_fn, imag_fn
+
+
+def _gradcheck_real_imag(
+    gradcheck_fn,
+    func,
+    func_out,
+    tupled_inputs,
+    outputs,
+    eps,
+    rtol,
+    atol,
+    check_grad_dtypes,
+    check_forward_ad,
+    check_backward_ad,
+    nondet_tol,
+    check_undefined_grad,
+):
+    complex_out_indices = [i for i, o in enumerate(outputs) if o.is_complex()]
+    has_any_complex_output = any(o.is_complex() for o in _as_tuple(func_out))
+    if check_backward_ad:
+        if has_any_complex_output:
+            real_fn, imag_fn = _real_and_imag_output(func)
+
+            imag_func_out = imag_fn(*tupled_inputs)
+            imag_outputs = _differentiable_outputs(imag_func_out)
+            gradcheck_fn(
+                imag_fn,
+                imag_func_out,
+                tupled_inputs,
+                imag_outputs,
+                eps,
+                rtol,
+                atol,
+                check_grad_dtypes,
+                nondet_tol,
+                complex_indices=complex_out_indices,
+                test_imag=True,
+            )
+
+            real_func_out = real_fn(*tupled_inputs)
+            real_outputs = _differentiable_outputs(real_func_out)
+            gradcheck_fn(
+                real_fn,
+                real_func_out,
+                tupled_inputs,
+                real_outputs,
+                eps,
+                rtol,
+                atol,
+                check_grad_dtypes,
+                nondet_tol,
+                complex_indices=complex_out_indices,
+            )
+        else:
+            gradcheck_fn(
+                func,
+                func_out,
+                tupled_inputs,
+                outputs,
+                eps,
+                rtol,
+                atol,
+                check_grad_dtypes,
+                nondet_tol,
+            )
+
+    if check_forward_ad:
+        complex_inp_indices = [
+            i
+            for i, inp in enumerate(tupled_inputs)
+            if is_tensor_like(inp) and inp.is_complex()
+        ]
+        if complex_inp_indices:
+            real_fn, imag_fn = _real_and_imag_input(
+                func, complex_inp_indices, tupled_inputs
+            )
+
+            imag_inputs = [
+                inp.imag if is_tensor_like(inp) and inp.is_complex() else inp
+                for inp in tupled_inputs
+            ]
+            imag_func_out = imag_fn(*imag_inputs)
+            diff_imag_func_out = _differentiable_outputs(imag_func_out)
+            gradcheck_fn(
+                imag_fn,
+                imag_func_out,
+                imag_inputs,
+                diff_imag_func_out,
+                eps,
+                rtol,
+                atol,
+                check_grad_dtypes,
+                nondet_tol,
+                complex_indices=complex_inp_indices,
+                test_imag=True,
+                use_forward_ad=True,
+            )
+
+            real_inputs = [
+                inp.real if is_tensor_like(inp) and inp.is_complex() else inp
+                for inp in tupled_inputs
+            ]
+            real_func_out = real_fn(*real_inputs)
+            diff_real_func_out = _differentiable_outputs(real_func_out)
+            gradcheck_fn(
+                real_fn,
+                real_func_out,
+                real_inputs,
+                diff_real_func_out,
+                eps,
+                rtol,
+                atol,
+                check_grad_dtypes,
+                nondet_tol,
+                complex_indices=complex_inp_indices,
+                use_forward_ad=True,
+            )
+            if check_undefined_grad:
+                _test_undefined_forward_mode(imag_fn, imag_func_out, imag_inputs)
+                _test_undefined_forward_mode(real_fn, real_func_out, real_inputs)
+        else:
+            gradcheck_fn(
+                func,
+                func_out,
+                tupled_inputs,
+                outputs,
+                eps,
+                rtol,
+                atol,
+                check_grad_dtypes,
+                nondet_tol,
+                use_forward_ad=True,
+            )
+            if check_undefined_grad:
+                _test_undefined_forward_mode(func, outputs, tupled_inputs)
+
+
+def _slow_gradcheck(
+    func,
+    func_out,
+    tupled_inputs,
+    outputs,
+    eps,
+    rtol,
+    atol,
+    check_grad_dtypes,
+    nondet_tol,
+    *,
+    use_forward_ad=False,
+    complex_indices=None,
+    test_imag=False,
+    masked=False,
+):
+    func_out = _as_tuple(func_out)
+    if not outputs:
+        return _check_no_differentiable_outputs(
+            func, tupled_inputs, func_out, eps=eps, is_forward_ad=use_forward_ad
+        )
+    tupled_inputs_numerical = tupled_inputs if masked else _densify(tupled_inputs)
+
+    numerical = _transpose(
+        _get_numerical_jacobian(
+            func,
+            tupled_inputs_numerical,
+            func_out,
+            eps=eps,
+            is_forward_ad=use_forward_ad,
+        )
+    )
+    # Note: [numerical vs analytical output length]
+    # The numerical path returns jacobian quantity for all outputs, even if requires_grad of that
+    # output is False. This behavior is necessary for _check_no_differentiable_outputs to work.
+    numerical = [nj for o, nj in zip(func_out, numerical) if o.requires_grad]
+    if use_forward_ad:
+        analytical_forward = _get_analytical_jacobian_forward_ad(
+            func, tupled_inputs, func_out, check_grad_dtypes=check_grad_dtypes
+        )
+
+        for i, n_per_out in enumerate(numerical):
+            for j, n in enumerate(n_per_out):
+                a = analytical_forward[j][i]
+                if not _allclose_with_type_promotion(a, n.to(a.device), rtol, atol):
+                    raise GradcheckError(
+                        _get_notallclose_msg(
+                            a, n, i, j, complex_indices, test_imag, is_forward_ad=True
+                        )
+                    )
+    else:
+        for i, o in enumerate(outputs):
+            analytical = _check_analytical_jacobian_attributes(
+                tupled_inputs, o, nondet_tol, check_grad_dtypes
+            )
+
+            for j, (a, n) in enumerate(zip(analytical, numerical[i])):
+                if not _allclose_with_type_promotion(a, n.to(a.device), rtol, atol):
+                    raise GradcheckError(
+                        _get_notallclose_msg(a, n, i, j, complex_indices, test_imag)
+                    )
+
+    return True
+
+
+def _dot_with_type_promotion(u, v):
+    assert u.dim() == 1 and v.dim() == 1
+    return (u * v).sum()
+
+
+def _allclose_with_type_promotion(a, b, rtol, atol):
+    promoted_type = torch.promote_types(a.dtype, b.dtype)
+    a = a.to(dtype=promoted_type)
+    b = b.to(dtype=promoted_type)
+    return torch.allclose(a, b, rtol, atol)
+
+
+def _to_real_dtype(dtype):
+    if dtype == torch.complex128:
+        return torch.float64
+    elif dtype == torch.complex64:
+        return torch.float32
+    else:
+        return dtype
+
+
+def _vec_from_tensor(x, generator, downcast_complex=False):
+    # Create a random vector with the same number of elements as x and the same
+    # dtype/device. If x is complex and downcast_complex is False, we create a
+    # complex tensor with only real component.
+    if x.layout == torch.sparse_coo:
+        # For sparse, create a random sparse vec with random values in the same
+        # indices. Make sure size is set so that it isn't inferred to be smaller.
+        x_values = x._values()
+        dtype = _to_real_dtype(x.dtype) if downcast_complex else x.dtype
+        values = (
+            torch.rand(x_values.numel(), generator=generator)
+            .to(dtype=dtype, device=x.device)
+            .view(x_values.shape)
+        )
+        values /= values.norm()
+        vec = torch.sparse_coo_tensor(x._indices(), values, x.size(), device=x.device)
+    elif _is_sparse_compressed_tensor(x):
+        if x.layout in {torch.sparse_csr, torch.sparse_bsr}:
+            compressed_indices, plain_indices = x.crow_indices(), x.col_indices()
+        else:
+            compressed_indices, plain_indices = x.ccol_indices(), x.row_indices()
+        x_values = x.values()
+        dtype = _to_real_dtype(x.dtype) if downcast_complex else x.dtype
+        values = (
+            torch.rand(x_values.numel(), generator=generator)
+            .to(dtype=dtype, device=x.device)
+            .view(x_values.shape)
+        )
+        values /= values.norm()
+        vec = torch.sparse_compressed_tensor(
+            compressed_indices,
+            plain_indices,
+            values,
+            x.size(),
+            layout=x.layout,
+            device=x.device,
+        )
+    else:
+        dtype = _to_real_dtype(x.dtype) if downcast_complex else x.dtype
+        vec = torch.rand(x.numel(), generator=generator).to(
+            dtype=dtype, device=x.device
+        )
+        vec /= vec.norm()
+    return vec
+
+
+def _get_inp_tensors(tupled_inputs):
+    inp_idx_tup = [
+        (i, t)
+        for i, t in enumerate(tupled_inputs)
+        if is_tensor_like(t) and t.requires_grad
+    ]
+    return [tup[0] for tup in inp_idx_tup], [tup[1] for tup in inp_idx_tup]
+
+
+def _adjusted_atol(atol, u, v):
+    # In slow gradcheck, we compare A and B element-wise, i.e., for some a, b we
+    # allow: |a - b| < atol + rtol * b. But since we now compare q1 = v^T A u and
+    # q2 = v^T B u, we must allow |q1 - q2| < v^T E u + rtol * v^T B u, where E is
+    # the correctly sized matrix in which each entry is atol.
+    #
+    # We see that atol needs to be scaled by v^T M u (where M is an all-ones M x N
+    # matrix): v^T M u = \sum_{i} \sum_{j} u_i * v_j = (\sum_{i} u_i)(\sum_{i} v_i)
+    # TODO: properly handle case when u is tuple instead of only taking first element
+    u = u[0] if isinstance(u, tuple) else u
+    sum_u = u.sum()
+    sum_v = 1.0 if v is None else v.sum()
+    return atol * float(sum_u) * float(sum_v)
+
+
+FAST_FAIL_SLOW_OK_MSG = """
+Fast gradcheck failed but element-wise differences are small. This means that the
+test might've passed in slow_mode!
+
+If you are adding a new operator, please file an issue and then use one of the
+workarounds. The workaround depends on how your test invokes gradcheck/gradgradcheck:
+
+If the test
+- manually invokes gradcheck/gradgradcheck, then call gradcheck/gradgradcheck
+  with `fast_mode=False` as a keyword argument.
+- is OpInfo-based (e.g., in test_ops_gradients.py), then modify the OpInfo for the test
+  to have `gradcheck_fast_mode=False`
+- is a Module test (e.g., in common_nn.py), then modify the corresponding
+  module_test entry to have `gradcheck_fast_mode=False`
+""".strip()
+
+
+def _run_slow_mode_and_get_error(
+    func, tupled_inputs, outputs, input_idx, output_idx, rtol, atol, eps, is_forward_ad
+):
+    # Compute jacobians in slow mode for better error message
+    slow_numerical = _get_numerical_jacobian(
+        func, tupled_inputs, outputs, eps=eps, is_forward_ad=is_forward_ad
+    )[input_idx][output_idx]
+    if is_forward_ad:
+
+        def new_fn(inp):
+            new_inputs = list(tupled_inputs)
+            new_inputs[input_idx] = inp
+            return _as_tuple(func(*new_inputs))[output_idx]
+
+        slow_analytical = _get_analytical_jacobian_forward_ad(
+            new_fn, (tupled_inputs[input_idx],), (outputs[output_idx],)
+        )[0][0]
+    else:
+        slow_analytical = _get_analytical_jacobian(
+            tupled_inputs, outputs, input_idx, output_idx
+        )
+
+    # Assume jacobians are non-empty and have the same shape
+    slow_max_diff = (slow_numerical - slow_analytical).abs().max()
+
+    slow_allclose = torch.allclose(slow_analytical, slow_numerical, rtol, atol)
+    msg = (
+        "\nThe above quantities relating the numerical and analytical jacobians are computed \n"
+        "in fast mode. See: https://github.com/pytorch/pytorch/issues/53876 for more background \n"
+        "about fast mode. Below, we recompute numerical and analytical jacobians in slow mode:\n\n"
+        f"Numerical:\n {slow_numerical}\n"
+        f"Analytical:\n{slow_analytical}\n\n"
+        f"The max per-element difference (slow mode) is: {slow_max_diff}.\n"
+    )
+    if slow_allclose:
+        # Slow gradcheck would've passed!
+        msg += FAST_FAIL_SLOW_OK_MSG
+    return msg
+
+
+def _to_flat_dense_if_sparse(tensor):
+    if _is_sparse_any_tensor(tensor):
+        return tensor.to_dense().reshape(-1)
+    else:
+        return tensor
+
+
+def _make_vectors(inp_tensors, outputs, *, use_forward_ad):
+    # Use our own generator to avoid messing with the user's RNG state
+    g_cpu = torch.Generator()
+
+    def _vec_from_tensor_cpu(*args):
+        # Default allocate all tensors on CPU, so they are on the same device as the generator
+        # even if the user specified a default device
+        with torch.device("cpu"):
+            return _vec_from_tensor(*args)
+
+    all_u = []
+    all_u_dense = []
+    for inp in inp_tensors:
+        ur = _vec_from_tensor_cpu(inp, g_cpu, True)
+        ur_dense = _to_flat_dense_if_sparse(ur)
+        if inp.is_complex():
+            ui = _vec_from_tensor_cpu(inp, g_cpu, True)
+            all_u.append((ur, ui))
+            ui_dense = _to_flat_dense_if_sparse(ui)
+            all_u_dense.append((ur_dense, ui_dense))
+        else:
+            all_u.append(ur)
+            all_u_dense.append(ur_dense)
+    all_v = (
+        None
+        if use_forward_ad
+        else [_vec_from_tensor_cpu(out, g_cpu) for out in outputs]
+    )
+    return all_v, all_u, all_u_dense
+
+
+def _check_analytical_numerical_equal(
+    all_analytical,
+    all_numerical,
+    complex_indices,
+    tupled_inputs,
+    outputs,
+    func,
+    all_v,
+    all_u,
+    rtol,
+    atol,
+    eps,
+    test_imag,
+    *,
+    is_forward_ad=False,
+):
+    for i, all_numerical_for_input_i in enumerate(all_numerical):
+        for j, n in enumerate(all_numerical_for_input_i):
+            # Forward AD generates the transpose of what this function expects
+            if is_forward_ad:
+                a = all_analytical[i][j]
+            else:
+                a = all_analytical[j][i]
+            n = n.to(device=a.device)
+            updated_atol = _adjusted_atol(atol, all_u[i], all_v[j] if all_v else None)
+            if not _allclose_with_type_promotion(a, n.to(a.device), rtol, updated_atol):
+                jacobians_str = _run_slow_mode_and_get_error(
+                    func, tupled_inputs, outputs, i, j, rtol, atol, eps, is_forward_ad
+                )
+                raise GradcheckError(
+                    _get_notallclose_msg(
+                        a, n, j, i, complex_indices, test_imag, is_forward_ad
+                    )
+                    + jacobians_str
+                )
+
+
+def _fast_gradcheck(
+    func,
+    func_out,
+    inputs,
+    outputs,
+    eps,
+    rtol,
+    atol,
+    check_grad_dtypes,
+    nondet_tol,
+    *,
+    use_forward_ad=False,
+    complex_indices=None,
+    test_imag=False,
+    masked=False,
+):
+    # See https://github.com/pytorch/pytorch/issues/53876 for details
+    inp_tensors_idx, inp_tensors = _get_inp_tensors(inputs)
+    # Backward mode computes v^T * J (VJP)
+    # Since we computed J * u (JVP) through finite difference method, we perform an equality check
+    # between VJP * u, v * JVP
+    # ----
+    # Forward mode computes J * u (JVP)
+    # Since we already compute JVP through finite difference method,
+    # we don't need v for correctness check here as asserted below
+    all_v, all_u, all_u_dense = _make_vectors(
+        inp_tensors, outputs, use_forward_ad=use_forward_ad
+    )
+
+    inputs_numerical, all_u_numerical, all_v_numerical = (
+        (inputs, all_u, all_v) if masked else _densify((inputs, all_u, all_v))
+    )
+
+    numerical_vJu = _get_numerical_vJu(
+        func,
+        inputs_numerical,
+        inp_tensors_idx,
+        func_out,
+        all_u_numerical,
+        all_v_numerical,
+        eps,
+        is_forward_ad=use_forward_ad,
+    )
+    # TODO: replicate https://github.com/pytorch/pytorch/pull/77743 for fast gradcheck as well
+    if use_forward_ad:
+        assert all_v is None
+        analytical_vJu = _get_analytical_jacobian_forward_ad(
+            func,
+            inputs,
+            _as_tuple(func_out),
+            all_u=all_u,
+            check_grad_dtypes=check_grad_dtypes,
+        )
+    else:
+        if not outputs:
+            _check_no_differentiable_outputs_fast(
+                func, func_out, inputs, inp_tensors_idx, all_u, eps, nondet_tol
+            )
+
+        analytical_vJu = _get_analytical_vJu_backward_mode(
+            inputs, outputs, nondet_tol, check_grad_dtypes, all_v, all_u_dense
+        )
+
+    _check_analytical_numerical_equal(
+        analytical_vJu,
+        numerical_vJu,
+        complex_indices,
+        inputs,
+        outputs,
+        func,
+        all_v,
+        all_u,
+        rtol,
+        atol,
+        eps,
+        test_imag,
+        is_forward_ad=use_forward_ad,
+    )
+
+    return True
+
+
+# Note [VarArg of Tensors]
+# ~~~~~~~~~~~~~~~~~~~~~~~~
+# 'func' accepts a vararg of tensors, which isn't expressable in the type system at the moment.
+# If https://mypy.readthedocs.io/en/latest/additional_features.html?highlight=callable#extended-callable-types is accepted,
+# the '...' first argument of Callable can be replaced with VarArg(Tensor).
+# For now, we permit any input.
+def gradcheck(
+    func: Callable[..., Union[_TensorOrTensors]],  # See Note [VarArg of Tensors]
+    inputs: _TensorOrTensors,
+    *,
+    eps: float = 1e-6,
+    atol: float = 1e-5,
+    rtol: float = 1e-3,
+    raise_exception: bool = True,
+    nondet_tol: float = 0.0,
+    check_undefined_grad: bool = True,
+    check_grad_dtypes: bool = False,
+    check_batched_grad: bool = False,
+    check_batched_forward_grad: bool = False,
+    check_forward_ad: bool = False,
+    check_backward_ad: bool = True,
+    fast_mode: bool = False,
+    masked: Optional[bool] = None,
+) -> bool:  # noqa: D400,D205
+    r"""Check gradients computed via small finite differences against analytical
+    gradients wrt tensors in :attr:`inputs` that are of floating point or complex type
+    and with ``requires_grad=True``.
+
+    The check between numerical and analytical gradients uses :func:`~torch.allclose`.
+
+    For most of the complex functions we consider for optimization purposes, no notion of
+    Jacobian exists. Instead, gradcheck verifies if the numerical and analytical values of
+    the Wirtinger and Conjugate Wirtinger derivatives are consistent. Because the gradient
+    computation is done under the assumption that the overall function has a real-valued
+    output, we treat functions with complex output in a special way. For these functions,
+    gradcheck is applied to two real-valued functions corresponding to taking the real
+    components of the complex outputs for the first, and taking the imaginary components
+    of the complex outputs for the second. For more details, check out
+    :ref:`complex_autograd-doc`.
+
+    .. note::
+        The default values are designed for :attr:`input` of double precision.
+        This check will likely fail if :attr:`input` is of less precision, e.g.,
+        ``FloatTensor``.
+
+    .. note::
+        Gradcheck may fail when evaluated on non-differentiable points
+        because the numerically computed gradients via finite differencing may differ
+        those computed analytically (not necessarily because either is incorrect).
+        For more context, see :ref:`non-differentiable-func-grad`.
+
+    .. warning::
+       If any checked tensor in :attr:`input` has overlapping memory, i.e.,
+       different indices pointing to the same memory address (e.g., from
+       :func:`torch.expand`), this check will likely fail because the numerical
+       gradients computed by point perturbation at such indices will change
+       values at all other indices that share the same memory address.
+
+    Args:
+        func (function): a Python function that takes Tensor inputs and returns
+            a Tensor or a tuple of Tensors
+        inputs (tuple of Tensor or Tensor): inputs to the function
+        eps (float, optional): perturbation for finite differences
+        atol (float, optional): absolute tolerance
+        rtol (float, optional): relative tolerance
+        raise_exception (bool, optional): indicating whether to raise an exception if
+            the check fails. The exception gives more information about the
+            exact nature of the failure. This is helpful when debugging gradchecks.
+        nondet_tol (float, optional): tolerance for non-determinism. When running
+            identical inputs through the differentiation, the results must either match
+            exactly (default, 0.0) or be within this tolerance.
+        check_undefined_grad (bool, optional): if ``True``, check if undefined output grads
+            are supported and treated as zeros, for ``Tensor`` outputs.
+        check_batched_grad (bool, optional): if ``True``, check if we can compute
+            batched gradients using prototype vmap support. Defaults to False.
+        check_batched_forward_grad (bool, optional): if ``True``, checks if we can compute
+            batched forward gradients using forward ad and prototype vmap support. Defaults to ``False``.
+        check_forward_ad (bool, optional): if ``True``, check that the gradients computed with forward
+            mode AD match the numerical ones. Defaults to ``False``.
+        check_backward_ad (bool, optional): if ``False``, do not perform any checks that rely on
+            backward mode AD to be implemented. Defaults to ``True``.
+        fast_mode (bool, optional): Fast mode for gradcheck and gradgradcheck is currently only
+            implemented for R to R functions. If none of the inputs and outputs are complex
+            a faster implementation of gradcheck that no longer computes the entire jacobian
+            is run; otherwise, we fall back to the slow implementation.
+        masked (bool, optional): if ``True``, the gradients of unspecified elements of
+            sparse tensors are ignored. Defaults to ``False``.
+    Returns:
+        ``True`` if all differences satisfy allclose condition
+
+    """
+    assert (
+        check_forward_ad or check_backward_ad
+    ), "Expected at least one of check_forward_ad or check_backward_ad to be True"
+    assert not (
+        check_batched_grad and not check_backward_ad
+    ), "Setting check_batched_grad=True requires check_backward_ad to be True"
+    assert not (
+        check_batched_forward_grad and not check_forward_ad
+    ), "Setting check_batched_forward_grad=True requires check_forward_ad to be True"
+    args = locals().copy()
+    args.pop("raise_exception")
+    if not raise_exception:
+        try:
+            return _gradcheck_helper(**args)
+        except GradcheckError as e:
+            return False
+    else:
+        return _gradcheck_helper(**args)
+
+
+def _gradcheck_helper(
+    func,
+    inputs,
+    eps,
+    atol,
+    rtol,
+    nondet_tol,
+    check_undefined_grad,
+    check_grad_dtypes,
+    check_batched_grad,
+    check_batched_forward_grad,
+    check_forward_ad,
+    check_backward_ad,
+    fast_mode,
+    masked,
+):
+    tupled_inputs = _as_tuple(inputs)
+    _check_inputs(tupled_inputs)
+
+    func_out = func(*tupled_inputs)
+    outputs = _differentiable_outputs(func_out)
+    _check_outputs(outputs)
+
+    gradcheck_fn = functools.partial(
+        _fast_gradcheck if fast_mode else _slow_gradcheck, masked=masked
+    )
+    _gradcheck_real_imag(
+        gradcheck_fn,
+        func,
+        func_out,
+        tupled_inputs,
+        outputs,
+        eps,
+        rtol,
+        atol,
+        check_grad_dtypes,
+        check_forward_ad=check_forward_ad,
+        check_backward_ad=check_backward_ad,
+        nondet_tol=nondet_tol,
+        check_undefined_grad=check_undefined_grad,
+    )
+
+    if check_batched_forward_grad:
+        _test_batched_grad_forward_ad(func, tupled_inputs)
+
+    # Short circuit because remaining tests rely on backward AD to be implemented
+    if not check_backward_ad:
+        return True
+
+    for i, o in enumerate(outputs):
+        if check_batched_grad:
+            _test_batched_grad(tupled_inputs, o, i)
+
+    _test_backward_mul_by_grad_output(outputs, tupled_inputs, masked)
+
+    if check_undefined_grad and check_backward_ad:
+        _test_undefined_backward_mode(func, outputs, tupled_inputs)
+    return True
+
+
+def gradgradcheck(
+    func: Callable[..., _TensorOrTensors],  # See Note [VarArg of Tensors]
+    inputs: _TensorOrTensors,
+    grad_outputs: Optional[_TensorOrTensors] = None,
+    *,
+    eps: float = 1e-6,
+    atol: float = 1e-5,
+    rtol: float = 1e-3,
+    gen_non_contig_grad_outputs: bool = False,
+    raise_exception: bool = True,
+    nondet_tol: float = 0.0,
+    check_undefined_grad: bool = True,
+    check_grad_dtypes: bool = False,
+    check_batched_grad: bool = False,
+    check_fwd_over_rev: bool = False,
+    check_rev_over_rev: bool = True,
+    fast_mode: bool = False,
+    masked: bool = False,
+) -> bool:  # noqa: D400,D205
+    r"""Check gradients of gradients computed via small finite differences
+    against analytical gradients wrt tensors in :attr:`inputs` and
+    :attr:`grad_outputs` that are of floating point or complex type and with
+    ``requires_grad=True``.
+
+    This function checks that backpropagating through the gradients computed
+    to the given :attr:`grad_outputs` are correct.
+
+    The check between numerical and analytical gradients uses :func:`~torch.allclose`.
+
+    .. note::
+        The default values are designed for :attr:`input` and
+        :attr:`grad_outputs` of double precision. This check will likely fail if
+        they are of less precision, e.g., ``FloatTensor``.
+
+    .. warning::
+       If any checked tensor in :attr:`input` and :attr:`grad_outputs` has
+       overlapping memory, i.e., different indices pointing to the same memory
+       address (e.g., from :func:`torch.expand`), this check will likely fail
+       because the numerical gradients computed by point perturbation at such
+       indices will change values at all other indices that share the same
+       memory address.
+
+    Args:
+        func (function): a Python function that takes Tensor inputs and returns
+            a Tensor or a tuple of Tensors
+        inputs (tuple of Tensor or Tensor): inputs to the function
+        grad_outputs (tuple of Tensor or Tensor, optional): The gradients with
+            respect to the function's outputs.
+        eps (float, optional): perturbation for finite differences
+        atol (float, optional): absolute tolerance
+        rtol (float, optional): relative tolerance
+        gen_non_contig_grad_outputs (bool, optional): if :attr:`grad_outputs` is
+            ``None`` and :attr:`gen_non_contig_grad_outputs` is ``True``, the
+            randomly generated gradient outputs are made to be noncontiguous
+        raise_exception (bool, optional): indicating whether to raise an exception if
+            the check fails. The exception gives more information about the
+            exact nature of the failure. This is helpful when debugging gradchecks.
+        nondet_tol (float, optional): tolerance for non-determinism. When running
+            identical inputs through the differentiation, the results must either match
+            exactly (default, 0.0) or be within this tolerance. Note that a small amount
+            of nondeterminism in the gradient will lead to larger inaccuracies in
+            the second derivative.
+        check_undefined_grad (bool, optional): if True, check if undefined output grads
+            are supported and treated as zeros
+        check_batched_grad (bool, optional): if True, check if we can compute
+            batched gradients using prototype vmap support. Defaults to False.
+        fast_mode (bool, optional): if True, run a faster implementation of gradgradcheck that
+            no longer computes the entire jacobian.
+        masked (bool, optional): if True, the gradients of unspecified elements of
+            sparse tensors are ignored (default, False).
+    Returns:
+        True if all differences satisfy allclose condition
+    """
+    assert (
+        check_fwd_over_rev or check_rev_over_rev
+    ), "Expected at least one of check_fwd_over_rev or check_rev_over_rev to be True"
+    assert not (
+        check_undefined_grad and not check_rev_over_rev
+    ), "Setting check_undefined_grad=True requires check_rev_over_rev to be True"
+    assert not (
+        check_batched_grad and not check_rev_over_rev
+    ), "Setting check_batched_grad=True requires check_rev_over_rev to be True"
+    # TODO: do we want to test this too?
+    # assert not (check_batched_forward_grad and not check_fwd_over_rev), (
+    #     "Setting check_batched_forward_grad=True requires check_fwd_over_rev to be True")
+    tupled_inputs = _as_tuple(inputs)
+
+    if grad_outputs is None:
+        # If grad_outputs is not specified, create random Tensors of the same shape, type, and device as the outputs
+
+        outputs = _differentiable_outputs(func(*tupled_inputs))
+        tupled_grad_outputs = tuple(
+            torch.testing.make_tensor(
+                x.shape,
+                dtype=x.dtype
+                if x.is_floating_point() or x.is_complex()
+                else torch.double,
+                device=x.device,
+                low=-1,
+                high=1,
+                requires_grad=True,
+                noncontiguous=gen_non_contig_grad_outputs,
+            )
+            for x in outputs
+        )
+    else:
+        tupled_grad_outputs = _as_tuple(grad_outputs)
+
+    num_outputs = len(tupled_grad_outputs)
+
+    # NB: We need to save the requires_grad information about the inputs here because gradcheck detaches inputs
+    #     before running forward mode AD
+    diff_input_args_indices = {
+        i for i, x in enumerate(tupled_inputs) if is_tensor_like(x) and x.requires_grad
+    }
+    diff_grad_output_indices = {
+        i for i, x in enumerate(tupled_grad_outputs) if x.requires_grad
+    }
+
+    def new_func(*args):
+        # Restore the requires_grad information
+        input_args = tuple(
+            x.requires_grad_() if i in diff_input_args_indices else x
+            for i, x in enumerate(args[:-num_outputs])
+        )
+        outputs = _differentiable_outputs(func(*input_args))
+        grad_outputs = tuple(
+            x.requires_grad_() if i in diff_grad_output_indices else x
+            for i, x in enumerate(args[-num_outputs:])
+        )
+        diff_input_args = tuple(
+            x for i, x in enumerate(input_args) if i in diff_input_args_indices
+        )
+        grad_inputs = torch.autograd.grad(
+            outputs, diff_input_args, grad_outputs, create_graph=True, allow_unused=True
+        )
+        grad_inputs = tuple(g for g in grad_inputs if g is not None)
+        return grad_inputs
+
+    return gradcheck(
+        new_func,
+        tupled_inputs + tupled_grad_outputs,
+        eps=eps,
+        atol=atol,
+        rtol=rtol,
+        raise_exception=raise_exception,
+        nondet_tol=nondet_tol,
+        check_undefined_grad=check_undefined_grad,
+        check_grad_dtypes=check_grad_dtypes,
+        check_batched_grad=check_batched_grad,
+        fast_mode=fast_mode,
+        check_forward_ad=check_fwd_over_rev,
+        check_backward_ad=check_rev_over_rev,
+        masked=masked,
+    )

venv/lib/python3.10/site-packages/torch/autograd/graph.py

@@ -0,0 +1,749 @@
+import abc
+import collections
+import contextlib
+import functools
+import logging
+import threading
+import weakref
+from collections import defaultdict, namedtuple
+from typing import (
+    Any,
+    Callable,
+    cast,
+    Deque,
+    Dict,
+    List,
+    Optional,
+    Sequence,
+    Set,
+    Tuple,
+    Union,
+)
+
+import torch
+from torch.autograd.variable import Variable
+from torch.utils._python_dispatch import TorchDispatchMode
+from torch.utils.hooks import RemovableHandle
+
+log = logging.getLogger(__name__)
+
+
+__all__ = [
+    "saved_tensors_hooks",
+    "save_on_cpu",
+    "disable_saved_tensors_hooks",
+    "register_multi_grad_hook",
+    "allow_mutation_on_saved_tensors",
+    "Node",
+    "GradientEdge",
+    "get_gradient_edge",
+    "increment_version",
+]
+
+
+class Node(abc.ABC):
+    @abc.abstractmethod
+    def name(self) -> str:
+        r"""Return the name.
+
+        Example::
+
+            >>> import torch
+            >>> a = torch.tensor([0., 0., 0.], requires_grad=True)
+            >>> b = a.clone()
+            >>> assert isinstance(b.grad_fn, torch.autograd.graph.Node)
+            >>> print(b.grad_fn.name())
+            CloneBackward0
+        """
+        ...
+
+    @property
+    @abc.abstractmethod
+    def next_functions(self) -> Tuple[Tuple[Optional["Node"], int], ...]:
+        ...
+
+    @abc.abstractmethod
+    def metadata(self) -> dict:
+        r"""Return the metadata."""
+        ...
+
+    @abc.abstractmethod
+    def _register_hook_dict(self, tensor: torch.Tensor) -> None:
+        ...
+
+    @abc.abstractmethod
+    def register_hook(self, fn: Callable[..., Any]) -> RemovableHandle:
+        r"""Register a backward hook.
+
+        The hook will be called every time a gradient with respect to the
+        Node is computed. The hook should have the following signature::
+
+            hook(grad_inputs: Tuple[Tensor], grad_outputs: Tuple[Tensor]) -> Tuple[Tensor] or None
+
+
+        The hook should not modify its argument, but it can optionally return
+        a new gradient which will be used in place of :attr:`grad_inputs`.
+
+        This function returns a handle with a method ``handle.remove()``
+        that removes the hook from the module.
+
+        .. note::
+            See :ref:`backward-hooks-execution` for more information on how when this hook
+            is executed, and how its execution is ordered relative to other hooks.
+
+        Example::
+
+            >>> import torch
+            >>> a = torch.tensor([0., 0., 0.], requires_grad=True)
+            >>> b = a.clone()
+            >>> assert isinstance(b.grad_fn, torch.autograd.graph.Node)
+            >>> handle = b.grad_fn.register_hook(lambda gI, gO: (gO[0] * 2,))
+            >>> b.sum().backward(retain_graph=True)
+            >>> print(a.grad)
+            tensor([2., 2., 2.])
+            >>> handle.remove() # Removes the hook
+            >>> a.grad = None
+            >>> b.sum().backward(retain_graph=True)
+            >>> print(a.grad)
+            tensor([1., 1., 1.])
+        """
+        ...
+
+    @abc.abstractmethod
+    def register_prehook(self, fn: Callable[..., Any]) -> RemovableHandle:
+        r"""Register a backward pre-hook.
+
+        The hook will be called every time a gradient with respect to the
+        Node is computed. The hook should have the following signature::
+
+            hook(grad_outputs: Tuple[Tensor]) -> Tuple[Tensor] or None
+
+        The hook should not modify its argument, but it can optionally return
+        a new gradient which will be used in place of :attr:`grad_outputs`.
+
+        This function returns a handle with a method ``handle.remove()``
+        that removes the hook from the module.
+
+        .. note::
+            See :ref:`backward-hooks-execution` for more information on how when this hook
+            is executed, and how its execution is ordered relative to other hooks.
+
+        Example::
+
+            >>> a = torch.tensor([0., 0., 0.], requires_grad=True)
+            >>> b = a.clone()
+            >>> assert isinstance(b.grad_fn, torch.autograd.graph.Node)
+            >>> handle = b.grad_fn.register_prehook(lambda gI: (gI[0] * 2,))
+            >>> b.sum().backward(retain_graph=True)
+            >>> print(a.grad)
+            tensor([2., 2., 2.])
+            >>> handle.remove()
+            >>> a.grad = None
+            >>> b.sum().backward(retain_graph=True)
+            >>> print(a.grad)
+            tensor([1., 1., 1.])
+        """
+        ...
+
+    @classmethod
+    def __subclasshook__(cls, C):
+        if cls is Node:
+            if (
+                C is not None and C is getattr(torch._C._functions, C.__name__, None)
+            ) or issubclass(C, torch.autograd.function.BackwardCFunction):
+                return True
+        return NotImplemented
+
+
+def _get_grad_fn_or_grad_acc(t):
+    if t.requires_grad and t.grad_fn is None:
+        return t.view_as(t).grad_fn.next_functions[0][0]
+    else:
+        return t.grad_fn
+
+
+GradientEdge = namedtuple("GradientEdge", ("node output_nr"))
+GradientEdge.__doc__ = """\
+Object representing a given gradient edge within the autograd graph.
+To get the gradient edge where a given Tensor gradient will be computed,
+you can do ``edge = autograd.graph.get_gradient_edge(tensor)``.
+"""
+
+
+def get_gradient_edge(tensor):
+    """Get the gradient edge for computing the gradient of the given Tensor.
+
+    In particular, it is equivalent to call
+    ``g = autograd.grad(loss, input)`` and ``g = autograd.grad(loss, get_gradient_edge(input))``.
+    """
+    if not tensor.requires_grad:
+        raise RuntimeError(
+            "It is not possible to get the gradient edge for a Tensor that does not require gradients"
+        )
+    grad_fn = _get_grad_fn_or_grad_acc(tensor)
+
+    # Note that output_nr default to 0 which is the right value
+    # for the AccumulateGrad node.
+    return GradientEdge(grad_fn, tensor.output_nr)
+
+
+def increment_version(tensor):
+    """Update autograd metadata tracking whether the given Tensor was modified in place.
+
+    This is to enable more accurate error checking within the autograd engine.
+    It is already done automatically by PyTorch functions and within custom Function
+    when mark_dirty() is called appropriately so you only need to call this explicitly
+    if you are doing inplace operation on the Tensor data in a way that Pytorch doesn't
+    know about. For example a custom kernel that reads the Tensor data_ptr and modifies
+    the memory inplace based on this pointer.
+
+    Note that incrementing the version counter multiple times for a single inplace operation
+    is not problematic.
+    """
+    torch._C._increment_version(tensor)
+
+
+class saved_tensors_hooks:
+    """Context-manager that sets a pair of pack / unpack hooks for saved tensors.
+
+    Use this context-manager to define how intermediary results of an operation
+    should be packed before saving, and unpacked on retrieval.
+
+    In that context, the ``pack_hook`` function will be called everytime an
+    operation saves a tensor for backward (this includes intermediary results
+    saved using
+    :func:`~torch.autograd.function._ContextMethodMixin.save_for_backward` but
+    also those recorded by a PyTorch-defined operation). The output of
+    ``pack_hook`` is then stored in the computation graph instead of the
+    original tensor.
+
+    The ``unpack_hook`` is called when the saved tensor needs to be accessed,
+    namely when executing :func:`torch.Tensor.backward()` or
+    :func:`torch.autograd.grad()`. It takes as argument the *packed* object
+    returned by ``pack_hook`` and should return a tensor which has the same
+    content as the original tensor (passed as input to the corresponding
+    ``pack_hook``).
+
+    The hooks should have the following signatures:
+
+        pack_hook(tensor: Tensor) -> Any
+
+        unpack_hook(Any) -> Tensor
+
+    where the return value of ``pack_hook`` is a valid input to ``unpack_hook``.
+
+    In general, you want ``unpack_hook(pack_hook(t))`` to be equal to ``t`` in terms
+    of value, size, dtype and device.
+
+    Example::
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> def pack_hook(x):
+        ...     print("Packing", x)
+        ...     return x
+        >>>
+        >>> def unpack_hook(x):
+        ...     print("Unpacking", x)
+        ...     return x
+        >>>
+        >>> a = torch.ones(5, requires_grad=True)
+        >>> b = torch.ones(5, requires_grad=True) * 2
+        >>> with torch.autograd.graph.saved_tensors_hooks(pack_hook, unpack_hook):
+        ...     y = a * b
+        Packing tensor([1., 1., 1., 1., 1.], requires_grad=True)
+        Packing tensor([2., 2., 2., 2., 2.], grad_fn=<MulBackward0>)
+        >>> y.sum().backward()
+        Unpacking tensor([1., 1., 1., 1., 1.], requires_grad=True)
+        Unpacking tensor([2., 2., 2., 2., 2.], grad_fn=<MulBackward0>)
+
+    .. warning ::
+        Performing an inplace operation on the input to either hooks may lead
+        to undefined behavior.
+
+    .. warning ::
+        Only one pair of hooks is allowed at a time. When recursively nesting this
+        context-manager, only the inner-most pair of hooks will be applied.
+    """
+
+    def __init__(
+        self,
+        pack_hook: Callable[[torch.Tensor], Any],
+        unpack_hook: Callable[[Any], torch.Tensor],
+    ):
+        self.pack_hook = pack_hook
+        self.unpack_hook = unpack_hook
+
+    def __enter__(self):
+        torch._C._autograd._push_saved_tensors_default_hooks(
+            self.pack_hook, self.unpack_hook
+        )
+
+    def __exit__(self, *args: object):
+        torch._C._autograd._pop_saved_tensors_default_hooks()
+
+
+class save_on_cpu(saved_tensors_hooks):
+    """Context manager under which tensors saved by the forward pass will be stored on cpu, then retrieved for backward.
+
+    When performing operations within this context manager, intermediary
+    results saved in the graph during the forward pass will be moved to CPU,
+    then copied back to the original device when needed for the backward pass.
+    If the graph was already on CPU, no tensor copy is performed.
+
+    Use this context-manager to trade compute for GPU memory usage (e.g.
+    when your model doesn't fit in GPU memory during training).
+
+    Args:
+        pin_memory (bool): If ``True`` tensors will be saved to CPU pinned memory
+                           during packing and copied to GPU asynchronously during unpacking.
+                           Defaults to ``False``.
+                           Also see :ref:`cuda-memory-pinning`.
+
+
+    Example::
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_CUDA)
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD)
+        >>> a = torch.randn(5, requires_grad=True, device="cuda")
+        >>> b = torch.randn(5, requires_grad=True, device="cuda")
+        >>> c = torch.randn(5, requires_grad=True, device="cuda")
+        >>>
+        >>> def f(a, b, c):
+        ...     prod_1 = a * b           # a and b are saved on GPU
+        ...     with torch.autograd.graph.save_on_cpu():
+        ...         prod_2 = prod_1 * c  # prod_1 and c are saved on CPU
+        ...     y = prod_2 * a           # prod_2 and a are saved on GPU
+        ...     return y
+        >>>
+        >>> y = f(a, b, c)
+        >>> del a, b, c  # for illustration only
+        >>> # the content of a, b, and prod_2 are still alive on GPU
+        >>> # the content of prod_1 and c only live on CPU
+        >>> y.sum().backward()  # all CPU tensors are moved back to GPU, for backward
+        >>> # all intermediary tensors are released (deleted) after the call to backward
+
+    """
+
+    def __init__(self, pin_memory=False, device_type="cuda"):
+        device_module = getattr(torch, device_type, torch.cuda)
+
+        def pack_to_cpu(tensor):
+            if not pin_memory:
+                return (tensor.device, tensor.cpu())
+            packed = torch.empty(
+                tensor.size(),
+                dtype=tensor.dtype,
+                layout=tensor.layout,
+                pin_memory=(device_module.is_available() and not tensor.is_sparse),
+            )
+            packed.copy_(tensor)
+            return (tensor.device, packed)
+
+        def unpack_from_cpu(packed):
+            device, tensor = packed
+            return tensor.to(device, non_blocking=pin_memory)
+
+        super().__init__(pack_to_cpu, unpack_from_cpu)
+
+
+@contextlib.contextmanager
+def disable_saved_tensors_hooks(error_message):
+    """Context-manager that disables the saved tensors default hooks feature.
+
+    Useful for if you are creating a feature that does not work with saved
+    tensors default hooks.
+
+    Args:
+        error_message (str): When saved tensors default hooks are used when they
+                             have been are disabled, a RuntimeError with this
+                             error message gets raised.
+
+    Example::
+
+        >>> # xdoctest: +SKIP(failing)
+        >>> message = "saved tensors default hooks are disabled"
+        >>> with torch.autograd.graph.disable_saved_tensors_hooks(message):
+        ...     # Raises RuntimeError: saved tensors default hooks are disabled
+        ...     with torch.autograd.graph.save_on_cpu():
+        ...         pass
+
+    """
+    try:
+        maybe_prev_message = (
+            torch._C._autograd._saved_tensors_hooks_get_disabled_error_message()
+        )
+        torch._C._autograd._saved_tensors_hooks_disable(error_message)
+        yield
+    finally:
+        # See NOTE: [disabled_error_message invariant]
+        if maybe_prev_message is None:
+            torch._C._autograd._saved_tensors_hooks_enable()
+        else:
+            torch._C._autograd._saved_tensors_hooks_disable(maybe_prev_message)
+
+
+def register_multi_grad_hook(
+    tensors: Sequence[torch.Tensor],
+    fn: Union[
+        Callable[[Sequence[Optional[torch.Tensor]]], None],
+        Callable[[torch.Tensor], None],
+    ],
+    *,
+    mode: str = "all",
+):
+    r"""Register a multi-grad backward hook.
+
+    There are two supported modes: ``"all"`` and ``"any"``.
+
+    Under the ``"all"`` mode, the hook will be called after gradients with respect to every tensor in
+    :attr:`tensors` have been computed. If a tensor is in :attr:`tensors` but
+    is not part of the graph, or if a tensor is not needed to compute the gradients
+    for any ``inputs`` specified for the current ``.backward()`` or ``.grad()`` call,
+    this tensor will be ignored and the hook will not wait for its gradient to be
+    computed.
+
+    After every non-ignored tensor's gradient has been computed, :attr:`fn` will be
+    called with those gradients. ``None`` will be passed for tensors that did not
+    have their gradients computed.
+
+    Under the ``"any"`` mode, the hook will be called after the first gradient
+    with respect to a tensor in :attr:`tensors` has been computed. The hook
+    will be called with that gradient as its argument.
+
+    The hook should not modify its arguments.
+
+    This function returns a handle with a method ``handle.remove()`` that removes the hook.
+
+    .. note::
+        See :ref:`backward-hooks-execution` for more information on how when this hook
+        is executed, and how its execution is ordered relative to other hooks.
+
+    Example::
+
+        >>> import torch
+        >>>
+        >>> a = torch.rand(2, 3, requires_grad=True)
+        >>> b = torch.rand(2, 3, requires_grad=True)
+        >>> c = a * b
+        >>> d = a * b
+        >>>
+        >>> def fn(grads):
+        ...     print([g is not None for g in grads])
+        ...
+        >>> torch.autograd.graph.register_multi_grad_hook((a, b, c, d), fn)
+        >>>
+        >>> c.sum().backward(retain_graph=True)
+        [True, True, True, False]
+        >>> c.sum().backward(inputs=(a,), retain_graph=True)
+        [True, False, True, False]
+        >>>
+    """
+    supported_modes = ("all", "any")
+    if mode not in supported_modes:
+        raise ValueError(f"Expects mode to be one of {supported_modes} but got {mode}")
+
+    class Handle(RemovableHandle):
+        handles: Tuple[RemovableHandle, ...]
+
+        def __init__(self, handles: Tuple[RemovableHandle, ...]):
+            self.handles = handles
+
+        def remove(self):
+            for handle in self.handles:
+                handle.remove()
+
+        def __getstate__(self):
+            return self.handles
+
+        def __setstate__(self, state):
+            self.handles = state
+
+    if mode == "all":
+        count: Dict[int, int] = dict()
+        nb_calls = None
+        buffer: Dict[int, List[Optional[torch.Tensor]]] = dict()
+
+        grad_fns = list(map(_get_grad_fn_or_grad_acc, tensors))
+        len_tensors = len(tensors)
+
+        def get_inner_hook(idx):
+            def inner_hook(grad: torch.Tensor):
+                nonlocal count, nb_calls, buffer, fn
+                id = torch._C._current_graph_task_id()
+                assert (
+                    id != -1
+                ), "expected this hook to be called inside a backward call"
+                count[id] = count.get(id, 0)
+                buffer[id] = buffer.get(id, [None] * len_tensors)
+
+                if count[id] == 0:
+                    # On the first call, compute the actual nb_calls and buffer
+                    nb_calls = sum(torch._C._will_engine_execute_node(g) for g in grad_fns)  # type: ignore[attr-defined]
+
+                buffer[id][idx] = grad
+                count[id] += 1
+
+                if count[id] == nb_calls:
+                    fn = cast(Callable[[Sequence[Optional[torch.Tensor]]], None], fn)
+                    fn(buffer[id])
+                    del count[id]
+                    del buffer[id]
+
+            return inner_hook
+
+        handles: Tuple[RemovableHandle] = tuple(
+            t.register_hook(get_inner_hook(i)) for i, t in enumerate(tensors)
+        )
+    elif mode == "any":
+        fn = cast(Callable[[torch.Tensor], None], fn)
+        lock = threading.Lock()
+        ran_hook: Dict[int, bool] = defaultdict(bool)
+
+        @functools.wraps(fn)
+        def wrapped_fn(grad: torch.Tensor):
+            nonlocal ran_hook
+            id = torch._C._current_graph_task_id()
+            assert id != -1, "expected this hook to be called inside a backward call"
+            with lock:
+                prev, ran_hook[id] = ran_hook[id], True
+            if prev:
+                return
+            fn(grad)
+
+        handles = tuple(
+            tensor.register_hook(wrapped_fn)
+            for tensor in tensors
+            if tensor.requires_grad
+        )
+
+    return Handle(handles)  # type: ignore[possibly-undefined]
+
+
+# NOTE [Allow mutation on tensors saved for backward]
+#
+# 1. Tensor gets saved for backward
+#    - remember the python object id and the version of the tensor
+#    - remember aliasing information (data_ptr of base + version)
+#    - save the original so we control its lifetime
+# 2. Any time a tensor gets in-placed
+#    - for each tensor aliased to it:
+#      - check using its object id and version to see if it has been saved
+#      - if it has been saved, clone it
+#      - delete the reference to the original
+# 3. during backward
+#    - if the clone exists, the tensor must've been modified in-place
+_allow_mutation_on_saved_tensors_enabled = False
+
+
+def _get_tid(t) -> Tuple[int, int, int]:
+    return (id(t), t.data_ptr(), t._version)
+
+
+def _get_sid(t) -> Tuple[int, int]:
+    return (t.data_ptr(), t._version)
+
+
+class _Handle:
+    pass
+
+
+class _swap_with_cloned(saved_tensors_hooks):
+    def __init__(self, ctx):
+        def pack_hook(t):
+            tid = _get_tid(t)
+            sid = _get_sid(t)
+            # Tensors saved for backward have an entry in _tid_to_weakhandle
+            handle: Optional[_Handle] = None
+
+            # Save aliasing information
+            ctx.sid_to_tid[sid].add(tid)
+
+            # NB: The same tensor (of the same version) can be saved multiple times
+            if tid not in ctx.tid_to_weakhandle:
+                handle = _Handle()
+                ctx.tid_to_weakhandle[tid] = handle
+                ctx.original[handle] = t
+            else:
+                # Store an additional strong reference to the handle
+                handle = ctx.tid_to_weakhandle[tid]
+            return handle
+
+        def unpack_hook(tup):
+            handle = tup
+            error_msg = (
+                "Trying to backward outside of the 'allow_mutation_on_saved_tensors' context"
+                "in which the graph was originally recorded."
+            )
+            assert _allow_mutation_on_saved_tensors_enabled, error_msg
+            if handle in ctx.cloned:
+                res = ctx.cloned[handle]
+            else:
+                assert handle in ctx.original, error_msg
+                res = ctx.original[handle]
+            return res
+
+        super().__init__(pack_hook, unpack_hook)
+
+
+class _CloneArgBeforeMutateMode(TorchDispatchMode):
+    def __init__(self, ctx):
+        self.ctx = ctx
+
+    def __torch_dispatch__(self, func, types, args=(), kwargs=None):
+        kwargs = kwargs or {}
+
+        for idx, arg in enumerate(func._schema.arguments):
+            if arg.alias_info is not None and arg.alias_info.is_write:
+                t = kwargs["out"] if arg.is_out else args[idx]
+                tid = _get_tid(t)
+                sid = _get_sid(t)
+                ctx = self.ctx
+                if sid in ctx.sid_to_tid:
+                    for tid in ctx.sid_to_tid[sid]:
+                        if tid not in ctx.tid_to_weakhandle:
+                            # We know that if tid is in sid_to_tid, then it must also be in
+                            # tid_to_weakhandle. However, it is possible for the tensor to be
+                            # saved at one point, but cleared by backward before it is modified
+                            # in-place. Consider the following example:
+                            #
+                            # >>> a = torch.randn(2, 3, requires_grad=True).clone()
+                            # >>> out = (a**2).sum()
+                            # >>> out.backward()
+                            # >>> a.sin_()
+                            continue
+                        handle = ctx.tid_to_weakhandle[tid]
+                        if handle in ctx.cloned:
+                            # The same exact tensor has been cloned already
+                            continue
+                        ctx.cloned[handle] = ctx.original[handle].clone()
+                        del ctx.original[handle]
+
+        rs = func(*args, **kwargs)
+        return rs
+
+
+class _AllowMutationOnSavedContext:
+    def __init__(self):
+        self.cloned: weakref.WeakKeyDictionary = weakref.WeakKeyDictionary()
+        self.original: weakref.WeakKeyDictionary = weakref.WeakKeyDictionary()
+        self.tid_to_weakhandle: weakref.WeakValueDictionary = (
+            weakref.WeakValueDictionary()
+        )
+        self.sid_to_tid: Dict[Tuple[int, int], Set[Tuple[int, int, int]]] = defaultdict(
+            set
+        )
+
+    def clear(self):
+        self.cloned.clear()
+        self.original.clear()
+        self.tid_to_weakhandle.clear()
+        self.sid_to_tid.clear()
+
+
+@contextlib.contextmanager
+def allow_mutation_on_saved_tensors():
+    """Context manager under which mutating tensors saved for backward is allowed.
+
+    Under this context manager, tensors saved for backward are cloned on mutation,
+    so the original version can still be used during backward. Normally, mutating a tensor
+    saved for backward will result in an error raised when it's used during backward.
+
+    To ensure the correct behavior, both the forward and backward should be run under
+    the same context manager.
+
+    returns:
+        An _AllowMutationOnSavedContext object storing the state managed by this
+        context manager. This object can be useful for debugging purposes. The state
+        managed by the context manager is automatically cleared upon exiting.
+
+    Example::
+
+        >>> import torch
+        >>> with torch.autograd.graph.allow_mutation_on_saved_tensors():
+        ...     # forward
+        ...     a = torch.ones(2, 3, requires_grad=True)
+        ...     b = a.clone()
+        ...     out = (b**2).sum()
+        ...     b.sin_()
+        ...     # backward
+        ...     out.sum().backward()
+        ...
+        tensor([[0.8415, 0.8415, 0.8415],
+                [0.8415, 0.8415, 0.8415]], grad_fn=<SinBackward0>)
+    """
+    global _allow_mutation_on_saved_tensors_enabled
+
+    ctx = _AllowMutationOnSavedContext()
+
+    with _swap_with_cloned(ctx), _CloneArgBeforeMutateMode(ctx):
+        try:
+            if _allow_mutation_on_saved_tensors_enabled:
+                raise RuntimeError(
+                    "allow_mutation_on_saved_tensors contexts cannot be nested"
+                )
+            _allow_mutation_on_saved_tensors_enabled = True
+            yield ctx
+        finally:
+            ctx.clear()
+            _allow_mutation_on_saved_tensors_enabled = False
+
+
+def _register_logging_hooks_on_whole_graph(t_outputs: List[torch.Tensor]):
+    grad_fns = list(map(_get_grad_fn_or_grad_acc, t_outputs))
+
+    def iter_graph(roots):
+        if not roots:
+            return
+        seen = set()
+        q: Deque = collections.deque()
+        for node in roots:
+            if node is not None:
+                seen.add(node)
+                q.append(node)
+
+        while q:
+            node = q.popleft()
+            for fn, _idx in node.next_functions:
+                if fn in seen or fn is None:
+                    continue
+                seen.add(fn)
+                q.append(fn)
+
+            yield node
+
+    def fmt(t):
+        # Avoid circular import
+        from torch.testing._internal.common_utils import dtype_abbrs
+
+        if t is None:
+            return "None"
+        return f"{dtype_abbrs[t.dtype]}[{', '.join(map(str, t.shape))}]"
+
+    def prehook(grad_outputs):
+        node = torch._C._current_autograd_node()
+        grad_outputs_str = f"[{','.join(fmt(t) for t in grad_outputs)}]"
+        log_str = f"Executing: {node} with grad_outputs: {grad_outputs_str}"
+        log.debug(log_str)
+
+    handles = []
+    for node in iter_graph(grad_fns):
+        handles.append(node.register_prehook(prehook))
+
+    def unregister_hooks():
+        for handle in handles:
+            handle.remove()
+
+    return unregister_hooks
+
+
+def _engine_run_backward(t_outputs, *args, **kwargs):
+    attach_logging_hooks = log.getEffectiveLevel() <= logging.DEBUG
+    if attach_logging_hooks:
+        unregister_hooks = _register_logging_hooks_on_whole_graph(t_outputs)
+    try:
+        return Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass
+            t_outputs, *args, **kwargs
+        )  # Calls into the C++ engine to run the backward pass
+    finally:
+        if attach_logging_hooks:
+            unregister_hooks()  # type: ignore[possibly-undefined]

venv/lib/python3.10/site-packages/torch/autograd/profiler.py

@@ -0,0 +1,1042 @@
+from collections import defaultdict
+from typing import Any, Dict, List, Optional
+from warnings import warn
+
+import torch
+
+import torch.cuda
+from torch._C import _get_privateuse1_backend_name
+from torch._C._profiler import _ExperimentalConfig
+
+from torch.autograd import (
+    _disable_profiler,
+    _enable_profiler,
+    _kineto_step,
+    _prepare_profiler,
+    _ProfilerResult,
+    _supported_activities,
+    DeviceType,
+    kineto_available,
+    ProfilerActivity,
+    ProfilerConfig,
+    ProfilerState,
+)
+from torch.autograd.profiler_util import (
+    _filter_name,
+    _filter_stack_entry,
+    _rewrite_name,
+    EventList,
+    FunctionEvent,
+    MEMORY_EVENT_NAME,
+    MemRecordsAcc,
+    OUT_OF_MEMORY_EVENT_NAME,
+)
+from torch.futures import Future
+
+__all__ = [
+    "profile",
+    "record_function",
+    "emit_itt",
+    "emit_nvtx",
+    "load_nvprof",
+    "EnforceUnique",
+    "parse_nvprof_trace",
+    "KinetoStepTracker",
+    "EventList",
+    "FunctionEvent",
+    "MemRecordsAcc",
+]
+
+try:
+    # Available in Python >= 3.2
+    from contextlib import ContextDecorator as _ContextDecorator
+except ImportError:
+    import functools
+
+    class _ContextDecorator:  # type: ignore[no-redef]
+        def __enter__(self):
+            raise NotImplementedError
+
+        def __exit__(self, exc_type, exc_val, exc_tb):
+            raise NotImplementedError
+
+        def __call__(self, func):
+            @functools.wraps(func)
+            def wrapped(*args, **kwargs):
+                with self:
+                    return func(*args, **kwargs)
+
+            return wrapped
+
+
+# global python state - whether profiler is currently enabled
+# useful for fast python checks to reduce latency
+_is_profiler_enabled: bool = False
+
+
+def _set_is_profiler_enabled(enable: bool):
+    global _is_profiler_enabled
+    _is_profiler_enabled = enable
+
+
+def _run_on_profiler_start():
+    _set_is_profiler_enabled(True)
+
+
+def _run_on_profiler_stop():
+    _set_is_profiler_enabled(False)
+
+
+class profile:
+    """Context manager that manages autograd profiler state and holds a summary of results.
+
+    Under the hood it just records events of functions being executed in C++ and
+    exposes those events to Python. You can wrap any code into it and it will
+    only report runtime of PyTorch functions.
+    Note: profiler is thread local and is automatically propagated into the async tasks
+
+    Args:
+        enabled (bool, optional): Setting this to False makes this context manager a no-op.
+
+        use_cuda (bool, optional): Enables timing of CUDA events as well using the cudaEvent API.
+            Adds approximately 4us of overhead to each tensor operation.
+
+        record_shapes (bool, optional): If shapes recording is set, information
+            about input dimensions will be collected. This allows one to see which
+            dimensions have been used under the hood and further group by them
+            using prof.key_averages(group_by_input_shape=True). Please note that
+            shape recording might skew your profiling data. It is recommended to
+            use separate runs with and without shape recording to validate the timing.
+            Most likely the skew will be negligible for bottom most events (in a case
+            of nested function calls). But for higher level functions the total
+            self cpu time might be artificially increased because of the shape
+            collection.
+
+        with_flops (bool, optional): If with_flops is set, the profiler will estimate
+            the FLOPs (floating point operations) value using the operator's input shape.
+            This allows one to estimate the hardware performance. Currently,
+            this option only works for the matrix multiplication and 2D convolution operators.
+
+        profile_memory (bool, optional): track tensor memory allocation/deallocation.
+
+        with_stack (bool, optional): record source information (file and line number) for the ops.
+
+        with_modules (bool): record module hierarchy (including function names)
+            corresponding to the callstack of the op. e.g. If module A's forward call's
+            module B's forward which contains an aten::add op,
+            then aten::add's module hierarchy is A.B
+            Note that this support exist, at the moment, only for TorchScript models
+            and not eager mode models.
+
+        use_kineto (bool, optional): experimental, enable profiling with Kineto profiler.
+
+        use_cpu (bool, optional): profile CPU events; setting to ``False`` requires
+            ``use_kineto=True`` and can be used to lower the overhead for GPU-only profiling.
+
+        experimental_config (_ExperimentalConfig) : A set of experimental options
+            used by profiler libraries like Kineto. Note, backward compatibility is not guaranteed.
+
+
+    .. warning:
+        Enabling memory profiling or source attribution incurs additional profiler
+        overhead
+
+    .. warning:
+        This context managers should not be called recursively, i.e. no nested
+        instances are allowed
+
+    .. warning:
+        Due to some CUDA multiprocessing limitations (multiprocessing-cuda-note_),
+        one cannot use the profiler with ``use_cuda = True`` to benchmark
+        DataLoaders with ``num_workers > 0``. If you wish to benchmark data loading,
+        please use ``use_cuda = False`` or ``num_workers = 0``.
+
+    Example:
+        >>> # xdoctest: +SKIP
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD_PROFILER)
+        >>> x = torch.randn((1, 1), requires_grad=True)
+        >>> with torch.autograd.profiler.profile() as prof:
+        >>>     for _ in range(100):  # any normal python code, really!
+        >>>         y = x ** 2
+        >>>         y.backward()
+        >>> # NOTE: some columns were removed for brevity
+        >>> print(prof.key_averages().table(sort_by="self_cpu_time_total"))
+        -----------------------------------  ---------------  ---------------  ---------------
+        Name                                 Self CPU total   CPU time avg     Number of Calls
+        -----------------------------------  ---------------  ---------------  ---------------
+        mul                                  32.048ms         32.048ms         200
+        pow                                  27.041ms         27.041ms         200
+        PowBackward0                         9.727ms          55.483ms         100
+        torch::autograd::AccumulateGrad      9.148ms          9.148ms          100
+        torch::autograd::GraphRoot           691.816us        691.816us        100
+        -----------------------------------  ---------------  ---------------  ---------------
+
+    """
+
+    def __init__(
+        self,
+        enabled=True,
+        *,
+        use_cuda=False,
+        use_device=None,
+        record_shapes=False,
+        with_flops=False,
+        profile_memory=False,
+        with_stack=False,
+        with_modules=False,
+        use_kineto=False,
+        use_cpu=True,
+        use_mtia=False,
+        experimental_config=None,
+    ):
+        self.enabled: bool = enabled
+        if not self.enabled:
+            return
+        self.use_cuda = use_cuda
+        self.use_device: Optional[str] = (
+            use_device if use_device != "privateuseone" else None
+        )
+        self.function_events: Optional[EventList] = None
+        self.entered = False
+        self.record_shapes = record_shapes
+        self.with_flops = with_flops
+        self.record_shapes |= self.with_flops
+        self.profile_memory = profile_memory
+        self.with_stack = with_stack
+        self.with_modules = with_modules
+        self.use_cpu = use_cpu
+        self.use_mtia = use_mtia
+        if experimental_config is None:
+            experimental_config = _ExperimentalConfig()
+        self.experimental_config = experimental_config
+        self.kineto_results: Optional[_ProfilerResult] = None
+
+        if not self.use_cpu:
+            assert (
+                use_kineto
+            ), "Device-only events supported only with Kineto (use_kineto=True)"
+
+        if self.use_device == "cuda":
+            self.use_device = None
+            self.use_cuda = True
+
+        if self.use_device and self.use_device != _get_privateuse1_backend_name():
+            warn(f"{self.use_device} doesn't support profile.")
+            self.use_device = None
+
+        if self.use_cuda and not torch.cuda.is_available():
+            warn("CUDA is not available, disabling CUDA profiling")
+            self.use_cuda = False
+
+        self.kineto_activities = set()
+        if self.use_cpu:
+            self.kineto_activities.add(ProfilerActivity.CPU)
+        if self.use_mtia:
+            self.kineto_activities.add(ProfilerActivity.MTIA)
+
+        self.profiler_kind = ProfilerState.KINETO
+        if self.use_cuda:
+            if not use_kineto or ProfilerActivity.CUDA not in _supported_activities():
+                assert self.use_cpu, "Legacy CUDA profiling requires use_cpu=True"
+                self.profiler_kind = ProfilerState.KINETO_GPU_FALLBACK
+            else:
+                self.kineto_activities.add(ProfilerActivity.CUDA)
+
+        if self.use_device:
+            if (
+                not use_kineto
+                or ProfilerActivity.PrivateUse1 not in _supported_activities()
+            ):
+                assert (
+                    self.use_cpu
+                ), "Legacy custombackend profiling requires use_cpu=True"
+                self.profiler_kind = ProfilerState.KINETO_PRIVATEUSE1_FALLBACK
+            else:
+                self.kineto_activities.add(ProfilerActivity.PrivateUse1)
+                self.profiler_kind = ProfilerState.KINETO_PRIVATEUSE1
+
+        assert (
+            len(self.kineto_activities) > 0
+        ), "No activities specified for the profiler"
+
+    def config(self):
+        return ProfilerConfig(
+            self.profiler_kind,
+            self.record_shapes,
+            self.profile_memory,
+            self.with_stack,
+            self.with_flops,
+            self.with_modules,
+            self.experimental_config,
+        )
+
+    def __enter__(self):
+        if not self.enabled:
+            return
+        if self.entered:
+            raise RuntimeError("Profiler context manager is not reentrant")
+        self._prepare_trace()
+        self._start_trace()
+        return self
+
+    def _prepare_trace(self):
+        self.entered = True
+        _prepare_profiler(self.config(), self.kineto_activities)
+
+    def _start_trace(self):
+        self.entered = True
+        _run_on_profiler_start()
+        _enable_profiler(self.config(), self.kineto_activities)
+
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        if not self.enabled:
+            return
+        if self.use_cuda:
+            torch.cuda.synchronize()
+        self.kineto_results = _disable_profiler()
+        _run_on_profiler_stop()
+        parsed_results = self._parse_kineto_results(self.kineto_results)
+        self.function_events = EventList(
+            parsed_results,
+            use_cuda=self.use_cuda,
+            use_device=self.use_device,
+            profile_memory=self.profile_memory,
+            with_flops=self.with_flops,
+        )
+        self.function_events._build_tree()
+        return False
+
+    def __repr__(self):
+        if self.function_events is None:
+            return "<unfinished torch.autograd.profile>"
+        return repr(self.function_events)
+
+    def __str__(self):
+        if self.function_events is None:
+            return "<unfinished torch.autograd.profile>"
+        return str(self.function_events)
+
+    def _check_finish(self):
+        if self.function_events is None:
+            raise RuntimeError("Profiler didn't finish running")
+
+    def table(
+        self,
+        sort_by=None,
+        row_limit=100,
+        max_src_column_width=75,
+        max_name_column_width=55,
+        max_shapes_column_width=80,
+        header=None,
+        top_level_events_only=False,
+    ):
+        self._check_finish()
+        assert self.function_events is not None
+        return self.function_events.table(
+            sort_by=sort_by,
+            row_limit=row_limit,
+            max_src_column_width=max_src_column_width,
+            max_name_column_width=max_name_column_width,
+            max_shapes_column_width=max_shapes_column_width,
+            header=header,
+            top_level_events_only=top_level_events_only,
+        )
+
+    table.__doc__ = EventList.table.__doc__
+
+    def export_chrome_trace(self, path):
+        self._check_finish()
+        if kineto_available():
+            self.kineto_results.save(path)  # type: ignore[union-attr]
+        else:
+            return self.function_events.export_chrome_trace(path)  # type: ignore[union-attr]
+
+    export_chrome_trace.__doc__ = EventList.export_chrome_trace.__doc__
+
+    def export_stacks(self, path: str, metric: str = "self_cpu_time_total"):
+        self._check_finish()
+        assert self.function_events is not None, "Expected profiling results"
+        assert self.with_stack, "export_stacks() requires with_stack=True"
+        return self.function_events.export_stacks(path, metric)
+
+    def key_averages(self, group_by_input_shape=False, group_by_stack_n=0):
+        self._check_finish()
+        assert self.function_events is not None, "Expected profiling results"
+        return self.function_events.key_averages(group_by_input_shape, group_by_stack_n)
+
+    key_averages.__doc__ = EventList.key_averages.__doc__
+
+    def total_average(self):
+        self._check_finish()
+        assert self.function_events is not None, "Expected profiling results"
+        return self.function_events.total_average()
+
+    total_average.__doc__ = EventList.total_average.__doc__
+
+    @property
+    def self_cpu_time_total(self):
+        """Returns total time spent on CPU.
+
+        The total time is a sum of all self times across all the events.
+        """
+        self._check_finish()
+        assert self.function_events is not None
+        return self.function_events.self_cpu_time_total
+
+    def _parse_kineto_results(self, result: _ProfilerResult):
+        # result.events() has most of the events - PyTorch op-level and device-level events
+
+        trace_start_us = result.trace_start_us()
+        mem_records = [
+            [evt, False] for evt in result.events() if evt.name() == MEMORY_EVENT_NAME
+        ]
+        oom_records = [
+            evt for evt in result.events() if evt.name() == OUT_OF_MEMORY_EVENT_NAME
+        ]
+        mem_records_acc = MemRecordsAcc(mem_records)
+
+        def _cpu_memory_usage(mem_record):
+            return (
+                mem_record.nbytes()
+                if mem_record.device_type()
+                in [DeviceType.CPU, DeviceType.MKLDNN, DeviceType.IDEEP]
+                else 0
+            )
+
+        def _cuda_memory_usage(mem_record):
+            return (
+                mem_record.nbytes()
+                if mem_record.device_type() in [DeviceType.CUDA, DeviceType.HIP]
+                else 0
+            )
+
+        def _privateuse1_memory_usage(mem_record):
+            return (
+                mem_record.nbytes()
+                if mem_record.device_type() in [DeviceType.PrivateUse1]
+                else 0
+            )
+
+        # Create and return FunctionEvent list
+        function_events = []
+        device_corr_map: Dict[int, List[FunctionEvent]] = {}
+        max_evt_id = 0
+        for kineto_event in result.events():
+            if _filter_name(kineto_event.name()):
+                continue
+            rel_start_us = kineto_event.start_us() - trace_start_us
+            rel_end_us = rel_start_us + kineto_event.duration_us()
+            abs_end_us = kineto_event.start_us() + kineto_event.duration_us()
+
+            cpu_memory_usage = 0
+            cuda_memory_usage = 0
+            privateuse1_memory_usage = 0
+            if kineto_event.device_type() == DeviceType.CPU:
+                # find the corresponding memory allocation events
+                for mem_record in mem_records_acc.in_interval(
+                    kineto_event.start_us(), abs_end_us
+                ):
+                    cpu_memory_usage += _cpu_memory_usage(mem_record[0])
+                    cuda_memory_usage += _cuda_memory_usage(mem_record[0])
+                    privateuse1_memory_usage += _privateuse1_memory_usage(mem_record[0])
+                    mem_record[1] = True
+
+            is_async = kineto_event.is_async() or (
+                kineto_event.start_thread_id() != kineto_event.end_thread_id()
+            )
+
+            fe = FunctionEvent(
+                id=kineto_event.correlation_id(),
+                name=_rewrite_name(name=kineto_event.name(), with_wildcard=True),
+                trace_name=_rewrite_name(name=kineto_event.name(), with_wildcard=False),
+                thread=kineto_event.start_thread_id(),
+                start_us=rel_start_us,
+                end_us=rel_end_us,
+                fwd_thread=kineto_event.fwd_thread_id(),
+                input_shapes=kineto_event.shapes(),
+                concrete_inputs=kineto_event.concrete_inputs(),
+                stack=[
+                    entry
+                    for entry in kineto_event.stack()
+                    if _filter_stack_entry(entry)
+                ],
+                scope=kineto_event.scope(),
+                use_device=self.use_device,
+                cpu_memory_usage=cpu_memory_usage,
+                cuda_memory_usage=cuda_memory_usage,
+                privateuse1_memory_usage=privateuse1_memory_usage,
+                is_async=is_async,
+                sequence_nr=kineto_event.sequence_nr(),
+                device_type=kineto_event.device_type(),
+                device_index=kineto_event.device_index(),
+                flops=kineto_event.flops(),
+            )
+            max_evt_id = max(max_evt_id, fe.id)
+            if fe.device_type == DeviceType.CPU and not fe.is_async:
+                if self.use_device:
+                    privateuse1_time = kineto_event.privateuse1_elapsed_us()
+                    if privateuse1_time > 0:
+                        fe.append_kernel(fe.name, fe.device_index, privateuse1_time)
+                        fe.is_legacy = True
+                else:
+                    # Check if we have CUDA time as a fallback
+                    cuda_time = kineto_event.cuda_elapsed_us()
+                    if cuda_time > 0:
+                        fe.append_kernel(fe.name, fe.device_index, cuda_time)
+                        fe.is_legacy = True
+            function_events.append(fe)
+            corr_id = kineto_event.linked_correlation_id()
+            if corr_id > 0:
+                if corr_id not in device_corr_map:
+                    device_corr_map[corr_id] = []
+                device_corr_map[corr_id].append(fe)
+
+        # associate CUDA kernels and CUDA runtime (CPU) with CPU events
+        for fe in function_events:
+            if (
+                fe.device_type == DeviceType.CPU
+                and not fe.is_async
+                and fe.id in device_corr_map
+            ):
+                for f_evt in device_corr_map[fe.id]:
+                    if f_evt.device_type == DeviceType.CUDA:
+                        fe.append_kernel(
+                            f_evt.name,
+                            f_evt.device_index,
+                            f_evt.time_range.end - f_evt.time_range.start,
+                        )
+                    elif f_evt.device_type == DeviceType.CPU:
+                        # make sure that 'thread' of a CPU Kineto (e.g. CUDA Runtime) event is associated
+                        # with the 'thread' of the corresponding linked PyTorch event to properly track
+                        # parents and children
+                        f_evt.thread = fe.thread
+
+        def createFunctionEventForMemoryEvents(evt):
+            rel_start_us = evt.start_us() - trace_start_us
+            fe = FunctionEvent(
+                id=max_evt_id,
+                name=evt.name(),
+                trace_name=None,  # not outputting in the trace
+                thread=evt.start_thread_id(),
+                start_us=rel_start_us,
+                end_us=rel_start_us,  # no duration
+                fwd_thread=evt.start_thread_id(),
+                input_shapes=[],
+                stack=[],
+                scope=0,  # RecordScope::FUNCTION
+                use_device=self.use_device,
+                cpu_memory_usage=_cpu_memory_usage(evt),
+                cuda_memory_usage=_cuda_memory_usage(evt),
+                privateuse1_memory_usage=_privateuse1_memory_usage(evt),
+                is_async=False,
+                sequence_nr=-1,
+                device_type=DeviceType.CPU,
+                device_index=0,
+            )
+            return fe
+
+        # output top-level memory events
+        for mem_record in mem_records:
+            if not mem_record[1]:
+                max_evt_id += 1
+                fe = createFunctionEventForMemoryEvents(mem_record[0])
+                function_events.append(fe)
+
+        for oom_record in oom_records:
+            max_evt_id += 1
+            fe = createFunctionEventForMemoryEvents(oom_record)
+            function_events.append(fe)
+
+        function_events.sort(
+            key=lambda evt: [evt.time_range.start, -evt.time_range.end]
+        )
+        return function_events
+
+
+class record_function(_ContextDecorator):
+    """Context manager/function decorator that adds a label to a code block/function when running autograd profiler.
+
+    It is useful when tracing the code profile.
+
+    Args:
+        name (str): Label assigned to the block of code.
+        node_id (int): ID of node, for distributed profiling. Unset in
+        non-distributed cases.
+
+    Example:
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD_PROFILER)
+        >>> x = torch.randn((1, 1), requires_grad=True)
+        >>> with torch.autograd.profiler.profile() as prof:
+        ...     y = x ** 2
+        ...     with torch.autograd.profiler.record_function("label-z"): # label the block
+        ...         z = y ** 3
+        ...     y.backward()
+        ...
+        >>> # xdoctest: +IGNORE_WANT
+        >>> # NOTE: some columns were removed for brevity
+        >>> print(prof.key_averages().table(sort_by="self_cpu_time_total"))
+        -----------------------------------  ---------------  ---------------  ---------------
+        Name                                 Self CPU total %  CPU time avg     Number of Calls
+        -----------------------------------  ---------------  ---------------  ---------------
+        pow                                  60.77%           47.470us         3
+        mul                                  21.73%           25.465us         2
+        PowBackward0                         12.03%           121.891us        1
+        torch::autograd::AccumulateGrad      2.70%            6.324us          1
+        label-z                              2.13%            12.421us         1
+        torch::autograd::GraphRoot           0.64%            1.503us          1
+        -----------------------------------  ---------------  ---------------  ---------------
+        Self CPU time total: 234.344us
+        CUDA time total: 0.000us
+
+    """
+
+    def __init__(self, name: str, args: Optional[str] = None):
+        self.name: str = name
+        self.args: Optional[str] = args
+        # Whether or not we should run record function's end callbacks when exiting.
+        self.run_callbacks_on_exit: bool = True
+        # TODO: TorchScript ignores standard type annotation here
+        # self.record: Optional["torch.classes.profiler._RecordFunction"] = None
+        self.record = torch.jit.annotate(
+            Optional["torch.classes.profiler._RecordFunction"], None
+        )
+
+    def __enter__(self):
+        self.record = torch.ops.profiler._record_function_enter_new(
+            self.name, self.args
+        )
+        return self
+
+    def __exit__(self, exc_type: Any, exc_value: Any, traceback: Any):
+        if not self.run_callbacks_on_exit:
+            return
+
+        # Local variable is needed by TorchScript to refine Optional[T] to T
+        record = self.record
+        assert record is not None
+
+        # TODO: Too slow with __torch_function__ handling enabled
+        # See https://github.com/pytorch/pytorch/issues/76410
+        if not torch.jit.is_scripting():
+            with torch._C.DisableTorchFunctionSubclass():
+                torch.ops.profiler._record_function_exit._RecordFunction(record)
+        else:
+            torch.ops.profiler._record_function_exit(record)
+
+    def _call_end_callbacks_on_future(self, fut: Future[Any]) -> Future[Any]:
+        """Use for profiling async calls that return a future.
+
+        Calling this function will extend recording beyond this scope, until the future is
+        satisfied. It is useful for profiling the end to end time of asynchronous calls.
+        This function should only be called once to attach the callback onto the future, and
+        will throw if called multiple times.
+
+        Args:
+            fut: (torch._C.Future): future for which to schedule
+            callback for.
+
+        Returns:
+            A future that completes with the value of the passed in future when
+            the profiling callbacks have ran.
+
+        """
+        # Throw if we have already attached a callback onto the future.
+        if not self.run_callbacks_on_exit:
+            raise RuntimeError("_call_end_callbacks_on_future can only be called once.")
+
+        # We are scheduling to run this RecordFunction's end callbacks when the
+        # passed in future completes, so don't run end callbacks on exit.
+        self.run_callbacks_on_exit = False
+
+        # Local variable is needed by TorchScript to refine Optional[T] to T
+        record = self.record
+        assert record is not None
+
+        # TODO: Too slow with __torch_function__ handling enabled
+        # See https://github.com/pytorch/pytorch/issues/76410
+        if not torch.jit.is_scripting():
+            with torch._C.DisableTorchFunctionSubclass():
+                profiled_future = (
+                    torch.ops.profiler._call_end_callbacks_on_jit_fut._RecordFunction(
+                        record, fut
+                    )
+                )
+        else:
+            profiled_future = torch.ops.profiler._call_end_callbacks_on_jit_fut(
+                record, fut
+            )
+        return profiled_future
+
+
+class emit_itt:
+    """Context manager that makes every autograd operation emit an ITT range.
+
+    It is useful when running the program under Intel(R) VTune Profiler::
+
+        vtune <--vtune-flags> <regular command here>
+
+    The Instrumentation and Tracing Technology (ITT) API enables your application to generate and
+    control the collection of trace data during its execution across different Intel tools.
+    This context manager is to annotate Intel(R) VTune Profiling trace. With help of this context manager,
+    you will be able to see labled ranges in Intel(R) VTune Profiler GUI.
+
+    .. warning:
+        This context manager should not be called recursively, i.e. at most one
+        instance should be enabled at any given time.
+
+    Args:
+        enabled (bool, optional): Setting ``enabled=False`` makes this context manager a no-op.
+            Default: ``True``.
+        record_shapes (bool, optional): If ``record_shapes=True``, the itt range wrapping
+            each autograd op will append information about the sizes of Tensor arguments received
+            by that op, in the following format:
+            ``[[arg0.size(0), arg0.size(1), ...], [arg1.size(0), arg1.size(1), ...], ...]``
+            Non-tensor arguments will be represented by ``[]``.
+            Arguments will be listed in the order they are received by the backend op.
+            Please note that this order may not match the order in which those arguments were passed
+            on the Python side.  Also note that shape recording may increase the overhead of itt range creation.
+            Default: ``False``
+
+    Example:
+        >>> # xdoctest: +SKIP("Undefined variables")
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD_PROFILER)
+        >>> with torch.autograd.profiler.emit_itt():
+        ...     model(x)
+
+    """
+
+    def __init__(self, enabled=True, record_shapes=False):
+        self.enabled = enabled
+        self.entered = False
+        self.record_shapes = record_shapes
+
+    def __enter__(self):
+        if not self.enabled:
+            return
+        if self.entered:
+            raise RuntimeError("ITT annotation context manager is not reentrant")
+        self.entered = True
+        _run_on_profiler_start()
+        _enable_profiler(
+            ProfilerConfig(
+                ProfilerState.ITT,
+                self.record_shapes,
+                False,
+                False,
+                False,
+                False,
+                _ExperimentalConfig(),
+            ),
+            set(),
+        )
+        return self
+
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        if not self.enabled:
+            return
+        _disable_profiler()
+        _run_on_profiler_stop()
+        return False
+
+
+class emit_nvtx:
+    """Context manager that makes every autograd operation emit an NVTX range.
+
+    It is useful when running the program under nvprof::
+
+        nvprof --profile-from-start off -o trace_name.prof -- <regular command here>
+
+    Unfortunately, there's no way to force nvprof to flush the data it collected
+    to disk, so for CUDA profiling one has to use this context manager to annotate
+    nvprof traces and wait for the process to exit before inspecting them.
+    Then, either NVIDIA Visual Profiler (nvvp) can be used to visualize the timeline, or
+    :func:`torch.autograd.profiler.load_nvprof` can load the results for inspection
+    e.g. in Python REPL.
+
+    .. warning:
+        This context manager should not be called recursively, i.e. at most one
+        instance should be enabled at any given time.
+
+    Args:
+        enabled (bool, optional): Setting ``enabled=False`` makes this context manager a no-op.
+            Default: ``True``.
+        record_shapes (bool, optional): If ``record_shapes=True``, the nvtx range wrapping
+            each autograd op will append information about the sizes of Tensor arguments received
+            by that op, in the following format:
+            ``[[arg0.size(0), arg0.size(1), ...], [arg1.size(0), arg1.size(1), ...], ...]``
+            Non-tensor arguments will be represented by ``[]``.
+            Arguments will be listed in the order they are received by the backend op.
+            Please note that this order may not match the order in which those arguments were passed
+            on the Python side.  Also note that shape recording may increase the overhead of nvtx range creation.
+            Default: ``False``
+
+    Example:
+        >>> # xdoctest: +SKIP("undefined variables")
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_AUTOGRAD_PROFILER)
+        >>> with torch.cuda.profiler.profile():
+        ...     model(x)  # Warmup CUDA memory allocator and profiler
+        ...     with torch.autograd.profiler.emit_nvtx():
+        ...         model(x)
+
+    **Forward-backward correlation**
+
+    When viewing a profile created using :class:`emit_nvtx` in the Nvidia Visual Profiler,
+    correlating each backward-pass op with the corresponding forward-pass op can be difficult.
+    To ease this task, :class:`emit_nvtx` appends sequence number information to the ranges it
+    generates.
+
+    During the forward pass, each function range is decorated with ``seq=<N>``.  ``seq`` is a running
+    counter, incremented each time a new backward Function object is created and stashed for backward.
+    Thus, the ``seq=<N>`` annotation associated with each forward function range tells you that
+    if a backward Function object is created by this forward function,
+    the backward object will receive sequence number N.
+    During the backward pass, the top-level range wrapping each C++ backward Function's
+    ``apply()`` call is decorated with ``stashed seq=<M>``.  ``M`` is the sequence number that
+    the backward object was created with.  By comparing ``stashed seq`` numbers in backward with ``seq``
+    numbers in forward, you can track down which forward op created each backward Function.
+
+    Any functions executed during the backward pass are also decorated with ``seq=<N>``.  During
+    default backward (with ``create_graph=False``) this information is irrelevant, and in fact,
+    ``N`` may simply be 0 for all such functions.  Only the top-level ranges associated with
+    backward Function objects' ``apply()`` methods are useful, as a way to correlate these Function
+    objects with the earlier forward pass.
+
+    **Double-backward**
+
+    If, on the other hand, a backward pass with ``create_graph=True`` is underway (in other words,
+    if you are setting up for a double-backward), each function's execution during backward
+    is given a nonzero, useful ``seq=<N>``.  Those functions may themselves create Function objects
+    to be executed later during double-backward, just as the original functions in the forward pass did.
+    The relationship between backward and double-backward is conceptually the same as the relationship
+    between forward and backward: The functions still emit current-sequence-number-tagged ranges,
+    the Function objects they create still stash those sequence numbers, and during the eventual
+    double-backward, the Function objects' ``apply()`` ranges are still tagged with ``stashed seq``
+    numbers, which can be compared to `seq` numbers from the backward pass.
+
+    .. warning:
+        The sequence number is thread-local, and some forward functions don't create an associated
+        backward Function object (instead delegating that to sub-functions further down the call chain).
+        For these reasons, the correspondence of stashed sequence numbers in
+        backward Function ``apply()`` ranges with `seq` numbers in forward-pass ranges is
+        not guaranteed to be 1 to 1.  The sequence numbers alone may not be enough to fully
+        disambiguate which forward function created which
+        backward Function object.  You may need to make a judgment based on analytic knowledge of what
+        the expected correspondence should be.
+    """
+
+    def __init__(self, enabled=True, record_shapes=False):
+        self.enabled = enabled
+        self.entered = False
+        self.record_shapes = record_shapes
+
+    def __enter__(self):
+        if not self.enabled:
+            return
+        if self.entered:
+            raise RuntimeError("NVTX annotation context manager is not reentrant")
+        self.entered = True
+        torch.cuda.synchronize()
+        _run_on_profiler_start()
+        _enable_profiler(
+            ProfilerConfig(
+                ProfilerState.NVTX,
+                self.record_shapes,
+                False,
+                False,
+                False,
+                False,
+                _ExperimentalConfig(),
+            ),
+            set(),
+        )
+        return self
+
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        if not self.enabled:
+            return
+        torch.cuda.synchronize()
+        _disable_profiler()
+        _run_on_profiler_stop()
+        return False
+
+
+def load_nvprof(path):
+    """Open an nvprof trace file and parses autograd annotations.
+
+    Args:
+        path (str): path to nvprof trace
+    """
+    return EventList(parse_nvprof_trace(path))
+
+
+class EnforceUnique:
+    """Raises an error if a key is seen more than once."""
+
+    def __init__(self):
+        self.seen = set()
+
+    def see(self, *key):
+        r"""
+        Observe a key and raise an error if it is seen multiple times.
+        """
+        if key in self.seen:
+            raise RuntimeError("duplicate key: " + str(key))
+        self.seen.add(key)
+
+
+def parse_nvprof_trace(path):
+    import sqlite3
+
+    conn = sqlite3.connect(path)
+    conn.row_factory = sqlite3.Row
+
+    # Parse strings table
+    strings = {}
+    for r in conn.execute("SELECT _id_ as id, value FROM StringTable"):
+        strings[r["id"]] = torch._C._demangle(r["value"])
+
+    # First, find all functions and create FunctionEvents for them
+    marker_query = """
+    SELECT
+        start.id AS marker_id, start.name, start.timestamp AS start_time, end.timestamp AS end_time
+    FROM
+        CUPTI_ACTIVITY_KIND_MARKER AS start INNER JOIN CUPTI_ACTIVITY_KIND_MARKER AS end
+        ON start.id = end.id
+    WHERE
+        start.name != 0 AND end.name = 0
+    """
+    functions = []
+    functions_map = {}
+    unique = EnforceUnique()
+    for row in conn.execute(marker_query):
+        unique.see(row["marker_id"])
+        evt = FunctionEvent(
+            id=row["marker_id"],
+            node_id=0,  # missing a node_id when calling FunctionEvent. This is just to ensure
+            # that pytorch doesn't crash when creating a FunctionEvent() object
+            name=strings[row["name"]],
+            start_us=row["start_time"],
+            end_us=row["end_time"],
+            thread=0,
+        )  # TODO: find in sqlite database
+        functions.append(evt)
+        functions_map[evt.id] = evt
+
+    # Now, correlate all kernels with FunctionEvents
+    kernel_query = """
+    SELECT
+        start.id AS marker_id, start.name, start.timestamp, end.timestamp,
+        runtime._id_ AS runtime_id, runtime.cbid, runtime.start AS runtime_start, runtime.end AS runtime_end,
+        kernel.start AS kernel_start, kernel.end AS kernel_end, kernel.name AS kernel_name
+    FROM
+        CUPTI_ACTIVITY_KIND_MARKER AS start
+        INNER JOIN CUPTI_ACTIVITY_KIND_MARKER AS end
+            ON start.id = end.id
+        INNER JOIN CUPTI_ACTIVITY_KIND_RUNTIME as runtime
+            ON (start.timestamp < runtime.start AND runtime.end < end.timestamp)
+        INNER JOIN CUPTI_ACTIVITY_KIND_CONCURRENT_KERNEL AS kernel
+            ON kernel.correlationId = runtime.correlationId
+    """
+    unique = EnforceUnique()
+    for row in conn.execute(kernel_query):
+        unique.see(row["marker_id"], row["runtime_id"])
+        # 211 is cudaKernelLaunch for cuda >= 9.2
+        assert row["cbid"] == 211
+        evt = functions_map[row["marker_id"]]
+        evt.append_kernel(
+            row["kernel_name"], 0, row["kernel_end"] - row["kernel_start"]
+        )
+
+    functions.sort(key=lambda evt: evt.time_range.start)
+    return functions
+
+
+class KinetoStepTracker:
+    """Provides an abstraction for incrementing the step count globally.
+
+    Previously, we only had one place to mark that a step() has occurred
+    in the program via pytorch profiler step(). We will now add step hooks
+    in the Optimizer class https://github.com/pytorch/pytorch/issues/88446
+
+    - This could mean programs that already call profiler.step() every
+      iteration can end up double incrementing step count.
+    - If a model uses multiple optimizers we can also have double or more
+      counting of the step.
+
+    We fix this by adding a layer of abstraction before calling step()
+    to the kineto library. The idea is to maintain steps per requester in a dict:
+
+    .. code-block::
+
+        {
+           "ProfilerStep": 100,  # triggered by profiler step() call
+           "Optimizer1Step": 100,   # Optimizer 1 or 2 are just examples, could be SGD, Adam etc
+           "Optimizer2Step": 100,
+        }
+
+    To figure out the global step count just take the max of dict values (100).
+
+    If one of the count increments the max will go up.
+
+    .. code-block::
+
+        {
+           "ProfilerStep": 100,
+           "Optimizer1Step": 101,   # Optimizer1 got incremented first say
+           "Optimizer2Step": 100,
+        }
+
+    Then global step count is 101
+    We only call the kineto step() function when global count increments.
+
+    NOTE: Please do not use the KinetoStepTracker in modules beside the Optimizer
+    for now. The result could be incorrect increments of the step count.
+    """
+
+    _current_step = 0
+    _step_dict: Dict[str, int] = defaultdict(int)
+
+    @classmethod
+    def init_step_count(cls, requester: str):
+        r"""
+        Initialize for a given requester.
+        """
+        cls._step_dict[requester] = cls._current_step
+
+    @classmethod
+    def erase_step_count(cls, requester: str) -> bool:
+        r"""
+        Remove a given requester.
+        """
+        return cls._step_dict.pop(requester, None) is not None
+
+    @classmethod
+    def increment_step(cls, requester: str) -> int:
+        """Increments the step count for the requester.
+
+        Additionally if the max over all step counts has incremented then
+        trigger the _kineto_step() returns global step count
+        """
+        if requester not in cls._step_dict:
+            cls.init_step_count(requester)
+        cls._step_dict[requester] += 1
+
+        new_step = max(cls._step_dict.values())
+        if new_step > cls._current_step:
+            delta = new_step - cls._current_step
+            if delta > 1:
+                warn(
+                    "Profiler step count has increased more than 1 - "
+                    f"current_step = {cls._current_step} step dict =  {cls._step_dict}"
+                )
+            for _ in range(0, delta):
+                _kineto_step()
+            cls._current_step = new_step
+        return cls._current_step
+
+    @classmethod
+    def current_step(cls) -> int:
+        r"""
+        Get the latest step for any requester
+        """
+        return cls._current_step

venv/lib/python3.10/site-packages/torch/autograd/profiler_legacy.py

@@ -0,0 +1,303 @@
+import itertools
+from warnings import warn
+
+import torch
+import torch.cuda
+
+from torch.autograd import (
+    _disable_profiler_legacy,
+    _enable_profiler_legacy,
+    DeviceType,
+    ProfilerConfig,
+    ProfilerState,
+)
+from torch.autograd.profiler_util import (
+    _filter_name,
+    _filter_stack_entry,
+    _rewrite_name,
+    EventList,
+    FunctionEvent,
+    MEMORY_EVENT_NAME,
+)
+
+__all__ = ["profile"]
+
+
+class profile:
+    """DEPRECATED: use torch.profiler instead."""
+
+    def __init__(
+        self,
+        enabled=True,
+        *,
+        use_cuda=False,
+        record_shapes=False,
+        with_flops=False,
+        profile_memory=False,
+        with_stack=False,
+        with_modules=False,
+    ):
+        self.enabled: bool = enabled
+        if not self.enabled:
+            return
+        self.use_cuda = use_cuda
+        self.function_events = None
+        self.entered = False
+        self.record_shapes = record_shapes
+        self.with_flops = with_flops
+        self.record_shapes |= self.with_flops
+        self.profile_memory = profile_memory
+        self.with_stack = with_stack
+        self.with_modules = with_modules
+
+        if self.use_cuda and not torch.cuda.is_available():
+            warn("CUDA is not available, disabling CUDA profiling")
+            self.use_cuda = False
+
+        if self.use_cuda:
+            self.profiler_kind = ProfilerState.CUDA
+        else:
+            self.profiler_kind = ProfilerState.CPU
+
+    def config(self):
+        return ProfilerConfig(
+            self.profiler_kind,
+            self.record_shapes,
+            self.profile_memory,
+            self.with_stack,
+            self.with_flops,
+            self.with_modules,
+            # avoid exposing _ExperimentalConfig this in legacy public API
+            torch._C._profiler._ExperimentalConfig(),
+        )
+
+    def __enter__(self):
+        if not self.enabled:
+            return
+        if self.entered:
+            raise RuntimeError("Profiler context manager is not reentrant")
+        self.entered = True
+        self._start_trace()
+        return self
+
+    def _start_trace(self):
+        _enable_profiler_legacy(self.config())
+
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        if not self.enabled:
+            return
+        if self.use_cuda:
+            torch.cuda.synchronize()
+
+        records = _disable_profiler_legacy()
+        parsed_results = _parse_legacy_records(records)
+        self.function_events = EventList(
+            parsed_results,
+            use_cuda=self.use_cuda,
+            profile_memory=self.profile_memory,
+            with_flops=self.with_flops,
+        )
+        self.function_events._build_tree()
+        return False
+
+    def __repr__(self):
+        if self.function_events is None:
+            return "<unfinished profiler_legacy.profile>"
+        return repr(self.function_events)
+
+    def __str__(self):
+        if self.function_events is None:
+            return "<unfinished profile.profiler_legacy.profile>"
+        return str(self.function_events)
+
+    def _check_finish(self):
+        if self.function_events is None:
+            raise RuntimeError("Profiler didn't finish running")
+
+    def table(
+        self,
+        sort_by=None,
+        row_limit=100,
+        max_src_column_width=75,
+        max_name_column_width=55,
+        max_shapes_column_width=80,
+        header=None,
+        top_level_events_only=False,
+    ):
+        self._check_finish()
+        assert self.function_events is not None
+        return self.function_events.table(
+            sort_by=sort_by,
+            row_limit=row_limit,
+            max_src_column_width=max_src_column_width,
+            max_name_column_width=max_name_column_width,
+            max_shapes_column_width=max_shapes_column_width,
+            header=header,
+            top_level_events_only=top_level_events_only,
+        )
+
+    table.__doc__ = EventList.table.__doc__
+
+    def export_chrome_trace(self, path):
+        self._check_finish()
+        assert self.function_events is not None
+        return self.function_events.export_chrome_trace(path)
+
+    export_chrome_trace.__doc__ = EventList.export_chrome_trace.__doc__
+
+    def export_stacks(self, path: str, metric: str = "self_cpu_time_total"):
+        self._check_finish()
+        assert self.function_events is not None, "Expected profiling results"
+        assert self.with_stack, "export_stacks() requires with_stack=True"
+        return self.function_events.export_stacks(path, metric)
+
+    def key_averages(self, group_by_input_shape=False, group_by_stack_n=0):
+        self._check_finish()
+        assert self.function_events is not None, "Expected profiling results"
+        return self.function_events.key_averages(group_by_input_shape, group_by_stack_n)
+
+    key_averages.__doc__ = EventList.key_averages.__doc__
+
+    def total_average(self):
+        self._check_finish()
+        assert self.function_events is not None, "Expected profiling results"
+        return self.function_events.total_average()
+
+    total_average.__doc__ = EventList.total_average.__doc__
+
+    @property
+    def self_cpu_time_total(self):
+        """Return CPU time as the sum of self times across all events."""
+        self._check_finish()
+        assert self.function_events is not None
+        return self.function_events.self_cpu_time_total
+
+
+def _parse_legacy_records(thread_records):
+    def _get_record_key(record):
+        """Return a tuple for correlating start and end records in `_parse_legacy_records`."""
+        return (record.handle(), record.node_id())
+
+    next_id = 0
+    start_record = None
+    functions = []
+    record_stack = []
+
+    # '__start_profile' is not guaranteed to be first, so we must find it here
+    for record in itertools.chain.from_iterable(thread_records):
+        name = record.name()
+        if start_record is None and name == "__start_profile":
+            start_record = record
+
+    assert start_record is not None and not start_record.is_remote()
+
+    for thread_record_list in thread_records:
+        # accumulated memory allocations per handle
+        cpu_memory_allocs = {}
+        cuda_memory_allocs = {}
+        # ranges per handle
+        range_starts = {}
+
+        filtered_handles = set()
+        prev_record = None
+        for record in thread_record_list:
+            record_key = _get_record_key(record)
+            if _filter_name(record.name()) or record_key in filtered_handles:
+                filtered_handles.add(record_key)
+                continue
+
+            if record.kind() == "push":
+                # workaround to reduce double logging from operator
+                # wrappers and redispatch
+                if prev_record is not None:
+                    duplicate = (
+                        prev_record.name() == record.name()
+                        and prev_record.kind() == record.kind()
+                        and prev_record.node_id() == record.node_id()
+                    )
+                    if duplicate:
+                        filtered_handles.add(record_key)
+                        continue
+
+                range_starts[record_key] = record
+                cpu_memory_allocs[record_key] = 0
+                cuda_memory_allocs[record_key] = 0
+            elif record.kind() == "pop":
+                assert (
+                    record_key in range_starts
+                ), f"""Expected record with key {record_key} to exist in range_starts.
+                    This means that the pop event did not have a corresponding push."""
+
+                start = range_starts[record_key]
+
+                cpu_memory_usage = cpu_memory_allocs[record_key]
+                cuda_memory_usage = cuda_memory_allocs[record_key]
+                is_async = start.is_async() or (start.thread_id() != record.thread_id())
+                is_remote_event = record.is_remote()
+                start_flops = start.flops()
+
+                fe = FunctionEvent(
+                    id=record.handle(),
+                    node_id=record.node_id(),
+                    name=_rewrite_name(name=start.name(), with_wildcard=True),
+                    trace_name=_rewrite_name(name=start.name(), with_wildcard=False),
+                    thread=start.thread_id(),
+                    start_us=start_record.cpu_elapsed_us(start),
+                    end_us=start_record.cpu_elapsed_us(record),
+                    fwd_thread=start.fwd_thread_id(),
+                    input_shapes=start.shapes(),
+                    stack=[
+                        entry for entry in start.stack() if _filter_stack_entry(entry)
+                    ],
+                    scope=start.scope(),
+                    cpu_memory_usage=cpu_memory_usage,
+                    cuda_memory_usage=cuda_memory_usage,
+                    is_async=is_async,
+                    is_remote=is_remote_event,
+                    sequence_nr=start.sequence_nr(),
+                    device_type=DeviceType.CPU,
+                    is_legacy=True,
+                    flops=start_flops,
+                )
+                # note: async events have only cpu total time
+                if not is_async and start.has_cuda():
+                    duration = start.cuda_elapsed_us(record)
+                    if duration > 0:
+                        fe.append_kernel(start.name(), start.device(), duration)
+                functions.append(fe)
+                del range_starts[record_key]
+                del cpu_memory_allocs[record_key]
+                del cuda_memory_allocs[record_key]
+            elif record.kind() == "memory_alloc":
+                num_open_handles_cpu = len(cpu_memory_allocs)
+                num_open_handles_cuda = len(cuda_memory_allocs)
+                assert num_open_handles_cpu == num_open_handles_cuda
+                for handle in cpu_memory_allocs.keys():
+                    cpu_memory_allocs[handle] += record.cpu_memory_usage()
+                for handle in cuda_memory_allocs.keys():
+                    cuda_memory_allocs[handle] += record.cuda_memory_usage()
+                if num_open_handles_cpu == 0:
+                    # output event as a top-level memory event
+                    fe = FunctionEvent(
+                        id=0,
+                        name=MEMORY_EVENT_NAME,
+                        trace_name=None,
+                        thread=0,
+                        start_us=0,
+                        end_us=0,
+                        stack=[],
+                        cpu_memory_usage=record.cpu_memory_usage(),
+                        cuda_memory_usage=record.cuda_memory_usage(),
+                        is_legacy=True,
+                    )
+                    functions.append(fe)
+            prev_record = record
+
+    # Sort functions by start time then by end time ascending.
+    # This ensures that--in the case of nested events which
+    # have the same start time (which may happen due to the
+    # granularity of the given clock tick)--we always show
+    # the outermost nested call first. This adds stability
+    # in how FunctionEvents appear
+    functions.sort(key=lambda evt: [evt.time_range.start, -evt.time_range.end])
+    return functions

venv/lib/python3.10/site-packages/torch/autograd/profiler_util.py

@@ -0,0 +1,1178 @@
+import bisect
+import itertools
+import math
+
+from collections import defaultdict, namedtuple
+from operator import attrgetter
+
+from typing import Any, Dict, List, Optional, Tuple
+
+import torch
+from torch.autograd import DeviceType
+
+__all__ = [
+    "EventList",
+    "FormattedTimesMixin",
+    "Interval",
+    "Kernel",
+    "FunctionEvent",
+    "FunctionEventAvg",
+    "StringTable",
+    "MemRecordsAcc",
+]
+
+
+class EventList(list):
+    """A list of Events (for pretty printing)."""
+
+    def __init__(self, *args, **kwargs):
+        use_cuda = kwargs.pop("use_cuda", True)
+        use_device = kwargs.pop("use_device", None)
+        profile_memory = kwargs.pop("profile_memory", False)
+        with_flops = kwargs.pop("with_flops", False)
+        super().__init__(*args, **kwargs)
+        self._use_cuda = use_cuda
+        self._use_device = use_device
+        self._profile_memory = profile_memory
+        self._tree_built = False
+        self._with_flops = with_flops
+
+    def _build_tree(self):
+        self._populate_cpu_children()
+        self._remove_dup_nodes()
+        self._set_backward_stacktraces()
+        self._tree_built = True
+
+    def __str__(self):
+        return self.table()
+
+    def _remove_dup_nodes(self):
+        while True:
+            to_delete = set()
+            for idx in range(len(self)):
+                if (
+                    self[idx].cpu_parent is not None
+                    and self[idx].cpu_parent.name == self[idx].name
+                    and len(self[idx].cpu_parent.cpu_children) == 1
+                ):
+                    self[idx].cpu_parent.cpu_children = self[idx].cpu_children
+                    self[idx].cpu_parent.kernels = self[idx].kernels  # lift kernels up
+                    for ch in self[idx].cpu_children:
+                        ch.cpu_parent = self[idx].cpu_parent
+                    to_delete.add(idx)
+            if len(to_delete) == 0:
+                break
+            new_evts = [ev for ind, ev in enumerate(self) if ind not in to_delete]
+            self.clear()
+            self.extend(new_evts)
+
+    def _populate_cpu_children(self):
+        """Populate child events into each underlying FunctionEvent object.
+
+        One event is a child of another if [s1, e1) is inside [s2, e2). Where
+        s1 and e1 would be start and end of the child event's interval. And
+        s2 and e2 start and end of the parent event's interval
+
+        Example: In event list [[0, 10], [1, 3], [3, 4]] would have make [0, 10]
+        be a parent of two other intervals.
+
+        If for any reason two intervals intersect only partially, this function
+        will not record a parent child relationship between then.
+        """
+        # Some events can be async (i.e. start and end on different threads),
+        # since it's generally undefined how to attribute children ranges to
+        # async ranges, we do not use them when calculating nested ranges and stats
+        sync_events = [
+            evt
+            for evt in self
+            if not evt.is_async and evt.device_type == DeviceType.CPU
+        ]
+        events = sorted(
+            sync_events,
+            key=attrgetter("thread"),
+        )
+        # Group by both thread and node_id, so that events that happen to have
+        # the same thread_id but are from different nodes aren't incorrectly
+        # grouped together.
+        threads = itertools.groupby(
+            events, key=lambda event: (event.thread, event.node_id)
+        )
+
+        # For each thread we keep a stack of current nested parents.
+        # We maintain the invariant that each interval is a subset of all other
+        # intervals lower in the stack.
+        #
+        # First we sort the intervals by their start time. Then we iterate over them.
+        # Every time we see a new interval we remove several parents from
+        # the top until we restore the invariant. Then parent child relationship
+        # if recorded if the stack is not empty.
+        # Finally we add new interval to the list
+        #
+        # Algorithm has O(N * log(N)) complexity where N is number of
+        # intervals
+        for thread_id, thread_events in threads:
+            thread_events_ = sorted(
+                thread_events,
+                key=lambda event: [event.time_range.start, -event.time_range.end],
+            )
+            current_events: List[FunctionEvent] = []
+            cur_end = 0
+            for event in thread_events_:
+                while len(current_events) > 0:
+                    parent = current_events[-1]
+                    if (
+                        event.time_range.start >= parent.time_range.end
+                        or event.time_range.end > parent.time_range.end
+                    ):
+                        # this can't be a parent
+                        current_events.pop()
+                    else:
+                        parent.append_cpu_child(event)
+                        assert (
+                            event.cpu_parent is None
+                        ), f"There is already a CPU parent event for {event.key}"
+                        event.set_cpu_parent(parent)
+                        break
+
+                current_events.append(event)
+
+    def _set_backward_stacktraces(self):
+        def bw_parent(evt):
+            if evt is None:
+                return None
+            elif evt.scope == 1:  # BACKWARD_FUNCTION
+                return evt
+            else:
+                return bw_parent(evt.cpu_parent)
+
+        fwd_stacks = {}
+        for evt in self:
+            if bw_parent(evt) is None and evt.stack is not None:
+                t = (evt.sequence_nr, evt.thread)
+                if t not in fwd_stacks:
+                    fwd_stacks[t] = evt.stack
+
+        for evt in self:
+            p = bw_parent(evt)
+            if p is not None:
+                assert p.fwd_thread is not None
+                t = (p.sequence_nr, p.fwd_thread)
+                if t in fwd_stacks:
+                    evt.stack = fwd_stacks[t]
+                else:
+                    evt.stack = []
+
+    @property
+    def self_cpu_time_total(self):
+        return sum([event.self_cpu_time_total for event in self])
+
+    def table(
+        self,
+        sort_by=None,
+        row_limit=100,
+        max_src_column_width=75,
+        max_name_column_width=55,
+        max_shapes_column_width=80,
+        header=None,
+        top_level_events_only=False,
+    ):
+        """Print an EventList as a nicely formatted table.
+
+        Args:
+            sort_by (str, optional): Attribute used to sort entries. By default
+                they are printed in the same order as they were registered.
+                Valid keys include: ``cpu_time``, ``cuda_time``, ``cpu_time_total``,
+                ``cuda_time_total``, ``cpu_memory_usage``, ``cuda_memory_usage``,
+                ``self_cpu_memory_usage``, ``self_cuda_memory_usage``, ``count``.
+            top_level_events_only(bool, optional): Boolean flag to determine the
+                selection of events to display. If true, the profiler will only
+                display events at top level like top-level invocation of python
+                `lstm`, python `add` or other functions, nested events like low-level
+                cpu/cuda ops events are omitted for profiler result readability.
+
+        Returns:
+            A string containing the table.
+        """
+        return _build_table(
+            self,
+            sort_by=sort_by,
+            row_limit=row_limit,
+            max_src_column_width=max_src_column_width,
+            max_name_column_width=max_name_column_width,
+            max_shapes_column_width=max_shapes_column_width,
+            header=header,
+            profile_memory=self._profile_memory,
+            with_flops=self._with_flops,
+            top_level_events_only=top_level_events_only,
+        )
+
+    def export_chrome_trace(self, path):
+        """Export an EventList as a Chrome tracing tools file.
+
+        The checkpoint can be later loaded and inspected under ``chrome://tracing`` URL.
+
+        Args:
+            path (str): Path where the trace will be written.
+        """
+        import os
+
+        device_name = "cuda" if not self._use_device else self._use_device
+        with open(path, "w") as f:
+            chrome_events = []
+            next_id = 0
+            # Use file IO over using json.dump since JSON dumping is very slow and
+            # this technique is proven to give a 4x speedup.
+            f.write("[")
+            for evt in self:
+                if evt.trace_name is None:
+                    continue
+                f.write(
+                    '{{"name": "{}", '
+                    '"ph": "X", '
+                    '"ts": {}, '
+                    '"dur": {}, '
+                    '"tid": {}, '
+                    '"pid": "CPU functions", '
+                    '"args": {{}}}}, '.format(
+                        evt.trace_name,
+                        evt.time_range.start,
+                        evt.time_range.elapsed_us(),
+                        evt.thread
+                        if not evt.is_remote
+                        else f'" node_id:{evt.node_id}, thread_id:{evt.thread} "',
+                    )
+                )
+                for k in evt.kernels:
+                    # 's' and 'f' draw Flow arrows from
+                    # the CPU launch to the GPU kernel
+                    f.write(
+                        f'{{"name": "{evt.trace_name}", '
+                        '"ph": "s", '
+                        f'"ts": {evt.time_range.start}, '
+                        f'"tid": {evt.thread}, '
+                        '"pid": "CPU functions", '
+                        f'"id": {next_id}, '
+                        f'"cat": "cpu_to_{device_name}", '
+                        '"args": {}}, '
+                    )
+                    # Note: use torch.profiler to get device kernel trace
+                    next_id += 1
+            if len(self) > 0:
+                # remove trailing whitespace and comma
+                f.seek(f.tell() - 2, os.SEEK_SET)
+                f.truncate()
+            f.write("]")
+
+    def supported_export_stacks_metrics(self):
+        return [
+            "self_cpu_time_total",
+            "self_cuda_time_total",
+            "self_privateuse1_time_total",
+        ]
+
+    def export_stacks(self, path: str, metric: str):
+        if metric not in self.supported_export_stacks_metrics():
+            raise ValueError(
+                "metric should be one of: "
+                + str(self.supported_export_stacks_metrics())
+            )
+        translate_table = str.maketrans(" ;\t\n", "____")
+        with open(path, "w") as f:
+            for evt in self:
+                if evt.stack and len(evt.stack) > 0:
+                    metric_value = getattr(evt, metric)
+                    if int(metric_value) > 0:
+                        stack_str = ""
+                        for entry in reversed(evt.stack):
+                            stack_str += entry.translate(translate_table)
+                            stack_str += ";"
+                        stack_str = stack_str[:-1] + " " + str(int(metric_value))
+                        f.write(stack_str + "\n")
+
+    def key_averages(self, group_by_input_shapes=False, group_by_stack_n=0):
+        """Averages all function events over their keys.
+
+        Args:
+            group_by_input_shapes: group entries by
+                (event name, input shapes) rather than just event name.
+                This is useful to see which input shapes contribute to the runtime
+                the most and may help with size-specific optimizations or
+                choosing the best candidates for quantization (aka fitting a roof line)
+
+            group_by_stack_n: group by top n stack trace entries
+
+        Returns:
+            An EventList containing FunctionEventAvg objects.
+        """
+        assert self._tree_built
+        stats: Dict[Tuple[str, ...], FunctionEventAvg] = defaultdict(FunctionEventAvg)
+
+        def get_key(event, group_by_input_shapes, group_by_stack_n) -> Tuple[str, ...]:
+            key = [
+                str(event.key),
+                str(event.node_id),
+                str(event.device_type),
+                str(event.is_legacy),
+            ]
+            if group_by_input_shapes:
+                key.append(str(event.input_shapes))
+            if group_by_stack_n > 0:
+                key += event.stack[:group_by_stack_n]
+            return tuple(key)
+
+        for evt in self:
+            stats[get_key(evt, group_by_input_shapes, group_by_stack_n)].add(evt)
+
+        avg_list = EventList(
+            stats.values(),
+            use_cuda=self._use_cuda,
+            use_device=self._use_device,
+            profile_memory=self._profile_memory,
+            with_flops=self._with_flops,
+        )
+        for evt in avg_list:
+            evt.stack = evt.stack[:group_by_stack_n]
+            if not group_by_input_shapes:
+                evt.input_shapes = ""
+        return avg_list
+
+    def total_average(self):
+        """Averages all events.
+
+        Returns:
+            A FunctionEventAvg object.
+        """
+        total_stat = FunctionEventAvg()
+        for evt in self:
+            total_stat += evt
+            total_stat.key = None
+        total_stat.key = "Total"
+        return total_stat
+
+
+def _format_time(time_us):
+    """Define how to format time in FunctionEvent."""
+    US_IN_SECOND = 1000.0 * 1000.0
+    US_IN_MS = 1000.0
+    if time_us >= US_IN_SECOND:
+        return f"{time_us / US_IN_SECOND:.3f}s"
+    if time_us >= US_IN_MS:
+        return f"{time_us / US_IN_MS:.3f}ms"
+    return f"{time_us:.3f}us"
+
+
+def _format_time_share(time_us, total_time_us):
+    """Define how to format time in FunctionEvent."""
+    if total_time_us == 0:
+        assert time_us == 0, f"Expected time_us == 0 but got {time_us}"
+        return "NaN"
+    return f"{time_us * 100.0 / total_time_us:.2f}%"
+
+
+def _format_memory(nbytes):
+    """Return a formatted memory size string."""
+    KB = 1024
+    MB = 1024 * KB
+    GB = 1024 * MB
+    if abs(nbytes) >= GB:
+        return f"{nbytes * 1.0 / GB:.2f} Gb"
+    elif abs(nbytes) >= MB:
+        return f"{nbytes * 1.0 / MB:.2f} Mb"
+    elif abs(nbytes) >= KB:
+        return f"{nbytes * 1.0 / KB:.2f} Kb"
+    else:
+        return str(nbytes) + " b"
+
+
+def _attr_formatter(name):
+    return property(lambda self: _format_time(getattr(self, name)))
+
+
+class FormattedTimesMixin:
+    """Helpers for FunctionEvent and FunctionEventAvg.
+
+    The subclass should define `*_time_total` and `count` attributes.
+    """
+
+    cpu_time_str = _attr_formatter("cpu_time")
+    cuda_time_str = _attr_formatter("cuda_time")
+    privateuse1_time_str = _attr_formatter("privateuse1_time")
+    cpu_time_total_str = _attr_formatter("cpu_time_total")
+    cuda_time_total_str = _attr_formatter("cuda_time_total")
+    privateuse1_time_total_str = _attr_formatter("privateuse1_time_total")
+    self_cpu_time_total_str = _attr_formatter("self_cpu_time_total")
+    self_cuda_time_total_str = _attr_formatter("self_cuda_time_total")
+    self_privateuse1_time_total_str = _attr_formatter("self_privateuse1_time_total")
+
+    @property
+    def cpu_time(self):
+        return 0.0 if self.count == 0 else 1.0 * self.cpu_time_total / self.count  # type: ignore[attr-defined]
+
+    @property
+    def cuda_time(self):
+        return 0.0 if self.count == 0 else 1.0 * self.cuda_time_total / self.count  # type: ignore[attr-defined]
+
+    @property
+    def privateuse1_time(self):
+        return 0.0 if self.count == 0 else 1.0 * self.privateuse1_time_total / self.count  # type: ignore[attr-defined]
+
+
+class Interval:
+    def __init__(self, start, end):
+        self.start = start
+        self.end = end
+
+    def elapsed_us(self):
+        r"""
+        Returns the length of the interval
+        """
+        return self.end - self.start
+
+
+Kernel = namedtuple("Kernel", ["name", "device", "duration"])
+
+
+class FunctionEvent(FormattedTimesMixin):
+    """Profiling information about a single function."""
+
+    def __init__(
+        self,
+        id,
+        name,
+        thread,
+        start_us,
+        end_us,
+        fwd_thread=None,
+        input_shapes=None,
+        stack=None,
+        scope=0,
+        use_device=None,
+        cpu_memory_usage=0,
+        cuda_memory_usage=0,
+        privateuse1_memory_usage=0,
+        is_async=False,
+        is_remote=False,
+        sequence_nr=-1,
+        node_id=-1,
+        device_type=DeviceType.CPU,
+        device_index=0,
+        is_legacy=False,
+        flops=None,
+        trace_name=None,
+        concrete_inputs=None,
+    ):
+        self.id: int = id
+        self.node_id: int = node_id
+        self.name: str = name
+        self.trace_name: str = trace_name
+        self.time_range: Interval = Interval(start_us, end_us)
+        self.thread: int = thread
+        self.fwd_thread: Optional[int] = fwd_thread
+        self.kernels: List[Kernel] = []
+        self.count: int = 1
+        self.cpu_children: List[FunctionEvent] = []
+        self.cpu_parent: Optional[FunctionEvent] = None
+        self.input_shapes: Tuple[int, ...] = input_shapes
+        self.concrete_inputs: List[Any] = concrete_inputs
+        self.stack: List = stack
+        self.scope: int = scope
+        self.use_device: Optional[str] = use_device
+        self.cpu_memory_usage: int = cpu_memory_usage
+        self.cuda_memory_usage: int = cuda_memory_usage
+        self.privateuse1_memory_usage: int = privateuse1_memory_usage
+        self.is_async: bool = is_async
+        self.is_remote: bool = is_remote
+        self.sequence_nr: int = sequence_nr
+        self.device_type: DeviceType = device_type
+        self.device_index: int = device_index
+        self.is_legacy: bool = is_legacy
+        self.flops: Optional[int] = flops
+
+    def append_kernel(self, name, device, duration):
+        assert self.device_type == DeviceType.CPU
+        self.kernels.append(Kernel(name, device, duration))
+
+    def append_cpu_child(self, child):
+        """Append a CPU child of type FunctionEvent.
+
+        One is supposed to append only direct children to the event to have
+        correct self cpu time being reported.
+        """
+        assert self.device_type == DeviceType.CPU
+        assert isinstance(child, FunctionEvent)
+        assert child.device_type == DeviceType.CPU
+        self.cpu_children.append(child)
+
+    def set_cpu_parent(self, parent):
+        """Set the immediate CPU parent of type FunctionEvent.
+
+        One profiling FunctionEvent should have only one CPU parent such that
+        the child's range interval is completely inside the parent's. We use
+        this connection to determine the event is from top-level op or not.
+        """
+        assert self.device_type == DeviceType.CPU
+        assert isinstance(parent, FunctionEvent)
+        assert parent.device_type == DeviceType.CPU
+        self.cpu_parent = parent
+
+    # Note: async events don't have children, are not used when computing 'self'
+    # metrics of other events, have only total cpu time
+    @property
+    def self_cpu_memory_usage(self):
+        if self.is_async or self.device_type != DeviceType.CPU:
+            return 0
+        return self.cpu_memory_usage - sum(
+            [child.cpu_memory_usage for child in self.cpu_children]
+        )
+
+    @property
+    def self_cuda_memory_usage(self):
+        if self.is_async or self.device_type != DeviceType.CPU:
+            return 0
+        return self.cuda_memory_usage - sum(
+            [child.cuda_memory_usage for child in self.cpu_children]
+        )
+
+    @property
+    def self_privateuse1_memory_usage(self):
+        if self.is_async or self.device_type != DeviceType.CPU:
+            return 0
+        return self.privateuse1_memory_usage - sum(
+            [child.privateuse1_memory_usage for child in self.cpu_children]
+        )
+
+    @property
+    def self_cpu_time_total(self):
+        if self.is_async or self.device_type != DeviceType.CPU:
+            return 0
+        return self.cpu_time_total - sum(
+            [child.cpu_time_total for child in self.cpu_children]
+        )
+
+    @property
+    def cuda_time_total(self):
+        if self.is_async or self.use_device:
+            return 0
+        if self.device_type == DeviceType.CPU:
+            if not self.is_legacy:
+                # account for the kernels in the children ops
+                return sum(kinfo.duration for kinfo in self.kernels) + sum(
+                    ch.cuda_time_total for ch in self.cpu_children
+                )
+            else:
+                # each legacy cpu events has a single (fake) kernel
+                return sum(kinfo.duration for kinfo in self.kernels)
+        else:
+            assert self.device_type == DeviceType.CUDA
+            return self.time_range.elapsed_us()
+
+    @property
+    def self_cuda_time_total(self):
+        if self.is_async or self.use_device:
+            return 0
+        if self.device_type == DeviceType.CPU:
+            return self.cuda_time_total - sum(
+                [child.cuda_time_total for child in self.cpu_children]
+            )
+        else:
+            assert self.device_type == DeviceType.CUDA
+            return self.cuda_time_total
+
+    @property
+    def cpu_time_total(self):
+        if self.device_type == DeviceType.CPU:
+            return self.time_range.elapsed_us()
+        else:
+            return 0
+
+    @property
+    def self_privateuse1_time_total(self):
+        if self.is_async or not self.use_device:
+            return 0
+        if self.device_type == DeviceType.CPU:
+            return self.privateuse1_time_total - sum(
+                [child.privateuse1_time_total for child in self.cpu_children]
+            )
+        else:
+            assert self.device_type == DeviceType.CUDA
+            return self.privateuse1_time_total
+
+    @property
+    def privateuse1_time_total(self):
+        if self.is_async or not self.use_device:
+            return 0
+        if self.device_type == DeviceType.CPU:
+            if not self.is_legacy:
+                # account for the kernels in the children ops
+                return sum(kinfo.duration for kinfo in self.kernels) + sum(
+                    ch.privateuse1_time_total for ch in self.cpu_children
+                )
+            else:
+                # each legacy cpu events has a single (fake) kernel
+                return sum(kinfo.duration for kinfo in self.kernels)
+        else:
+            assert self.device_type == DeviceType.PrivateUse1
+            return self.time_range.elapsed_us()
+
+    @property
+    def key(self):
+        return self.name
+
+    def __repr__(self):
+        device_name = "cuda" if not self.use_device else self.use_device
+        device_time = (
+            self.cuda_time_str if not self.use_device else self.privateuse1_time_str
+        )
+        device_memory_usage = (
+            self.cuda_memory_usage
+            if not self.use_device
+            else self.privateuse1_memory_usage
+        )
+        return (
+            "<FunctionEvent id={} name={} device_type={} node_id={} cpu_time={} start_us={} end_us={} "
+            "cpu_children={} {}_time={} name={} thread={} input_shapes={} "
+            "cpu_memory_usage={} {}_memory_usage={} is_async={} is_remote={} seq_nr={} is_legacy={}>".format(
+                self.id,
+                self.name,
+                self.device_type,
+                self.node_id,
+                self.cpu_time_str,
+                self.time_range.start,
+                self.time_range.end,
+                str([child.id for child in self.cpu_children]),
+                device_name,
+                device_time,
+                self.name,
+                self.thread,
+                str(self.input_shapes),
+                self.cpu_memory_usage,
+                device_name,
+                device_memory_usage,
+                self.is_async,
+                self.is_remote,
+                self.sequence_nr,
+                self.is_legacy,
+            )
+        )
+
+
+class FunctionEventAvg(FormattedTimesMixin):
+    """Used to average stats over multiple FunctionEvent objects."""
+
+    def __init__(self):
+        self.key: Optional[str] = None
+        self.count: int = 0
+        self.node_id: int = 0
+        self.is_async: bool = False
+        self.is_remote: bool = False
+        self.use_device: Optional[str] = None
+        self.cpu_time_total: int = 0
+        self.cuda_time_total: int = 0
+        self.privateuse1_time_total: int = 0
+        self.self_cpu_time_total: int = 0
+        self.self_cuda_time_total: int = 0
+        self.self_privateuse1_time_total: int = 0
+        self.input_shapes: Optional[List[List[int]]] = None
+        self.stack: Optional[List] = None
+        self.scope: Optional[int] = None
+        self.cpu_memory_usage: int = 0
+        self.cuda_memory_usage: int = 0
+        self.privateuse1_memory_usage: int = 0
+        self.self_cpu_memory_usage: int = 0
+        self.self_cuda_memory_usage: int = 0
+        self.self_privateuse1_memory_usage: int = 0
+        self.cpu_children: Optional[List[FunctionEvent]] = None
+        self.cpu_parent: Optional[FunctionEvent] = None
+        self.device_type: DeviceType = DeviceType.CPU
+        self.is_legacy: bool = False
+        self.flops: int = 0
+
+    def add(self, other):
+        if self.key is None:
+            # First function being recorded as part of FunctionEventAvg, propagate
+            # fields.
+            self.key = other.key
+            self.node_id = other.node_id
+            self.is_async = other.is_async
+            self.is_remote = other.is_remote
+            self.cpu_parent = other.cpu_parent
+            self.cpu_children = other.cpu_children
+
+            self.input_shapes = other.input_shapes
+            self.stack = other.stack
+            self.scope = other.scope
+            self.device_type = other.device_type
+            self.is_legacy = other.is_legacy
+            self.use_device = other.use_device
+
+        assert isinstance(other, (FunctionEvent, FunctionEventAvg))
+        assert other.key == self.key
+        self.cpu_time_total += other.cpu_time_total
+        self.cuda_time_total += other.cuda_time_total
+        self.privateuse1_time_total += other.privateuse1_time_total
+        self.self_cpu_time_total += other.self_cpu_time_total
+        self.self_cuda_time_total += other.self_cuda_time_total
+        self.self_privateuse1_time_total += other.self_privateuse1_time_total
+        self.cpu_memory_usage += other.cpu_memory_usage
+        self.cuda_memory_usage += other.cuda_memory_usage
+        self.privateuse1_memory_usage += other.privateuse1_memory_usage
+        self.self_cpu_memory_usage += other.self_cpu_memory_usage
+        self.self_cuda_memory_usage += other.self_cuda_memory_usage
+        self.self_privateuse1_memory_usage += other.self_privateuse1_memory_usage
+        self.count += other.count
+        if self.flops is None:
+            self.flops = other.flops
+        elif other.flops is not None:
+            self.flops += other.flops
+        return self
+
+    def __iadd__(self, other):
+        return self.add(other)
+
+    def __repr__(self):
+        device_name = "cuda" if not self.use_device else self.use_device
+        self_device_time = (
+            self.self_cuda_time_total_str
+            if not self.use_device
+            else self.self_privateuse1_time_total_str
+        )
+        device_time = (
+            self.cuda_time_str if not self.use_device else self.privateuse1_time_str
+        )
+        device_memory = (
+            self.cuda_memory_usage
+            if not self.use_device
+            else self.privateuse1_memory_usage
+        )
+        return (
+            "<FunctionEventAvg key={} self_cpu_time={} cpu_time={} "
+            " self_{}_time={} {}_time={} input_shapes={} "
+            "cpu_memory_usage={} {}_memory_usage={}>".format(
+                self.key,
+                self.self_cpu_time_total_str,
+                self.cpu_time_str,
+                device_name,
+                self_device_time,
+                device_name,
+                device_time,
+                str(self.input_shapes),
+                self.cpu_memory_usage,
+                device_name,
+                device_memory,
+            )
+        )
+
+
+class StringTable(defaultdict):
+    def __missing__(self, key):
+        # manage cases like 't' (demangled to 'unsigned short') separately,
+        # for now simply check the length to avoid unexpected results for
+        # the short sequences
+        self[key] = torch._C._demangle(key) if len(key) > 1 else key
+        return self[key]
+
+
+class MemRecordsAcc:
+    """Acceleration structure for accessing mem_records in interval."""
+
+    def __init__(self, mem_records):
+        self._mem_records = mem_records
+        self._start_uses: List[int] = []
+        self._indices: List[int] = []
+        if len(mem_records) > 0:
+            tmp = sorted([(r[0].start_us(), i) for i, r in enumerate(mem_records)])
+            self._start_uses, self._indices = zip(*tmp)  # type: ignore[assignment]
+
+    def in_interval(self, start_us, end_us):
+        r"""
+        Return all records in the given interval
+        """
+        start_idx = bisect.bisect_left(self._start_uses, start_us)
+        end_idx = bisect.bisect_right(self._start_uses, end_us)
+        for i in range(start_idx, end_idx):
+            yield self._mem_records[self._indices[i]]
+
+
+def _filter_stack_entry(entry):
+    filtered_entries = [
+        ("autograd/__init__", "_make_grads"),
+        ("autograd/__init__", "backward"),
+        ("torch/tensor", "backward"),
+        ("_internal/common_utils", "prof_callable"),
+        ("_internal/common_utils", "prof_func_call"),
+        ("_internal/common_utils", "prof_meth_call"),
+    ]
+    return all(not (f[0] in entry and f[1] in entry) for f in filtered_entries)
+
+
+MEMORY_EVENT_NAME = "[memory]"
+OUT_OF_MEMORY_EVENT_NAME = "[OutOfMemory]"
+
+
+def _filter_name(name):
+    # ignoring the following utility ops
+    filtered_out_names = [
+        MEMORY_EVENT_NAME,  # used only for the top-level memory events
+        OUT_OF_MEMORY_EVENT_NAME,
+        "profiler::_record_function_enter",
+        "profiler::_record_function_enter_new",
+        "profiler::_record_function_exit",
+        "aten::is_leaf",
+        "aten::output_nr",
+        "aten::_version",
+    ]
+    return name in filtered_out_names
+
+
+# Demangles and optionally rewrites the provided event name,
+# with_wildcard - whether to replace certain numbered event names
+# with a wildcard name to aggregate them together in the profiler table
+# output
+def _rewrite_name(name, with_wildcard=False):
+    string_table = StringTable()
+    name = string_table[name]
+    if with_wildcard:
+        if name.startswith("ProfilerStep#"):
+            name = "ProfilerStep*"
+    return name
+
+
+def _build_table(
+    events,
+    sort_by=None,
+    header=None,
+    row_limit=100,
+    max_src_column_width=75,
+    max_name_column_width=55,
+    max_shapes_column_width=80,
+    with_flops=False,
+    profile_memory=False,
+    top_level_events_only=False,
+):
+    """Print a summary of events (which can be a list of FunctionEvent or FunctionEventAvg)."""
+    if len(events) == 0:
+        return ""
+
+    has_cuda_time = any(event.self_cuda_time_total > 0 for event in events)
+    has_cuda_mem = any(event.self_cuda_memory_usage > 0 for event in events)
+    has_privateuse1_time = any(
+        event.self_privateuse1_time_total > 0 for event in events
+    )
+    has_privateuse1_mem = any(
+        event.self_privateuse1_memory_usage > 0 for event in events
+    )
+    use_device = events[0].use_device
+    if not use_device and (has_privateuse1_mem or has_privateuse1_time):
+        raise RuntimeError(
+            "use_device is None, but there is private device performance data."
+        )
+
+    has_input_shapes = any(
+        (event.input_shapes is not None and len(event.input_shapes) > 0)
+        for event in events
+    )
+
+    if sort_by is not None:
+        events = EventList(
+            sorted(events, key=lambda evt: getattr(evt, sort_by), reverse=True),
+            use_cuda=has_cuda_time,
+            use_device=use_device,
+            profile_memory=profile_memory,
+            with_flops=with_flops,
+        )
+
+    name_column_width = max([len(evt.key) for evt in events]) + 4
+    if max_name_column_width is not None:
+        name_column_width = min(name_column_width, max_name_column_width)
+
+    shapes_column_width = max([len(str(evt.input_shapes)) for evt in events]) + 4
+    if max_shapes_column_width is not None:
+        shapes_column_width = min(shapes_column_width, max_shapes_column_width)
+
+    DEFAULT_COLUMN_WIDTH = 12
+    flops_column_width = DEFAULT_COLUMN_WIDTH
+
+    src_column_width = None
+    stacks = []
+    for evt in events:
+        if evt.stack is not None and len(evt.stack) > 0:
+            stacks.append(evt.stack)
+    has_stack = len(stacks) > 0
+    if has_stack:
+        src_column_width = (
+            max([max([len(entry) for entry in stack]) for stack in stacks]) + 4
+        )
+        if max_src_column_width is not None:
+            src_column_width = min(src_column_width, max_src_column_width)
+
+    headers = [
+        "Name",
+        "Self CPU %",
+        "Self CPU",
+        "CPU total %",
+        "CPU total",
+        "CPU time avg",
+    ]
+    if has_cuda_time:
+        headers.extend(
+            [
+                "Self CUDA",
+                "Self CUDA %",
+                "CUDA total",
+                "CUDA time avg",
+            ]
+        )
+    if has_privateuse1_time:
+        privateuse1 = use_device.upper()
+        headers.extend(
+            [
+                f"Self {privateuse1}",
+                f"Self {privateuse1} %",
+                f"{privateuse1} total",
+                f"{privateuse1} time avg",
+            ]
+        )
+    if profile_memory:
+        headers.extend(
+            [
+                "CPU Mem",
+                "Self CPU Mem",
+            ]
+        )
+        if has_cuda_mem:
+            headers.extend(
+                [
+                    "CUDA Mem",
+                    "Self CUDA Mem",
+                ]
+            )
+        if has_privateuse1_mem:
+            privateuse1 = use_device.upper()
+            headers.extend(
+                [
+                    f"{privateuse1} Mem",
+                    f"Self {privateuse1} Mem",
+                ]
+            )
+    headers.append("# of Calls")
+    # Only append Node ID if any event has a valid (>= 0) Node ID
+    append_node_id = any(evt.node_id != -1 for evt in events)
+    if append_node_id:
+        headers.append("Node ID")
+
+    # Have to use a list because nonlocal is Py3 only...
+    SPACING_SIZE = 2
+    row_format_lst = [""]
+    header_sep_lst = [""]
+    line_length_lst = [-SPACING_SIZE]
+    MAX_STACK_ENTRY = 5
+
+    def add_column(padding, text_dir=">"):
+        row_format_lst[0] += (
+            "{: " + text_dir + str(padding) + "}" + (" " * SPACING_SIZE)
+        )
+        header_sep_lst[0] += "-" * padding + (" " * SPACING_SIZE)
+        line_length_lst[0] += padding + SPACING_SIZE
+
+    def auto_scale_flops(flops):
+        flop_headers = [
+            "FLOPs",
+            "KFLOPs",
+            "MFLOPs",
+            "GFLOPs",
+            "TFLOPs",
+            "PFLOPs",
+        ]
+        assert flops > 0
+        log_flops = max(0, min(math.log10(flops) / 3, float(len(flop_headers) - 1)))
+        assert log_flops >= 0 and log_flops < len(flop_headers)
+        return (pow(10, (math.floor(log_flops) * -3.0)), flop_headers[int(log_flops)])
+
+    add_column(name_column_width)
+    for _ in headers[1:]:
+        add_column(DEFAULT_COLUMN_WIDTH)
+
+    if has_input_shapes:
+        headers.append("Input Shapes")
+        add_column(shapes_column_width)
+
+    if has_stack:
+        headers.append("Source Location")
+        add_column(src_column_width, text_dir="<")
+
+    if with_flops:
+        # Auto-scaling of flops header
+        raw_flops = []
+        for evt in events:
+            if evt.flops > 0:
+                raw_flops.append(evt.flops)
+        if len(raw_flops) != 0:
+            (flops_scale, flops_header) = auto_scale_flops(min(raw_flops))
+            headers.append(f"Total {flops_header}")
+            add_column(flops_column_width)
+        else:
+            with_flops = False  # can't find any valid flops
+
+    row_format = row_format_lst[0]
+    header_sep = header_sep_lst[0]
+    line_length = line_length_lst[0]
+    add_column = None  # type: ignore[assignment]
+
+    # Have to use a list because nonlocal is Py3 only...
+    result = []
+
+    def append(s):
+        result.append(s)
+        result.append("\n")  # Yes, newline after the end as well
+
+    sum_self_cpu_time_total = sum([event.self_cpu_time_total for event in events])
+    sum_self_cuda_time_total = 0
+    sum_self_privateuse1_time_total = 0
+    for evt in events:
+        if evt.device_type == DeviceType.CPU:
+            # in legacy profiler, kernel info is stored in cpu events
+            if evt.is_legacy:
+                if not use_device:
+                    sum_self_cuda_time_total += evt.self_cuda_time_total
+                else:
+                    sum_self_privateuse1_time_total += evt.self_privateuse1_time_total
+        elif evt.device_type == DeviceType.CUDA:
+            # in kineto profiler, there're events with the correct device type (e.g. CUDA)
+            sum_self_cuda_time_total += evt.self_cuda_time_total
+        elif evt.device_type == DeviceType.PrivateUse1:
+            sum_self_privateuse1_time_total += evt.self_privateuse1_time_total
+
+    # Actual printing
+    if header is not None:
+        append("=" * line_length)
+        append(header)
+    if top_level_events_only:
+        append("=" * line_length)
+        append("This report only display top-level ops statistics")
+    append(header_sep)
+    append(row_format.format(*headers))
+
+    append(header_sep)
+
+    def trim_path(path, src_column_width):
+        if len(path) > src_column_width:
+            offset = len(path) - src_column_width
+            path = path[offset:]
+            if len(path) > 3:
+                path = "..." + path[3:]
+        return path
+
+    event_limit = 0
+    for evt in events:
+        if event_limit == row_limit:
+            break
+        if top_level_events_only and evt.cpu_parent is not None:
+            continue
+        else:
+            event_limit += 1
+        name = evt.key
+        if max_name_column_width is not None and len(name) >= max_name_column_width - 3:
+            name = name[: (max_name_column_width - 3)] + "..."
+        row_values = [
+            name,
+            # Self CPU total %, 0 for async events.
+            _format_time_share(evt.self_cpu_time_total, sum_self_cpu_time_total),
+            evt.self_cpu_time_total_str,  # Self CPU total
+            # CPU total %, 0 for async events.
+            _format_time_share(evt.cpu_time_total, sum_self_cpu_time_total)
+            if not evt.is_async
+            else 0,
+            evt.cpu_time_total_str,  # CPU total
+            evt.cpu_time_str,  # CPU time avg
+        ]
+        if has_cuda_time:
+            row_values.extend(
+                [
+                    evt.self_cuda_time_total_str,
+                    # CUDA time total %
+                    _format_time_share(
+                        evt.self_cuda_time_total, sum_self_cuda_time_total
+                    ),
+                    evt.cuda_time_total_str,
+                    evt.cuda_time_str,  # Cuda time avg
+                ]
+            )
+        if has_privateuse1_time:
+            row_values.extend(
+                [
+                    evt.self_privateuse1_time_total_str,
+                    # PrivateUse1 time total %
+                    _format_time_share(
+                        evt.self_privateuse1_time_total, sum_self_privateuse1_time_total
+                    ),
+                    evt.privateuse1_time_total_str,
+                    evt.privateuse1_time_str,  # PrivateUse1 time avg
+                ]
+            )
+        if profile_memory:
+            row_values.extend(
+                [
+                    # CPU Mem Total
+                    _format_memory(evt.cpu_memory_usage),
+                    # Self CPU Mem Total
+                    _format_memory(evt.self_cpu_memory_usage),
+                ]
+            )
+            if has_cuda_mem:
+                row_values.extend(
+                    [
+                        # CUDA Mem Total
+                        _format_memory(evt.cuda_memory_usage),
+                        # Self CUDA Mem Total
+                        _format_memory(evt.self_cuda_memory_usage),
+                    ]
+                )
+            if has_privateuse1_mem:
+                row_values.extend(
+                    [
+                        # PrivateUse1 Mem Total
+                        _format_memory(evt.privateuse1_memory_usage),
+                        # Self PrivateUse1 Mem Total
+                        _format_memory(evt.self_privateuse1_memory_usage),
+                    ]
+                )
+        row_values.append(
+            evt.count,  # Number of calls
+        )
+
+        if append_node_id:
+            row_values.append(evt.node_id)
+        if has_input_shapes:
+            row_values.append(str(evt.input_shapes)[:shapes_column_width])
+        if with_flops:
+            if evt.flops <= 0:
+                row_values.append("--")
+            else:
+                row_values.append(f"{evt.flops * flops_scale:8.3f}")  # type: ignore[possibly-undefined]
+        if has_stack:
+            src_field = ""
+            if len(evt.stack) > 0:
+                src_field = trim_path(evt.stack[0], src_column_width)
+            row_values.append(src_field)
+        append(row_format.format(*row_values))
+
+        if has_stack:
+            empty_headers = [""] * (len(headers) - 1)
+            for entry in evt.stack[1:MAX_STACK_ENTRY]:
+                append(
+                    row_format.format(
+                        *(empty_headers + [trim_path(entry, src_column_width)])
+                    )
+                )
+            empty_headers.append("")
+            append(row_format.format(*empty_headers))
+
+    append(header_sep)
+    append(f"Self CPU time total: {_format_time(sum_self_cpu_time_total)}")
+    if has_cuda_time:
+        append(f"Self CUDA time total: {_format_time(sum_self_cuda_time_total)}")
+    if has_privateuse1_time:
+        append(
+            f"Self {use_device.upper()} time total: {_format_time(sum_self_privateuse1_time_total)}"
+        )
+    return "".join(result)

venv/lib/python3.10/site-packages/torch/autograd/variable.py

@@ -0,0 +1,14 @@
+import torch
+from torch._C import _ImperativeEngine as ImperativeEngine
+
+
+__all__ = ["VariableMeta", "Variable"]
+
+
+class VariableMeta(type):
+    def __instancecheck__(cls, other):
+        return isinstance(other, torch.Tensor)
+
+
+class Variable(torch._C._LegacyVariableBase, metaclass=VariableMeta):  # type: ignore[misc]
+    _execution_engine = ImperativeEngine()

venv/lib/python3.10/site-packages/torch/distributions/__init__.py

@@ -0,0 +1,171 @@
+r"""
+The ``distributions`` package contains parameterizable probability distributions
+and sampling functions. This allows the construction of stochastic computation
+graphs and stochastic gradient estimators for optimization. This package
+generally follows the design of the `TensorFlow Distributions`_ package.
+
+.. _`TensorFlow Distributions`:
+    https://arxiv.org/abs/1711.10604
+
+It is not possible to directly backpropagate through random samples. However,
+there are two main methods for creating surrogate functions that can be
+backpropagated through. These are the score function estimator/likelihood ratio
+estimator/REINFORCE and the pathwise derivative estimator. REINFORCE is commonly
+seen as the basis for policy gradient methods in reinforcement learning, and the
+pathwise derivative estimator is commonly seen in the reparameterization trick
+in variational autoencoders. Whilst the score function only requires the value
+of samples :math:`f(x)`, the pathwise derivative requires the derivative
+:math:`f'(x)`. The next sections discuss these two in a reinforcement learning
+example. For more details see
+`Gradient Estimation Using Stochastic Computation Graphs`_ .
+
+.. _`Gradient Estimation Using Stochastic Computation Graphs`:
+     https://arxiv.org/abs/1506.05254
+
+Score function
+^^^^^^^^^^^^^^
+
+When the probability density function is differentiable with respect to its
+parameters, we only need :meth:`~torch.distributions.Distribution.sample` and
+:meth:`~torch.distributions.Distribution.log_prob` to implement REINFORCE:
+
+.. math::
+
+    \Delta\theta  = \alpha r \frac{\partial\log p(a|\pi^\theta(s))}{\partial\theta}
+
+where :math:`\theta` are the parameters, :math:`\alpha` is the learning rate,
+:math:`r` is the reward and :math:`p(a|\pi^\theta(s))` is the probability of
+taking action :math:`a` in state :math:`s` given policy :math:`\pi^\theta`.
+
+In practice we would sample an action from the output of a network, apply this
+action in an environment, and then use ``log_prob`` to construct an equivalent
+loss function. Note that we use a negative because optimizers use gradient
+descent, whilst the rule above assumes gradient ascent. With a categorical
+policy, the code for implementing REINFORCE would be as follows::
+
+    probs = policy_network(state)
+    # Note that this is equivalent to what used to be called multinomial
+    m = Categorical(probs)
+    action = m.sample()
+    next_state, reward = env.step(action)
+    loss = -m.log_prob(action) * reward
+    loss.backward()
+
+Pathwise derivative
+^^^^^^^^^^^^^^^^^^^
+
+The other way to implement these stochastic/policy gradients would be to use the
+reparameterization trick from the
+:meth:`~torch.distributions.Distribution.rsample` method, where the
+parameterized random variable can be constructed via a parameterized
+deterministic function of a parameter-free random variable. The reparameterized
+sample therefore becomes differentiable. The code for implementing the pathwise
+derivative would be as follows::
+
+    params = policy_network(state)
+    m = Normal(*params)
+    # Any distribution with .has_rsample == True could work based on the application
+    action = m.rsample()
+    next_state, reward = env.step(action)  # Assuming that reward is differentiable
+    loss = -reward
+    loss.backward()
+"""
+
+from .bernoulli import Bernoulli
+from .beta import Beta
+from .binomial import Binomial
+from .categorical import Categorical
+from .cauchy import Cauchy
+from .chi2 import Chi2
+from .constraint_registry import biject_to, transform_to
+from .continuous_bernoulli import ContinuousBernoulli
+from .dirichlet import Dirichlet
+from .distribution import Distribution
+from .exp_family import ExponentialFamily
+from .exponential import Exponential
+from .fishersnedecor import FisherSnedecor
+from .gamma import Gamma
+from .geometric import Geometric
+from .gumbel import Gumbel
+from .half_cauchy import HalfCauchy
+from .half_normal import HalfNormal
+from .independent import Independent
+from .inverse_gamma import InverseGamma
+from .kl import _add_kl_info, kl_divergence, register_kl
+from .kumaraswamy import Kumaraswamy
+from .laplace import Laplace
+from .lkj_cholesky import LKJCholesky
+from .log_normal import LogNormal
+from .logistic_normal import LogisticNormal
+from .lowrank_multivariate_normal import LowRankMultivariateNormal
+from .mixture_same_family import MixtureSameFamily
+from .multinomial import Multinomial
+from .multivariate_normal import MultivariateNormal
+from .negative_binomial import NegativeBinomial
+from .normal import Normal
+from .one_hot_categorical import OneHotCategorical, OneHotCategoricalStraightThrough
+from .pareto import Pareto
+from .poisson import Poisson
+from .relaxed_bernoulli import RelaxedBernoulli
+from .relaxed_categorical import RelaxedOneHotCategorical
+from .studentT import StudentT
+from .transformed_distribution import TransformedDistribution
+from .transforms import *  # noqa: F403
+from . import transforms
+from .uniform import Uniform
+from .von_mises import VonMises
+from .weibull import Weibull
+from .wishart import Wishart
+
+_add_kl_info()
+del _add_kl_info
+
+__all__ = [
+    "Bernoulli",
+    "Beta",
+    "Binomial",
+    "Categorical",
+    "Cauchy",
+    "Chi2",
+    "ContinuousBernoulli",
+    "Dirichlet",
+    "Distribution",
+    "Exponential",
+    "ExponentialFamily",
+    "FisherSnedecor",
+    "Gamma",
+    "Geometric",
+    "Gumbel",
+    "HalfCauchy",
+    "HalfNormal",
+    "Independent",
+    "InverseGamma",
+    "Kumaraswamy",
+    "LKJCholesky",
+    "Laplace",
+    "LogNormal",
+    "LogisticNormal",
+    "LowRankMultivariateNormal",
+    "MixtureSameFamily",
+    "Multinomial",
+    "MultivariateNormal",
+    "NegativeBinomial",
+    "Normal",
+    "OneHotCategorical",
+    "OneHotCategoricalStraightThrough",
+    "Pareto",
+    "RelaxedBernoulli",
+    "RelaxedOneHotCategorical",
+    "StudentT",
+    "Poisson",
+    "Uniform",
+    "VonMises",
+    "Weibull",
+    "Wishart",
+    "TransformedDistribution",
+    "biject_to",
+    "kl_divergence",
+    "register_kl",
+    "transform_to",
+]
+__all__.extend(transforms.__all__)

venv/lib/python3.10/site-packages/torch/distributions/bernoulli.py

@@ -0,0 +1,130 @@
+from numbers import Number
+
+import torch
+from torch import nan
+from torch.distributions import constraints
+from torch.distributions.exp_family import ExponentialFamily
+from torch.distributions.utils import (
+    broadcast_all,
+    lazy_property,
+    logits_to_probs,
+    probs_to_logits,
+)
+from torch.nn.functional import binary_cross_entropy_with_logits
+
+__all__ = ["Bernoulli"]
+
+
+class Bernoulli(ExponentialFamily):
+    r"""
+    Creates a Bernoulli distribution parameterized by :attr:`probs`
+    or :attr:`logits` (but not both).
+
+    Samples are binary (0 or 1). They take the value `1` with probability `p`
+    and `0` with probability `1 - p`.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Bernoulli(torch.tensor([0.3]))
+        >>> m.sample()  # 30% chance 1; 70% chance 0
+        tensor([ 0.])
+
+    Args:
+        probs (Number, Tensor): the probability of sampling `1`
+        logits (Number, Tensor): the log-odds of sampling `1`
+    """
+    arg_constraints = {"probs": constraints.unit_interval, "logits": constraints.real}
+    support = constraints.boolean
+    has_enumerate_support = True
+    _mean_carrier_measure = 0
+
+    def __init__(self, probs=None, logits=None, validate_args=None):
+        if (probs is None) == (logits is None):
+            raise ValueError(
+                "Either `probs` or `logits` must be specified, but not both."
+            )
+        if probs is not None:
+            is_scalar = isinstance(probs, Number)
+            (self.probs,) = broadcast_all(probs)
+        else:
+            is_scalar = isinstance(logits, Number)
+            (self.logits,) = broadcast_all(logits)
+        self._param = self.probs if probs is not None else self.logits
+        if is_scalar:
+            batch_shape = torch.Size()
+        else:
+            batch_shape = self._param.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Bernoulli, _instance)
+        batch_shape = torch.Size(batch_shape)
+        if "probs" in self.__dict__:
+            new.probs = self.probs.expand(batch_shape)
+            new._param = new.probs
+        if "logits" in self.__dict__:
+            new.logits = self.logits.expand(batch_shape)
+            new._param = new.logits
+        super(Bernoulli, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def _new(self, *args, **kwargs):
+        return self._param.new(*args, **kwargs)
+
+    @property
+    def mean(self):
+        return self.probs
+
+    @property
+    def mode(self):
+        mode = (self.probs >= 0.5).to(self.probs)
+        mode[self.probs == 0.5] = nan
+        return mode
+
+    @property
+    def variance(self):
+        return self.probs * (1 - self.probs)
+
+    @lazy_property
+    def logits(self):
+        return probs_to_logits(self.probs, is_binary=True)
+
+    @lazy_property
+    def probs(self):
+        return logits_to_probs(self.logits, is_binary=True)
+
+    @property
+    def param_shape(self):
+        return self._param.size()
+
+    def sample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        with torch.no_grad():
+            return torch.bernoulli(self.probs.expand(shape))
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        logits, value = broadcast_all(self.logits, value)
+        return -binary_cross_entropy_with_logits(logits, value, reduction="none")
+
+    def entropy(self):
+        return binary_cross_entropy_with_logits(
+            self.logits, self.probs, reduction="none"
+        )
+
+    def enumerate_support(self, expand=True):
+        values = torch.arange(2, dtype=self._param.dtype, device=self._param.device)
+        values = values.view((-1,) + (1,) * len(self._batch_shape))
+        if expand:
+            values = values.expand((-1,) + self._batch_shape)
+        return values
+
+    @property
+    def _natural_params(self):
+        return (torch.logit(self.probs),)
+
+    def _log_normalizer(self, x):
+        return torch.log1p(torch.exp(x))

venv/lib/python3.10/site-packages/torch/distributions/binomial.py

@@ -0,0 +1,165 @@
+import torch
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import (
+    broadcast_all,
+    lazy_property,
+    logits_to_probs,
+    probs_to_logits,
+)
+
+__all__ = ["Binomial"]
+
+
+def _clamp_by_zero(x):
+    # works like clamp(x, min=0) but has grad at 0 is 0.5
+    return (x.clamp(min=0) + x - x.clamp(max=0)) / 2
+
+
+class Binomial(Distribution):
+    r"""
+    Creates a Binomial distribution parameterized by :attr:`total_count` and
+    either :attr:`probs` or :attr:`logits` (but not both). :attr:`total_count` must be
+    broadcastable with :attr:`probs`/:attr:`logits`.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Binomial(100, torch.tensor([0 , .2, .8, 1]))
+        >>> x = m.sample()
+        tensor([   0.,   22.,   71.,  100.])
+
+        >>> m = Binomial(torch.tensor([[5.], [10.]]), torch.tensor([0.5, 0.8]))
+        >>> x = m.sample()
+        tensor([[ 4.,  5.],
+                [ 7.,  6.]])
+
+    Args:
+        total_count (int or Tensor): number of Bernoulli trials
+        probs (Tensor): Event probabilities
+        logits (Tensor): Event log-odds
+    """
+    arg_constraints = {
+        "total_count": constraints.nonnegative_integer,
+        "probs": constraints.unit_interval,
+        "logits": constraints.real,
+    }
+    has_enumerate_support = True
+
+    def __init__(self, total_count=1, probs=None, logits=None, validate_args=None):
+        if (probs is None) == (logits is None):
+            raise ValueError(
+                "Either `probs` or `logits` must be specified, but not both."
+            )
+        if probs is not None:
+            (
+                self.total_count,
+                self.probs,
+            ) = broadcast_all(total_count, probs)
+            self.total_count = self.total_count.type_as(self.probs)
+        else:
+            (
+                self.total_count,
+                self.logits,
+            ) = broadcast_all(total_count, logits)
+            self.total_count = self.total_count.type_as(self.logits)
+
+        self._param = self.probs if probs is not None else self.logits
+        batch_shape = self._param.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Binomial, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.total_count = self.total_count.expand(batch_shape)
+        if "probs" in self.__dict__:
+            new.probs = self.probs.expand(batch_shape)
+            new._param = new.probs
+        if "logits" in self.__dict__:
+            new.logits = self.logits.expand(batch_shape)
+            new._param = new.logits
+        super(Binomial, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def _new(self, *args, **kwargs):
+        return self._param.new(*args, **kwargs)
+
+    @constraints.dependent_property(is_discrete=True, event_dim=0)
+    def support(self):
+        return constraints.integer_interval(0, self.total_count)
+
+    @property
+    def mean(self):
+        return self.total_count * self.probs
+
+    @property
+    def mode(self):
+        return ((self.total_count + 1) * self.probs).floor().clamp(max=self.total_count)
+
+    @property
+    def variance(self):
+        return self.total_count * self.probs * (1 - self.probs)
+
+    @lazy_property
+    def logits(self):
+        return probs_to_logits(self.probs, is_binary=True)
+
+    @lazy_property
+    def probs(self):
+        return logits_to_probs(self.logits, is_binary=True)
+
+    @property
+    def param_shape(self):
+        return self._param.size()
+
+    def sample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        with torch.no_grad():
+            return torch.binomial(
+                self.total_count.expand(shape), self.probs.expand(shape)
+            )
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        log_factorial_n = torch.lgamma(self.total_count + 1)
+        log_factorial_k = torch.lgamma(value + 1)
+        log_factorial_nmk = torch.lgamma(self.total_count - value + 1)
+        # k * log(p) + (n - k) * log(1 - p) = k * (log(p) - log(1 - p)) + n * log(1 - p)
+        #     (case logit < 0)              = k * logit - n * log1p(e^logit)
+        #     (case logit > 0)              = k * logit - n * (log(p) - log(1 - p)) + n * log(p)
+        #                                   = k * logit - n * logit - n * log1p(e^-logit)
+        #     (merge two cases)             = k * logit - n * max(logit, 0) - n * log1p(e^-|logit|)
+        normalize_term = (
+            self.total_count * _clamp_by_zero(self.logits)
+            + self.total_count * torch.log1p(torch.exp(-torch.abs(self.logits)))
+            - log_factorial_n
+        )
+        return (
+            value * self.logits - log_factorial_k - log_factorial_nmk - normalize_term
+        )
+
+    def entropy(self):
+        total_count = int(self.total_count.max())
+        if not self.total_count.min() == total_count:
+            raise NotImplementedError(
+                "Inhomogeneous total count not supported by `entropy`."
+            )
+
+        log_prob = self.log_prob(self.enumerate_support(False))
+        return -(torch.exp(log_prob) * log_prob).sum(0)
+
+    def enumerate_support(self, expand=True):
+        total_count = int(self.total_count.max())
+        if not self.total_count.min() == total_count:
+            raise NotImplementedError(
+                "Inhomogeneous total count not supported by `enumerate_support`."
+            )
+        values = torch.arange(
+            1 + total_count, dtype=self._param.dtype, device=self._param.device
+        )
+        values = values.view((-1,) + (1,) * len(self._batch_shape))
+        if expand:
+            values = values.expand((-1,) + self._batch_shape)
+        return values

venv/lib/python3.10/site-packages/torch/distributions/continuous_bernoulli.py

@@ -0,0 +1,235 @@
+import math
+from numbers import Number
+
+import torch
+from torch.distributions import constraints
+from torch.distributions.exp_family import ExponentialFamily
+from torch.distributions.utils import (
+    broadcast_all,
+    clamp_probs,
+    lazy_property,
+    logits_to_probs,
+    probs_to_logits,
+)
+from torch.nn.functional import binary_cross_entropy_with_logits
+
+__all__ = ["ContinuousBernoulli"]
+
+
+class ContinuousBernoulli(ExponentialFamily):
+    r"""
+    Creates a continuous Bernoulli distribution parameterized by :attr:`probs`
+    or :attr:`logits` (but not both).
+
+    The distribution is supported in [0, 1] and parameterized by 'probs' (in
+    (0,1)) or 'logits' (real-valued). Note that, unlike the Bernoulli, 'probs'
+    does not correspond to a probability and 'logits' does not correspond to
+    log-odds, but the same names are used due to the similarity with the
+    Bernoulli. See [1] for more details.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = ContinuousBernoulli(torch.tensor([0.3]))
+        >>> m.sample()
+        tensor([ 0.2538])
+
+    Args:
+        probs (Number, Tensor): (0,1) valued parameters
+        logits (Number, Tensor): real valued parameters whose sigmoid matches 'probs'
+
+    [1] The continuous Bernoulli: fixing a pervasive error in variational
+    autoencoders, Loaiza-Ganem G and Cunningham JP, NeurIPS 2019.
+    https://arxiv.org/abs/1907.06845
+    """
+    arg_constraints = {"probs": constraints.unit_interval, "logits": constraints.real}
+    support = constraints.unit_interval
+    _mean_carrier_measure = 0
+    has_rsample = True
+
+    def __init__(
+        self, probs=None, logits=None, lims=(0.499, 0.501), validate_args=None
+    ):
+        if (probs is None) == (logits is None):
+            raise ValueError(
+                "Either `probs` or `logits` must be specified, but not both."
+            )
+        if probs is not None:
+            is_scalar = isinstance(probs, Number)
+            (self.probs,) = broadcast_all(probs)
+            # validate 'probs' here if necessary as it is later clamped for numerical stability
+            # close to 0 and 1, later on; otherwise the clamped 'probs' would always pass
+            if validate_args is not None:
+                if not self.arg_constraints["probs"].check(self.probs).all():
+                    raise ValueError("The parameter probs has invalid values")
+            self.probs = clamp_probs(self.probs)
+        else:
+            is_scalar = isinstance(logits, Number)
+            (self.logits,) = broadcast_all(logits)
+        self._param = self.probs if probs is not None else self.logits
+        if is_scalar:
+            batch_shape = torch.Size()
+        else:
+            batch_shape = self._param.size()
+        self._lims = lims
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(ContinuousBernoulli, _instance)
+        new._lims = self._lims
+        batch_shape = torch.Size(batch_shape)
+        if "probs" in self.__dict__:
+            new.probs = self.probs.expand(batch_shape)
+            new._param = new.probs
+        if "logits" in self.__dict__:
+            new.logits = self.logits.expand(batch_shape)
+            new._param = new.logits
+        super(ContinuousBernoulli, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def _new(self, *args, **kwargs):
+        return self._param.new(*args, **kwargs)
+
+    def _outside_unstable_region(self):
+        return torch.max(
+            torch.le(self.probs, self._lims[0]), torch.gt(self.probs, self._lims[1])
+        )
+
+    def _cut_probs(self):
+        return torch.where(
+            self._outside_unstable_region(),
+            self.probs,
+            self._lims[0] * torch.ones_like(self.probs),
+        )
+
+    def _cont_bern_log_norm(self):
+        """computes the log normalizing constant as a function of the 'probs' parameter"""
+        cut_probs = self._cut_probs()
+        cut_probs_below_half = torch.where(
+            torch.le(cut_probs, 0.5), cut_probs, torch.zeros_like(cut_probs)
+        )
+        cut_probs_above_half = torch.where(
+            torch.ge(cut_probs, 0.5), cut_probs, torch.ones_like(cut_probs)
+        )
+        log_norm = torch.log(
+            torch.abs(torch.log1p(-cut_probs) - torch.log(cut_probs))
+        ) - torch.where(
+            torch.le(cut_probs, 0.5),
+            torch.log1p(-2.0 * cut_probs_below_half),
+            torch.log(2.0 * cut_probs_above_half - 1.0),
+        )
+        x = torch.pow(self.probs - 0.5, 2)
+        taylor = math.log(2.0) + (4.0 / 3.0 + 104.0 / 45.0 * x) * x
+        return torch.where(self._outside_unstable_region(), log_norm, taylor)
+
+    @property
+    def mean(self):
+        cut_probs = self._cut_probs()
+        mus = cut_probs / (2.0 * cut_probs - 1.0) + 1.0 / (
+            torch.log1p(-cut_probs) - torch.log(cut_probs)
+        )
+        x = self.probs - 0.5
+        taylor = 0.5 + (1.0 / 3.0 + 16.0 / 45.0 * torch.pow(x, 2)) * x
+        return torch.where(self._outside_unstable_region(), mus, taylor)
+
+    @property
+    def stddev(self):
+        return torch.sqrt(self.variance)
+
+    @property
+    def variance(self):
+        cut_probs = self._cut_probs()
+        vars = cut_probs * (cut_probs - 1.0) / torch.pow(
+            1.0 - 2.0 * cut_probs, 2
+        ) + 1.0 / torch.pow(torch.log1p(-cut_probs) - torch.log(cut_probs), 2)
+        x = torch.pow(self.probs - 0.5, 2)
+        taylor = 1.0 / 12.0 - (1.0 / 15.0 - 128.0 / 945.0 * x) * x
+        return torch.where(self._outside_unstable_region(), vars, taylor)
+
+    @lazy_property
+    def logits(self):
+        return probs_to_logits(self.probs, is_binary=True)
+
+    @lazy_property
+    def probs(self):
+        return clamp_probs(logits_to_probs(self.logits, is_binary=True))
+
+    @property
+    def param_shape(self):
+        return self._param.size()
+
+    def sample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        u = torch.rand(shape, dtype=self.probs.dtype, device=self.probs.device)
+        with torch.no_grad():
+            return self.icdf(u)
+
+    def rsample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        u = torch.rand(shape, dtype=self.probs.dtype, device=self.probs.device)
+        return self.icdf(u)
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        logits, value = broadcast_all(self.logits, value)
+        return (
+            -binary_cross_entropy_with_logits(logits, value, reduction="none")
+            + self._cont_bern_log_norm()
+        )
+
+    def cdf(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        cut_probs = self._cut_probs()
+        cdfs = (
+            torch.pow(cut_probs, value) * torch.pow(1.0 - cut_probs, 1.0 - value)
+            + cut_probs
+            - 1.0
+        ) / (2.0 * cut_probs - 1.0)
+        unbounded_cdfs = torch.where(self._outside_unstable_region(), cdfs, value)
+        return torch.where(
+            torch.le(value, 0.0),
+            torch.zeros_like(value),
+            torch.where(torch.ge(value, 1.0), torch.ones_like(value), unbounded_cdfs),
+        )
+
+    def icdf(self, value):
+        cut_probs = self._cut_probs()
+        return torch.where(
+            self._outside_unstable_region(),
+            (
+                torch.log1p(-cut_probs + value * (2.0 * cut_probs - 1.0))
+                - torch.log1p(-cut_probs)
+            )
+            / (torch.log(cut_probs) - torch.log1p(-cut_probs)),
+            value,
+        )
+
+    def entropy(self):
+        log_probs0 = torch.log1p(-self.probs)
+        log_probs1 = torch.log(self.probs)
+        return (
+            self.mean * (log_probs0 - log_probs1)
+            - self._cont_bern_log_norm()
+            - log_probs0
+        )
+
+    @property
+    def _natural_params(self):
+        return (self.logits,)
+
+    def _log_normalizer(self, x):
+        """computes the log normalizing constant as a function of the natural parameter"""
+        out_unst_reg = torch.max(
+            torch.le(x, self._lims[0] - 0.5), torch.gt(x, self._lims[1] - 0.5)
+        )
+        cut_nat_params = torch.where(
+            out_unst_reg, x, (self._lims[0] - 0.5) * torch.ones_like(x)
+        )
+        log_norm = torch.log(torch.abs(torch.exp(cut_nat_params) - 1.0)) - torch.log(
+            torch.abs(cut_nat_params)
+        )
+        taylor = 0.5 * x + torch.pow(x, 2) / 24.0 - torch.pow(x, 4) / 2880.0
+        return torch.where(out_unst_reg, log_norm, taylor)

venv/lib/python3.10/site-packages/torch/distributions/dirichlet.py

@@ -0,0 +1,123 @@
+import torch
+from torch.autograd import Function
+from torch.autograd.function import once_differentiable
+from torch.distributions import constraints
+from torch.distributions.exp_family import ExponentialFamily
+
+__all__ = ["Dirichlet"]
+
+
+# This helper is exposed for testing.
+def _Dirichlet_backward(x, concentration, grad_output):
+    total = concentration.sum(-1, True).expand_as(concentration)
+    grad = torch._dirichlet_grad(x, concentration, total)
+    return grad * (grad_output - (x * grad_output).sum(-1, True))
+
+
+class _Dirichlet(Function):
+    @staticmethod
+    def forward(ctx, concentration):
+        x = torch._sample_dirichlet(concentration)
+        ctx.save_for_backward(x, concentration)
+        return x
+
+    @staticmethod
+    @once_differentiable
+    def backward(ctx, grad_output):
+        x, concentration = ctx.saved_tensors
+        return _Dirichlet_backward(x, concentration, grad_output)
+
+
+class Dirichlet(ExponentialFamily):
+    r"""
+    Creates a Dirichlet distribution parameterized by concentration :attr:`concentration`.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Dirichlet(torch.tensor([0.5, 0.5]))
+        >>> m.sample()  # Dirichlet distributed with concentration [0.5, 0.5]
+        tensor([ 0.1046,  0.8954])
+
+    Args:
+        concentration (Tensor): concentration parameter of the distribution
+            (often referred to as alpha)
+    """
+    arg_constraints = {
+        "concentration": constraints.independent(constraints.positive, 1)
+    }
+    support = constraints.simplex
+    has_rsample = True
+
+    def __init__(self, concentration, validate_args=None):
+        if concentration.dim() < 1:
+            raise ValueError(
+                "`concentration` parameter must be at least one-dimensional."
+            )
+        self.concentration = concentration
+        batch_shape, event_shape = concentration.shape[:-1], concentration.shape[-1:]
+        super().__init__(batch_shape, event_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Dirichlet, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.concentration = self.concentration.expand(batch_shape + self.event_shape)
+        super(Dirichlet, new).__init__(
+            batch_shape, self.event_shape, validate_args=False
+        )
+        new._validate_args = self._validate_args
+        return new
+
+    def rsample(self, sample_shape=()):
+        shape = self._extended_shape(sample_shape)
+        concentration = self.concentration.expand(shape)
+        return _Dirichlet.apply(concentration)
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        return (
+            torch.xlogy(self.concentration - 1.0, value).sum(-1)
+            + torch.lgamma(self.concentration.sum(-1))
+            - torch.lgamma(self.concentration).sum(-1)
+        )
+
+    @property
+    def mean(self):
+        return self.concentration / self.concentration.sum(-1, True)
+
+    @property
+    def mode(self):
+        concentrationm1 = (self.concentration - 1).clamp(min=0.0)
+        mode = concentrationm1 / concentrationm1.sum(-1, True)
+        mask = (self.concentration < 1).all(axis=-1)
+        mode[mask] = torch.nn.functional.one_hot(
+            mode[mask].argmax(axis=-1), concentrationm1.shape[-1]
+        ).to(mode)
+        return mode
+
+    @property
+    def variance(self):
+        con0 = self.concentration.sum(-1, True)
+        return (
+            self.concentration
+            * (con0 - self.concentration)
+            / (con0.pow(2) * (con0 + 1))
+        )
+
+    def entropy(self):
+        k = self.concentration.size(-1)
+        a0 = self.concentration.sum(-1)
+        return (
+            torch.lgamma(self.concentration).sum(-1)
+            - torch.lgamma(a0)
+            - (k - a0) * torch.digamma(a0)
+            - ((self.concentration - 1.0) * torch.digamma(self.concentration)).sum(-1)
+        )
+
+    @property
+    def _natural_params(self):
+        return (self.concentration,)
+
+    def _log_normalizer(self, x):
+        return x.lgamma().sum(-1) - torch.lgamma(x.sum(-1))

venv/lib/python3.10/site-packages/torch/distributions/exp_family.py

@@ -0,0 +1,62 @@
+import torch
+from torch.distributions.distribution import Distribution
+
+__all__ = ["ExponentialFamily"]
+
+
+class ExponentialFamily(Distribution):
+    r"""
+    ExponentialFamily is the abstract base class for probability distributions belonging to an
+    exponential family, whose probability mass/density function has the form is defined below
+
+    .. math::
+
+        p_{F}(x; \theta) = \exp(\langle t(x), \theta\rangle - F(\theta) + k(x))
+
+    where :math:`\theta` denotes the natural parameters, :math:`t(x)` denotes the sufficient statistic,
+    :math:`F(\theta)` is the log normalizer function for a given family and :math:`k(x)` is the carrier
+    measure.
+
+    Note:
+        This class is an intermediary between the `Distribution` class and distributions which belong
+        to an exponential family mainly to check the correctness of the `.entropy()` and analytic KL
+        divergence methods. We use this class to compute the entropy and KL divergence using the AD
+        framework and Bregman divergences (courtesy of: Frank Nielsen and Richard Nock, Entropies and
+        Cross-entropies of Exponential Families).
+    """
+
+    @property
+    def _natural_params(self):
+        """
+        Abstract method for natural parameters. Returns a tuple of Tensors based
+        on the distribution
+        """
+        raise NotImplementedError
+
+    def _log_normalizer(self, *natural_params):
+        """
+        Abstract method for log normalizer function. Returns a log normalizer based on
+        the distribution and input
+        """
+        raise NotImplementedError
+
+    @property
+    def _mean_carrier_measure(self):
+        """
+        Abstract method for expected carrier measure, which is required for computing
+        entropy.
+        """
+        raise NotImplementedError
+
+    def entropy(self):
+        """
+        Method to compute the entropy using Bregman divergence of the log normalizer.
+        """
+        result = -self._mean_carrier_measure
+        nparams = [p.detach().requires_grad_() for p in self._natural_params]
+        lg_normal = self._log_normalizer(*nparams)
+        gradients = torch.autograd.grad(lg_normal.sum(), nparams, create_graph=True)
+        result += lg_normal
+        for np, g in zip(nparams, gradients):
+            result -= (np * g).reshape(self._batch_shape + (-1,)).sum(-1)
+        return result

venv/lib/python3.10/site-packages/torch/distributions/fishersnedecor.py

@@ -0,0 +1,98 @@
+from numbers import Number
+
+import torch
+from torch import nan
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.gamma import Gamma
+from torch.distributions.utils import broadcast_all
+
+__all__ = ["FisherSnedecor"]
+
+
+class FisherSnedecor(Distribution):
+    r"""
+    Creates a Fisher-Snedecor distribution parameterized by :attr:`df1` and :attr:`df2`.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = FisherSnedecor(torch.tensor([1.0]), torch.tensor([2.0]))
+        >>> m.sample()  # Fisher-Snedecor-distributed with df1=1 and df2=2
+        tensor([ 0.2453])
+
+    Args:
+        df1 (float or Tensor): degrees of freedom parameter 1
+        df2 (float or Tensor): degrees of freedom parameter 2
+    """
+    arg_constraints = {"df1": constraints.positive, "df2": constraints.positive}
+    support = constraints.positive
+    has_rsample = True
+
+    def __init__(self, df1, df2, validate_args=None):
+        self.df1, self.df2 = broadcast_all(df1, df2)
+        self._gamma1 = Gamma(self.df1 * 0.5, self.df1)
+        self._gamma2 = Gamma(self.df2 * 0.5, self.df2)
+
+        if isinstance(df1, Number) and isinstance(df2, Number):
+            batch_shape = torch.Size()
+        else:
+            batch_shape = self.df1.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(FisherSnedecor, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.df1 = self.df1.expand(batch_shape)
+        new.df2 = self.df2.expand(batch_shape)
+        new._gamma1 = self._gamma1.expand(batch_shape)
+        new._gamma2 = self._gamma2.expand(batch_shape)
+        super(FisherSnedecor, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    @property
+    def mean(self):
+        df2 = self.df2.clone(memory_format=torch.contiguous_format)
+        df2[df2 <= 2] = nan
+        return df2 / (df2 - 2)
+
+    @property
+    def mode(self):
+        mode = (self.df1 - 2) / self.df1 * self.df2 / (self.df2 + 2)
+        mode[self.df1 <= 2] = nan
+        return mode
+
+    @property
+    def variance(self):
+        df2 = self.df2.clone(memory_format=torch.contiguous_format)
+        df2[df2 <= 4] = nan
+        return (
+            2
+            * df2.pow(2)
+            * (self.df1 + df2 - 2)
+            / (self.df1 * (df2 - 2).pow(2) * (df2 - 4))
+        )
+
+    def rsample(self, sample_shape=torch.Size(())):
+        shape = self._extended_shape(sample_shape)
+        #   X1 ~ Gamma(df1 / 2, 1 / df1), X2 ~ Gamma(df2 / 2, 1 / df2)
+        #   Y = df2 * df1 * X1 / (df1 * df2 * X2) = X1 / X2 ~ F(df1, df2)
+        X1 = self._gamma1.rsample(sample_shape).view(shape)
+        X2 = self._gamma2.rsample(sample_shape).view(shape)
+        tiny = torch.finfo(X2.dtype).tiny
+        X2.clamp_(min=tiny)
+        Y = X1 / X2
+        Y.clamp_(min=tiny)
+        return Y
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        ct1 = self.df1 * 0.5
+        ct2 = self.df2 * 0.5
+        ct3 = self.df1 / self.df2
+        t1 = (ct1 + ct2).lgamma() - ct1.lgamma() - ct2.lgamma()
+        t2 = ct1 * ct3.log() + (ct1 - 1) * torch.log(value)
+        t3 = (ct1 + ct2) * torch.log1p(ct3 * value)
+        return t1 + t2 - t3

venv/lib/python3.10/site-packages/torch/distributions/geometric.py

@@ -0,0 +1,128 @@
+from numbers import Number
+
+import torch
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import (
+    broadcast_all,
+    lazy_property,
+    logits_to_probs,
+    probs_to_logits,
+)
+from torch.nn.functional import binary_cross_entropy_with_logits
+
+__all__ = ["Geometric"]
+
+
+class Geometric(Distribution):
+    r"""
+    Creates a Geometric distribution parameterized by :attr:`probs`,
+    where :attr:`probs` is the probability of success of Bernoulli trials.
+
+    .. math::
+
+        P(X=k) = (1-p)^{k} p, k = 0, 1, ...
+
+    .. note::
+        :func:`torch.distributions.geometric.Geometric` :math:`(k+1)`-th trial is the first success
+        hence draws samples in :math:`\{0, 1, \ldots\}`, whereas
+        :func:`torch.Tensor.geometric_` `k`-th trial is the first success hence draws samples in :math:`\{1, 2, \ldots\}`.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Geometric(torch.tensor([0.3]))
+        >>> m.sample()  # underlying Bernoulli has 30% chance 1; 70% chance 0
+        tensor([ 2.])
+
+    Args:
+        probs (Number, Tensor): the probability of sampling `1`. Must be in range (0, 1]
+        logits (Number, Tensor): the log-odds of sampling `1`.
+    """
+    arg_constraints = {"probs": constraints.unit_interval, "logits": constraints.real}
+    support = constraints.nonnegative_integer
+
+    def __init__(self, probs=None, logits=None, validate_args=None):
+        if (probs is None) == (logits is None):
+            raise ValueError(
+                "Either `probs` or `logits` must be specified, but not both."
+            )
+        if probs is not None:
+            (self.probs,) = broadcast_all(probs)
+        else:
+            (self.logits,) = broadcast_all(logits)
+        probs_or_logits = probs if probs is not None else logits
+        if isinstance(probs_or_logits, Number):
+            batch_shape = torch.Size()
+        else:
+            batch_shape = probs_or_logits.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+        if self._validate_args and probs is not None:
+            # Add an extra check beyond unit_interval
+            value = self.probs
+            valid = value > 0
+            if not valid.all():
+                invalid_value = value.data[~valid]
+                raise ValueError(
+                    "Expected parameter probs "
+                    f"({type(value).__name__} of shape {tuple(value.shape)}) "
+                    f"of distribution {repr(self)} "
+                    f"to be positive but found invalid values:\n{invalid_value}"
+                )
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Geometric, _instance)
+        batch_shape = torch.Size(batch_shape)
+        if "probs" in self.__dict__:
+            new.probs = self.probs.expand(batch_shape)
+        if "logits" in self.__dict__:
+            new.logits = self.logits.expand(batch_shape)
+        super(Geometric, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    @property
+    def mean(self):
+        return 1.0 / self.probs - 1.0
+
+    @property
+    def mode(self):
+        return torch.zeros_like(self.probs)
+
+    @property
+    def variance(self):
+        return (1.0 / self.probs - 1.0) / self.probs
+
+    @lazy_property
+    def logits(self):
+        return probs_to_logits(self.probs, is_binary=True)
+
+    @lazy_property
+    def probs(self):
+        return logits_to_probs(self.logits, is_binary=True)
+
+    def sample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        tiny = torch.finfo(self.probs.dtype).tiny
+        with torch.no_grad():
+            if torch._C._get_tracing_state():
+                # [JIT WORKAROUND] lack of support for .uniform_()
+                u = torch.rand(shape, dtype=self.probs.dtype, device=self.probs.device)
+                u = u.clamp(min=tiny)
+            else:
+                u = self.probs.new(shape).uniform_(tiny, 1)
+            return (u.log() / (-self.probs).log1p()).floor()
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        value, probs = broadcast_all(value, self.probs)
+        probs = probs.clone(memory_format=torch.contiguous_format)
+        probs[(probs == 1) & (value == 0)] = 0
+        return value * (-probs).log1p() + self.probs.log()
+
+    def entropy(self):
+        return (
+            binary_cross_entropy_with_logits(self.logits, self.probs, reduction="none")
+            / self.probs
+        )

venv/lib/python3.10/site-packages/torch/distributions/gumbel.py

@@ -0,0 +1,81 @@
+import math
+from numbers import Number
+
+import torch
+from torch.distributions import constraints
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import AffineTransform, ExpTransform
+from torch.distributions.uniform import Uniform
+from torch.distributions.utils import broadcast_all, euler_constant
+
+__all__ = ["Gumbel"]
+
+
+class Gumbel(TransformedDistribution):
+    r"""
+    Samples from a Gumbel Distribution.
+
+    Examples::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Gumbel(torch.tensor([1.0]), torch.tensor([2.0]))
+        >>> m.sample()  # sample from Gumbel distribution with loc=1, scale=2
+        tensor([ 1.0124])
+
+    Args:
+        loc (float or Tensor): Location parameter of the distribution
+        scale (float or Tensor): Scale parameter of the distribution
+    """
+    arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
+    support = constraints.real
+
+    def __init__(self, loc, scale, validate_args=None):
+        self.loc, self.scale = broadcast_all(loc, scale)
+        finfo = torch.finfo(self.loc.dtype)
+        if isinstance(loc, Number) and isinstance(scale, Number):
+            base_dist = Uniform(finfo.tiny, 1 - finfo.eps, validate_args=validate_args)
+        else:
+            base_dist = Uniform(
+                torch.full_like(self.loc, finfo.tiny),
+                torch.full_like(self.loc, 1 - finfo.eps),
+                validate_args=validate_args,
+            )
+        transforms = [
+            ExpTransform().inv,
+            AffineTransform(loc=0, scale=-torch.ones_like(self.scale)),
+            ExpTransform().inv,
+            AffineTransform(loc=loc, scale=-self.scale),
+        ]
+        super().__init__(base_dist, transforms, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Gumbel, _instance)
+        new.loc = self.loc.expand(batch_shape)
+        new.scale = self.scale.expand(batch_shape)
+        return super().expand(batch_shape, _instance=new)
+
+    # Explicitly defining the log probability function for Gumbel due to precision issues
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        y = (self.loc - value) / self.scale
+        return (y - y.exp()) - self.scale.log()
+
+    @property
+    def mean(self):
+        return self.loc + self.scale * euler_constant
+
+    @property
+    def mode(self):
+        return self.loc
+
+    @property
+    def stddev(self):
+        return (math.pi / math.sqrt(6)) * self.scale
+
+    @property
+    def variance(self):
+        return self.stddev.pow(2)
+
+    def entropy(self):
+        return self.scale.log() + (1 + euler_constant)

venv/lib/python3.10/site-packages/torch/distributions/half_cauchy.py

@@ -0,0 +1,82 @@
+import math
+
+import torch
+from torch import inf
+from torch.distributions import constraints
+from torch.distributions.cauchy import Cauchy
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import AbsTransform
+
+__all__ = ["HalfCauchy"]
+
+
+class HalfCauchy(TransformedDistribution):
+    r"""
+    Creates a half-Cauchy distribution parameterized by `scale` where::
+
+        X ~ Cauchy(0, scale)
+        Y = |X| ~ HalfCauchy(scale)
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = HalfCauchy(torch.tensor([1.0]))
+        >>> m.sample()  # half-cauchy distributed with scale=1
+        tensor([ 2.3214])
+
+    Args:
+        scale (float or Tensor): scale of the full Cauchy distribution
+    """
+    arg_constraints = {"scale": constraints.positive}
+    support = constraints.nonnegative
+    has_rsample = True
+
+    def __init__(self, scale, validate_args=None):
+        base_dist = Cauchy(0, scale, validate_args=False)
+        super().__init__(base_dist, AbsTransform(), validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(HalfCauchy, _instance)
+        return super().expand(batch_shape, _instance=new)
+
+    @property
+    def scale(self):
+        return self.base_dist.scale
+
+    @property
+    def mean(self):
+        return torch.full(
+            self._extended_shape(),
+            math.inf,
+            dtype=self.scale.dtype,
+            device=self.scale.device,
+        )
+
+    @property
+    def mode(self):
+        return torch.zeros_like(self.scale)
+
+    @property
+    def variance(self):
+        return self.base_dist.variance
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        value = torch.as_tensor(
+            value, dtype=self.base_dist.scale.dtype, device=self.base_dist.scale.device
+        )
+        log_prob = self.base_dist.log_prob(value) + math.log(2)
+        log_prob = torch.where(value >= 0, log_prob, -inf)
+        return log_prob
+
+    def cdf(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        return 2 * self.base_dist.cdf(value) - 1
+
+    def icdf(self, prob):
+        return self.base_dist.icdf((prob + 1) / 2)
+
+    def entropy(self):
+        return self.base_dist.entropy() - math.log(2)

venv/lib/python3.10/site-packages/torch/distributions/half_normal.py

@@ -0,0 +1,74 @@
+import math
+
+import torch
+from torch import inf
+from torch.distributions import constraints
+from torch.distributions.normal import Normal
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import AbsTransform
+
+__all__ = ["HalfNormal"]
+
+
+class HalfNormal(TransformedDistribution):
+    r"""
+    Creates a half-normal distribution parameterized by `scale` where::
+
+        X ~ Normal(0, scale)
+        Y = |X| ~ HalfNormal(scale)
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = HalfNormal(torch.tensor([1.0]))
+        >>> m.sample()  # half-normal distributed with scale=1
+        tensor([ 0.1046])
+
+    Args:
+        scale (float or Tensor): scale of the full Normal distribution
+    """
+    arg_constraints = {"scale": constraints.positive}
+    support = constraints.nonnegative
+    has_rsample = True
+
+    def __init__(self, scale, validate_args=None):
+        base_dist = Normal(0, scale, validate_args=False)
+        super().__init__(base_dist, AbsTransform(), validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(HalfNormal, _instance)
+        return super().expand(batch_shape, _instance=new)
+
+    @property
+    def scale(self):
+        return self.base_dist.scale
+
+    @property
+    def mean(self):
+        return self.scale * math.sqrt(2 / math.pi)
+
+    @property
+    def mode(self):
+        return torch.zeros_like(self.scale)
+
+    @property
+    def variance(self):
+        return self.scale.pow(2) * (1 - 2 / math.pi)
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        log_prob = self.base_dist.log_prob(value) + math.log(2)
+        log_prob = torch.where(value >= 0, log_prob, -inf)
+        return log_prob
+
+    def cdf(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        return 2 * self.base_dist.cdf(value) - 1
+
+    def icdf(self, prob):
+        return self.base_dist.icdf((prob + 1) / 2)
+
+    def entropy(self):
+        return self.base_dist.entropy() - math.log(2)

venv/lib/python3.10/site-packages/torch/distributions/kl.py

@@ -0,0 +1,971 @@
+import math
+import warnings
+from functools import total_ordering
+from typing import Callable, Dict, Tuple, Type
+
+import torch
+from torch import inf
+
+from .bernoulli import Bernoulli
+from .beta import Beta
+from .binomial import Binomial
+from .categorical import Categorical
+from .cauchy import Cauchy
+from .continuous_bernoulli import ContinuousBernoulli
+from .dirichlet import Dirichlet
+from .distribution import Distribution
+from .exp_family import ExponentialFamily
+from .exponential import Exponential
+from .gamma import Gamma
+from .geometric import Geometric
+from .gumbel import Gumbel
+from .half_normal import HalfNormal
+from .independent import Independent
+from .laplace import Laplace
+from .lowrank_multivariate_normal import (
+    _batch_lowrank_logdet,
+    _batch_lowrank_mahalanobis,
+    LowRankMultivariateNormal,
+)
+from .multivariate_normal import _batch_mahalanobis, MultivariateNormal
+from .normal import Normal
+from .one_hot_categorical import OneHotCategorical
+from .pareto import Pareto
+from .poisson import Poisson
+from .transformed_distribution import TransformedDistribution
+from .uniform import Uniform
+from .utils import _sum_rightmost, euler_constant as _euler_gamma
+
+_KL_REGISTRY: Dict[
+    Tuple[Type, Type], Callable
+] = {}  # Source of truth mapping a few general (type, type) pairs to functions.
+_KL_MEMOIZE: Dict[
+    Tuple[Type, Type], Callable
+] = {}  # Memoized version mapping many specific (type, type) pairs to functions.
+
+__all__ = ["register_kl", "kl_divergence"]
+
+
+def register_kl(type_p, type_q):
+    """
+    Decorator to register a pairwise function with :meth:`kl_divergence`.
+    Usage::
+
+        @register_kl(Normal, Normal)
+        def kl_normal_normal(p, q):
+            # insert implementation here
+
+    Lookup returns the most specific (type,type) match ordered by subclass. If
+    the match is ambiguous, a `RuntimeWarning` is raised. For example to
+    resolve the ambiguous situation::
+
+        @register_kl(BaseP, DerivedQ)
+        def kl_version1(p, q): ...
+        @register_kl(DerivedP, BaseQ)
+        def kl_version2(p, q): ...
+
+    you should register a third most-specific implementation, e.g.::
+
+        register_kl(DerivedP, DerivedQ)(kl_version1)  # Break the tie.
+
+    Args:
+        type_p (type): A subclass of :class:`~torch.distributions.Distribution`.
+        type_q (type): A subclass of :class:`~torch.distributions.Distribution`.
+    """
+    if not isinstance(type_p, type) and issubclass(type_p, Distribution):
+        raise TypeError(
+            f"Expected type_p to be a Distribution subclass but got {type_p}"
+        )
+    if not isinstance(type_q, type) and issubclass(type_q, Distribution):
+        raise TypeError(
+            f"Expected type_q to be a Distribution subclass but got {type_q}"
+        )
+
+    def decorator(fun):
+        _KL_REGISTRY[type_p, type_q] = fun
+        _KL_MEMOIZE.clear()  # reset since lookup order may have changed
+        return fun
+
+    return decorator
+
+
+@total_ordering
+class _Match:
+    __slots__ = ["types"]
+
+    def __init__(self, *types):
+        self.types = types
+
+    def __eq__(self, other):
+        return self.types == other.types
+
+    def __le__(self, other):
+        for x, y in zip(self.types, other.types):
+            if not issubclass(x, y):
+                return False
+            if x is not y:
+                break
+        return True
+
+
+def _dispatch_kl(type_p, type_q):
+    """
+    Find the most specific approximate match, assuming single inheritance.
+    """
+    matches = [
+        (super_p, super_q)
+        for super_p, super_q in _KL_REGISTRY
+        if issubclass(type_p, super_p) and issubclass(type_q, super_q)
+    ]
+    if not matches:
+        return NotImplemented
+    # Check that the left- and right- lexicographic orders agree.
+    # mypy isn't smart enough to know that _Match implements __lt__
+    # see: https://github.com/python/typing/issues/760#issuecomment-710670503
+    left_p, left_q = min(_Match(*m) for m in matches).types  # type: ignore[type-var]
+    right_q, right_p = min(_Match(*reversed(m)) for m in matches).types  # type: ignore[type-var]
+    left_fun = _KL_REGISTRY[left_p, left_q]
+    right_fun = _KL_REGISTRY[right_p, right_q]
+    if left_fun is not right_fun:
+        warnings.warn(
+            "Ambiguous kl_divergence({}, {}). Please register_kl({}, {})".format(
+                type_p.__name__, type_q.__name__, left_p.__name__, right_q.__name__
+            ),
+            RuntimeWarning,
+        )
+    return left_fun
+
+
+def _infinite_like(tensor):
+    """
+    Helper function for obtaining infinite KL Divergence throughout
+    """
+    return torch.full_like(tensor, inf)
+
+
+def _x_log_x(tensor):
+    """
+    Utility function for calculating x log x
+    """
+    return tensor * tensor.log()
+
+
+def _batch_trace_XXT(bmat):
+    """
+    Utility function for calculating the trace of XX^{T} with X having arbitrary trailing batch dimensions
+    """
+    n = bmat.size(-1)
+    m = bmat.size(-2)
+    flat_trace = bmat.reshape(-1, m * n).pow(2).sum(-1)
+    return flat_trace.reshape(bmat.shape[:-2])
+
+
+def kl_divergence(p: Distribution, q: Distribution) -> torch.Tensor:
+    r"""
+    Compute Kullback-Leibler divergence :math:`KL(p \| q)` between two distributions.
+
+    .. math::
+
+        KL(p \| q) = \int p(x) \log\frac {p(x)} {q(x)} \,dx
+
+    Args:
+        p (Distribution): A :class:`~torch.distributions.Distribution` object.
+        q (Distribution): A :class:`~torch.distributions.Distribution` object.
+
+    Returns:
+        Tensor: A batch of KL divergences of shape `batch_shape`.
+
+    Raises:
+        NotImplementedError: If the distribution types have not been registered via
+            :meth:`register_kl`.
+    """
+    try:
+        fun = _KL_MEMOIZE[type(p), type(q)]
+    except KeyError:
+        fun = _dispatch_kl(type(p), type(q))
+        _KL_MEMOIZE[type(p), type(q)] = fun
+    if fun is NotImplemented:
+        raise NotImplementedError(
+            f"No KL(p || q) is implemented for p type {p.__class__.__name__} and q type {q.__class__.__name__}"
+        )
+    return fun(p, q)
+
+
+################################################################################
+# KL Divergence Implementations
+################################################################################
+
+# Same distributions
+
+
+@register_kl(Bernoulli, Bernoulli)
+def _kl_bernoulli_bernoulli(p, q):
+    t1 = p.probs * (
+        torch.nn.functional.softplus(-q.logits)
+        - torch.nn.functional.softplus(-p.logits)
+    )
+    t1[q.probs == 0] = inf
+    t1[p.probs == 0] = 0
+    t2 = (1 - p.probs) * (
+        torch.nn.functional.softplus(q.logits) - torch.nn.functional.softplus(p.logits)
+    )
+    t2[q.probs == 1] = inf
+    t2[p.probs == 1] = 0
+    return t1 + t2
+
+
+@register_kl(Beta, Beta)
+def _kl_beta_beta(p, q):
+    sum_params_p = p.concentration1 + p.concentration0
+    sum_params_q = q.concentration1 + q.concentration0
+    t1 = q.concentration1.lgamma() + q.concentration0.lgamma() + (sum_params_p).lgamma()
+    t2 = p.concentration1.lgamma() + p.concentration0.lgamma() + (sum_params_q).lgamma()
+    t3 = (p.concentration1 - q.concentration1) * torch.digamma(p.concentration1)
+    t4 = (p.concentration0 - q.concentration0) * torch.digamma(p.concentration0)
+    t5 = (sum_params_q - sum_params_p) * torch.digamma(sum_params_p)
+    return t1 - t2 + t3 + t4 + t5
+
+
+@register_kl(Binomial, Binomial)
+def _kl_binomial_binomial(p, q):
+    # from https://math.stackexchange.com/questions/2214993/
+    # kullback-leibler-divergence-for-binomial-distributions-p-and-q
+    if (p.total_count < q.total_count).any():
+        raise NotImplementedError(
+            "KL between Binomials where q.total_count > p.total_count is not implemented"
+        )
+    kl = p.total_count * (
+        p.probs * (p.logits - q.logits) + (-p.probs).log1p() - (-q.probs).log1p()
+    )
+    inf_idxs = p.total_count > q.total_count
+    kl[inf_idxs] = _infinite_like(kl[inf_idxs])
+    return kl
+
+
+@register_kl(Categorical, Categorical)
+def _kl_categorical_categorical(p, q):
+    t = p.probs * (p.logits - q.logits)
+    t[(q.probs == 0).expand_as(t)] = inf
+    t[(p.probs == 0).expand_as(t)] = 0
+    return t.sum(-1)
+
+
+@register_kl(ContinuousBernoulli, ContinuousBernoulli)
+def _kl_continuous_bernoulli_continuous_bernoulli(p, q):
+    t1 = p.mean * (p.logits - q.logits)
+    t2 = p._cont_bern_log_norm() + torch.log1p(-p.probs)
+    t3 = -q._cont_bern_log_norm() - torch.log1p(-q.probs)
+    return t1 + t2 + t3
+
+
+@register_kl(Dirichlet, Dirichlet)
+def _kl_dirichlet_dirichlet(p, q):
+    # From http://bariskurt.com/kullback-leibler-divergence-between-two-dirichlet-and-beta-distributions/
+    sum_p_concentration = p.concentration.sum(-1)
+    sum_q_concentration = q.concentration.sum(-1)
+    t1 = sum_p_concentration.lgamma() - sum_q_concentration.lgamma()
+    t2 = (p.concentration.lgamma() - q.concentration.lgamma()).sum(-1)
+    t3 = p.concentration - q.concentration
+    t4 = p.concentration.digamma() - sum_p_concentration.digamma().unsqueeze(-1)
+    return t1 - t2 + (t3 * t4).sum(-1)
+
+
+@register_kl(Exponential, Exponential)
+def _kl_exponential_exponential(p, q):
+    rate_ratio = q.rate / p.rate
+    t1 = -rate_ratio.log()
+    return t1 + rate_ratio - 1
+
+
+@register_kl(ExponentialFamily, ExponentialFamily)
+def _kl_expfamily_expfamily(p, q):
+    if not type(p) == type(q):
+        raise NotImplementedError(
+            "The cross KL-divergence between different exponential families cannot \
+                            be computed using Bregman divergences"
+        )
+    p_nparams = [np.detach().requires_grad_() for np in p._natural_params]
+    q_nparams = q._natural_params
+    lg_normal = p._log_normalizer(*p_nparams)
+    gradients = torch.autograd.grad(lg_normal.sum(), p_nparams, create_graph=True)
+    result = q._log_normalizer(*q_nparams) - lg_normal
+    for pnp, qnp, g in zip(p_nparams, q_nparams, gradients):
+        term = (qnp - pnp) * g
+        result -= _sum_rightmost(term, len(q.event_shape))
+    return result
+
+
+@register_kl(Gamma, Gamma)
+def _kl_gamma_gamma(p, q):
+    t1 = q.concentration * (p.rate / q.rate).log()
+    t2 = torch.lgamma(q.concentration) - torch.lgamma(p.concentration)
+    t3 = (p.concentration - q.concentration) * torch.digamma(p.concentration)
+    t4 = (q.rate - p.rate) * (p.concentration / p.rate)
+    return t1 + t2 + t3 + t4
+
+
+@register_kl(Gumbel, Gumbel)
+def _kl_gumbel_gumbel(p, q):
+    ct1 = p.scale / q.scale
+    ct2 = q.loc / q.scale
+    ct3 = p.loc / q.scale
+    t1 = -ct1.log() - ct2 + ct3
+    t2 = ct1 * _euler_gamma
+    t3 = torch.exp(ct2 + (1 + ct1).lgamma() - ct3)
+    return t1 + t2 + t3 - (1 + _euler_gamma)
+
+
+@register_kl(Geometric, Geometric)
+def _kl_geometric_geometric(p, q):
+    return -p.entropy() - torch.log1p(-q.probs) / p.probs - q.logits
+
+
+@register_kl(HalfNormal, HalfNormal)
+def _kl_halfnormal_halfnormal(p, q):
+    return _kl_normal_normal(p.base_dist, q.base_dist)
+
+
+@register_kl(Laplace, Laplace)
+def _kl_laplace_laplace(p, q):
+    # From http://www.mast.queensu.ca/~communications/Papers/gil-msc11.pdf
+    scale_ratio = p.scale / q.scale
+    loc_abs_diff = (p.loc - q.loc).abs()
+    t1 = -scale_ratio.log()
+    t2 = loc_abs_diff / q.scale
+    t3 = scale_ratio * torch.exp(-loc_abs_diff / p.scale)
+    return t1 + t2 + t3 - 1
+
+
+@register_kl(LowRankMultivariateNormal, LowRankMultivariateNormal)
+def _kl_lowrankmultivariatenormal_lowrankmultivariatenormal(p, q):
+    if p.event_shape != q.event_shape:
+        raise ValueError(
+            "KL-divergence between two Low Rank Multivariate Normals with\
+                          different event shapes cannot be computed"
+        )
+
+    term1 = _batch_lowrank_logdet(
+        q._unbroadcasted_cov_factor, q._unbroadcasted_cov_diag, q._capacitance_tril
+    ) - _batch_lowrank_logdet(
+        p._unbroadcasted_cov_factor, p._unbroadcasted_cov_diag, p._capacitance_tril
+    )
+    term3 = _batch_lowrank_mahalanobis(
+        q._unbroadcasted_cov_factor,
+        q._unbroadcasted_cov_diag,
+        q.loc - p.loc,
+        q._capacitance_tril,
+    )
+    # Expands term2 according to
+    # inv(qcov) @ pcov = [inv(qD) - inv(qD) @ qW @ inv(qC) @ qW.T @ inv(qD)] @ (pW @ pW.T + pD)
+    #                  = [inv(qD) - A.T @ A] @ (pD + pW @ pW.T)
+    qWt_qDinv = q._unbroadcasted_cov_factor.mT / q._unbroadcasted_cov_diag.unsqueeze(-2)
+    A = torch.linalg.solve_triangular(q._capacitance_tril, qWt_qDinv, upper=False)
+    term21 = (p._unbroadcasted_cov_diag / q._unbroadcasted_cov_diag).sum(-1)
+    term22 = _batch_trace_XXT(
+        p._unbroadcasted_cov_factor * q._unbroadcasted_cov_diag.rsqrt().unsqueeze(-1)
+    )
+    term23 = _batch_trace_XXT(A * p._unbroadcasted_cov_diag.sqrt().unsqueeze(-2))
+    term24 = _batch_trace_XXT(A.matmul(p._unbroadcasted_cov_factor))
+    term2 = term21 + term22 - term23 - term24
+    return 0.5 * (term1 + term2 + term3 - p.event_shape[0])
+
+
+@register_kl(MultivariateNormal, LowRankMultivariateNormal)
+def _kl_multivariatenormal_lowrankmultivariatenormal(p, q):
+    if p.event_shape != q.event_shape:
+        raise ValueError(
+            "KL-divergence between two (Low Rank) Multivariate Normals with\
+                          different event shapes cannot be computed"
+        )
+
+    term1 = _batch_lowrank_logdet(
+        q._unbroadcasted_cov_factor, q._unbroadcasted_cov_diag, q._capacitance_tril
+    ) - 2 * p._unbroadcasted_scale_tril.diagonal(dim1=-2, dim2=-1).log().sum(-1)
+    term3 = _batch_lowrank_mahalanobis(
+        q._unbroadcasted_cov_factor,
+        q._unbroadcasted_cov_diag,
+        q.loc - p.loc,
+        q._capacitance_tril,
+    )
+    # Expands term2 according to
+    # inv(qcov) @ pcov = [inv(qD) - inv(qD) @ qW @ inv(qC) @ qW.T @ inv(qD)] @ p_tril @ p_tril.T
+    #                  = [inv(qD) - A.T @ A] @ p_tril @ p_tril.T
+    qWt_qDinv = q._unbroadcasted_cov_factor.mT / q._unbroadcasted_cov_diag.unsqueeze(-2)
+    A = torch.linalg.solve_triangular(q._capacitance_tril, qWt_qDinv, upper=False)
+    term21 = _batch_trace_XXT(
+        p._unbroadcasted_scale_tril * q._unbroadcasted_cov_diag.rsqrt().unsqueeze(-1)
+    )
+    term22 = _batch_trace_XXT(A.matmul(p._unbroadcasted_scale_tril))
+    term2 = term21 - term22
+    return 0.5 * (term1 + term2 + term3 - p.event_shape[0])
+
+
+@register_kl(LowRankMultivariateNormal, MultivariateNormal)
+def _kl_lowrankmultivariatenormal_multivariatenormal(p, q):
+    if p.event_shape != q.event_shape:
+        raise ValueError(
+            "KL-divergence between two (Low Rank) Multivariate Normals with\
+                          different event shapes cannot be computed"
+        )
+
+    term1 = 2 * q._unbroadcasted_scale_tril.diagonal(dim1=-2, dim2=-1).log().sum(
+        -1
+    ) - _batch_lowrank_logdet(
+        p._unbroadcasted_cov_factor, p._unbroadcasted_cov_diag, p._capacitance_tril
+    )
+    term3 = _batch_mahalanobis(q._unbroadcasted_scale_tril, (q.loc - p.loc))
+    # Expands term2 according to
+    # inv(qcov) @ pcov = inv(q_tril @ q_tril.T) @ (pW @ pW.T + pD)
+    combined_batch_shape = torch._C._infer_size(
+        q._unbroadcasted_scale_tril.shape[:-2], p._unbroadcasted_cov_factor.shape[:-2]
+    )
+    n = p.event_shape[0]
+    q_scale_tril = q._unbroadcasted_scale_tril.expand(combined_batch_shape + (n, n))
+    p_cov_factor = p._unbroadcasted_cov_factor.expand(
+        combined_batch_shape + (n, p.cov_factor.size(-1))
+    )
+    p_cov_diag = torch.diag_embed(p._unbroadcasted_cov_diag.sqrt()).expand(
+        combined_batch_shape + (n, n)
+    )
+    term21 = _batch_trace_XXT(
+        torch.linalg.solve_triangular(q_scale_tril, p_cov_factor, upper=False)
+    )
+    term22 = _batch_trace_XXT(
+        torch.linalg.solve_triangular(q_scale_tril, p_cov_diag, upper=False)
+    )
+    term2 = term21 + term22
+    return 0.5 * (term1 + term2 + term3 - p.event_shape[0])
+
+
+@register_kl(MultivariateNormal, MultivariateNormal)
+def _kl_multivariatenormal_multivariatenormal(p, q):
+    # From https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Kullback%E2%80%93Leibler_divergence
+    if p.event_shape != q.event_shape:
+        raise ValueError(
+            "KL-divergence between two Multivariate Normals with\
+                          different event shapes cannot be computed"
+        )
+
+    half_term1 = q._unbroadcasted_scale_tril.diagonal(dim1=-2, dim2=-1).log().sum(
+        -1
+    ) - p._unbroadcasted_scale_tril.diagonal(dim1=-2, dim2=-1).log().sum(-1)
+    combined_batch_shape = torch._C._infer_size(
+        q._unbroadcasted_scale_tril.shape[:-2], p._unbroadcasted_scale_tril.shape[:-2]
+    )
+    n = p.event_shape[0]
+    q_scale_tril = q._unbroadcasted_scale_tril.expand(combined_batch_shape + (n, n))
+    p_scale_tril = p._unbroadcasted_scale_tril.expand(combined_batch_shape + (n, n))
+    term2 = _batch_trace_XXT(
+        torch.linalg.solve_triangular(q_scale_tril, p_scale_tril, upper=False)
+    )
+    term3 = _batch_mahalanobis(q._unbroadcasted_scale_tril, (q.loc - p.loc))
+    return half_term1 + 0.5 * (term2 + term3 - n)
+
+
+@register_kl(Normal, Normal)
+def _kl_normal_normal(p, q):
+    var_ratio = (p.scale / q.scale).pow(2)
+    t1 = ((p.loc - q.loc) / q.scale).pow(2)
+    return 0.5 * (var_ratio + t1 - 1 - var_ratio.log())
+
+
+@register_kl(OneHotCategorical, OneHotCategorical)
+def _kl_onehotcategorical_onehotcategorical(p, q):
+    return _kl_categorical_categorical(p._categorical, q._categorical)
+
+
+@register_kl(Pareto, Pareto)
+def _kl_pareto_pareto(p, q):
+    # From http://www.mast.queensu.ca/~communications/Papers/gil-msc11.pdf
+    scale_ratio = p.scale / q.scale
+    alpha_ratio = q.alpha / p.alpha
+    t1 = q.alpha * scale_ratio.log()
+    t2 = -alpha_ratio.log()
+    result = t1 + t2 + alpha_ratio - 1
+    result[p.support.lower_bound < q.support.lower_bound] = inf
+    return result
+
+
+@register_kl(Poisson, Poisson)
+def _kl_poisson_poisson(p, q):
+    return p.rate * (p.rate.log() - q.rate.log()) - (p.rate - q.rate)
+
+
+@register_kl(TransformedDistribution, TransformedDistribution)
+def _kl_transformed_transformed(p, q):
+    if p.transforms != q.transforms:
+        raise NotImplementedError
+    if p.event_shape != q.event_shape:
+        raise NotImplementedError
+    return kl_divergence(p.base_dist, q.base_dist)
+
+
+@register_kl(Uniform, Uniform)
+def _kl_uniform_uniform(p, q):
+    result = ((q.high - q.low) / (p.high - p.low)).log()
+    result[(q.low > p.low) | (q.high < p.high)] = inf
+    return result
+
+
+# Different distributions
+@register_kl(Bernoulli, Poisson)
+def _kl_bernoulli_poisson(p, q):
+    return -p.entropy() - (p.probs * q.rate.log() - q.rate)
+
+
+@register_kl(Beta, ContinuousBernoulli)
+def _kl_beta_continuous_bernoulli(p, q):
+    return (
+        -p.entropy()
+        - p.mean * q.logits
+        - torch.log1p(-q.probs)
+        - q._cont_bern_log_norm()
+    )
+
+
+@register_kl(Beta, Pareto)
+def _kl_beta_infinity(p, q):
+    return _infinite_like(p.concentration1)
+
+
+@register_kl(Beta, Exponential)
+def _kl_beta_exponential(p, q):
+    return (
+        -p.entropy()
+        - q.rate.log()
+        + q.rate * (p.concentration1 / (p.concentration1 + p.concentration0))
+    )
+
+
+@register_kl(Beta, Gamma)
+def _kl_beta_gamma(p, q):
+    t1 = -p.entropy()
+    t2 = q.concentration.lgamma() - q.concentration * q.rate.log()
+    t3 = (q.concentration - 1) * (
+        p.concentration1.digamma() - (p.concentration1 + p.concentration0).digamma()
+    )
+    t4 = q.rate * p.concentration1 / (p.concentration1 + p.concentration0)
+    return t1 + t2 - t3 + t4
+
+
+# TODO: Add Beta-Laplace KL Divergence
+
+
+@register_kl(Beta, Normal)
+def _kl_beta_normal(p, q):
+    E_beta = p.concentration1 / (p.concentration1 + p.concentration0)
+    var_normal = q.scale.pow(2)
+    t1 = -p.entropy()
+    t2 = 0.5 * (var_normal * 2 * math.pi).log()
+    t3 = (
+        E_beta * (1 - E_beta) / (p.concentration1 + p.concentration0 + 1)
+        + E_beta.pow(2)
+    ) * 0.5
+    t4 = q.loc * E_beta
+    t5 = q.loc.pow(2) * 0.5
+    return t1 + t2 + (t3 - t4 + t5) / var_normal
+
+
+@register_kl(Beta, Uniform)
+def _kl_beta_uniform(p, q):
+    result = -p.entropy() + (q.high - q.low).log()
+    result[(q.low > p.support.lower_bound) | (q.high < p.support.upper_bound)] = inf
+    return result
+
+
+# Note that the KL between a ContinuousBernoulli and Beta has no closed form
+
+
+@register_kl(ContinuousBernoulli, Pareto)
+def _kl_continuous_bernoulli_infinity(p, q):
+    return _infinite_like(p.probs)
+
+
+@register_kl(ContinuousBernoulli, Exponential)
+def _kl_continuous_bernoulli_exponential(p, q):
+    return -p.entropy() - torch.log(q.rate) + q.rate * p.mean
+
+
+# Note that the KL between a ContinuousBernoulli and Gamma has no closed form
+# TODO: Add ContinuousBernoulli-Laplace KL Divergence
+
+
+@register_kl(ContinuousBernoulli, Normal)
+def _kl_continuous_bernoulli_normal(p, q):
+    t1 = -p.entropy()
+    t2 = 0.5 * (math.log(2.0 * math.pi) + torch.square(q.loc / q.scale)) + torch.log(
+        q.scale
+    )
+    t3 = (p.variance + torch.square(p.mean) - 2.0 * q.loc * p.mean) / (
+        2.0 * torch.square(q.scale)
+    )
+    return t1 + t2 + t3
+
+
+@register_kl(ContinuousBernoulli, Uniform)
+def _kl_continuous_bernoulli_uniform(p, q):
+    result = -p.entropy() + (q.high - q.low).log()
+    return torch.where(
+        torch.max(
+            torch.ge(q.low, p.support.lower_bound),
+            torch.le(q.high, p.support.upper_bound),
+        ),
+        torch.ones_like(result) * inf,
+        result,
+    )
+
+
+@register_kl(Exponential, Beta)
+@register_kl(Exponential, ContinuousBernoulli)
+@register_kl(Exponential, Pareto)
+@register_kl(Exponential, Uniform)
+def _kl_exponential_infinity(p, q):
+    return _infinite_like(p.rate)
+
+
+@register_kl(Exponential, Gamma)
+def _kl_exponential_gamma(p, q):
+    ratio = q.rate / p.rate
+    t1 = -q.concentration * torch.log(ratio)
+    return (
+        t1
+        + ratio
+        + q.concentration.lgamma()
+        + q.concentration * _euler_gamma
+        - (1 + _euler_gamma)
+    )
+
+
+@register_kl(Exponential, Gumbel)
+def _kl_exponential_gumbel(p, q):
+    scale_rate_prod = p.rate * q.scale
+    loc_scale_ratio = q.loc / q.scale
+    t1 = scale_rate_prod.log() - 1
+    t2 = torch.exp(loc_scale_ratio) * scale_rate_prod / (scale_rate_prod + 1)
+    t3 = scale_rate_prod.reciprocal()
+    return t1 - loc_scale_ratio + t2 + t3
+
+
+# TODO: Add Exponential-Laplace KL Divergence
+
+
+@register_kl(Exponential, Normal)
+def _kl_exponential_normal(p, q):
+    var_normal = q.scale.pow(2)
+    rate_sqr = p.rate.pow(2)
+    t1 = 0.5 * torch.log(rate_sqr * var_normal * 2 * math.pi)
+    t2 = rate_sqr.reciprocal()
+    t3 = q.loc / p.rate
+    t4 = q.loc.pow(2) * 0.5
+    return t1 - 1 + (t2 - t3 + t4) / var_normal
+
+
+@register_kl(Gamma, Beta)
+@register_kl(Gamma, ContinuousBernoulli)
+@register_kl(Gamma, Pareto)
+@register_kl(Gamma, Uniform)
+def _kl_gamma_infinity(p, q):
+    return _infinite_like(p.concentration)
+
+
+@register_kl(Gamma, Exponential)
+def _kl_gamma_exponential(p, q):
+    return -p.entropy() - q.rate.log() + q.rate * p.concentration / p.rate
+
+
+@register_kl(Gamma, Gumbel)
+def _kl_gamma_gumbel(p, q):
+    beta_scale_prod = p.rate * q.scale
+    loc_scale_ratio = q.loc / q.scale
+    t1 = (
+        (p.concentration - 1) * p.concentration.digamma()
+        - p.concentration.lgamma()
+        - p.concentration
+    )
+    t2 = beta_scale_prod.log() + p.concentration / beta_scale_prod
+    t3 = (
+        torch.exp(loc_scale_ratio)
+        * (1 + beta_scale_prod.reciprocal()).pow(-p.concentration)
+        - loc_scale_ratio
+    )
+    return t1 + t2 + t3
+
+
+# TODO: Add Gamma-Laplace KL Divergence
+
+
+@register_kl(Gamma, Normal)
+def _kl_gamma_normal(p, q):
+    var_normal = q.scale.pow(2)
+    beta_sqr = p.rate.pow(2)
+    t1 = (
+        0.5 * torch.log(beta_sqr * var_normal * 2 * math.pi)
+        - p.concentration
+        - p.concentration.lgamma()
+    )
+    t2 = 0.5 * (p.concentration.pow(2) + p.concentration) / beta_sqr
+    t3 = q.loc * p.concentration / p.rate
+    t4 = 0.5 * q.loc.pow(2)
+    return (
+        t1
+        + (p.concentration - 1) * p.concentration.digamma()
+        + (t2 - t3 + t4) / var_normal
+    )
+
+
+@register_kl(Gumbel, Beta)
+@register_kl(Gumbel, ContinuousBernoulli)
+@register_kl(Gumbel, Exponential)
+@register_kl(Gumbel, Gamma)
+@register_kl(Gumbel, Pareto)
+@register_kl(Gumbel, Uniform)
+def _kl_gumbel_infinity(p, q):
+    return _infinite_like(p.loc)
+
+
+# TODO: Add Gumbel-Laplace KL Divergence
+
+
+@register_kl(Gumbel, Normal)
+def _kl_gumbel_normal(p, q):
+    param_ratio = p.scale / q.scale
+    t1 = (param_ratio / math.sqrt(2 * math.pi)).log()
+    t2 = (math.pi * param_ratio * 0.5).pow(2) / 3
+    t3 = ((p.loc + p.scale * _euler_gamma - q.loc) / q.scale).pow(2) * 0.5
+    return -t1 + t2 + t3 - (_euler_gamma + 1)
+
+
+@register_kl(Laplace, Beta)
+@register_kl(Laplace, ContinuousBernoulli)
+@register_kl(Laplace, Exponential)
+@register_kl(Laplace, Gamma)
+@register_kl(Laplace, Pareto)
+@register_kl(Laplace, Uniform)
+def _kl_laplace_infinity(p, q):
+    return _infinite_like(p.loc)
+
+
+@register_kl(Laplace, Normal)
+def _kl_laplace_normal(p, q):
+    var_normal = q.scale.pow(2)
+    scale_sqr_var_ratio = p.scale.pow(2) / var_normal
+    t1 = 0.5 * torch.log(2 * scale_sqr_var_ratio / math.pi)
+    t2 = 0.5 * p.loc.pow(2)
+    t3 = p.loc * q.loc
+    t4 = 0.5 * q.loc.pow(2)
+    return -t1 + scale_sqr_var_ratio + (t2 - t3 + t4) / var_normal - 1
+
+
+@register_kl(Normal, Beta)
+@register_kl(Normal, ContinuousBernoulli)
+@register_kl(Normal, Exponential)
+@register_kl(Normal, Gamma)
+@register_kl(Normal, Pareto)
+@register_kl(Normal, Uniform)
+def _kl_normal_infinity(p, q):
+    return _infinite_like(p.loc)
+
+
+@register_kl(Normal, Gumbel)
+def _kl_normal_gumbel(p, q):
+    mean_scale_ratio = p.loc / q.scale
+    var_scale_sqr_ratio = (p.scale / q.scale).pow(2)
+    loc_scale_ratio = q.loc / q.scale
+    t1 = var_scale_sqr_ratio.log() * 0.5
+    t2 = mean_scale_ratio - loc_scale_ratio
+    t3 = torch.exp(-mean_scale_ratio + 0.5 * var_scale_sqr_ratio + loc_scale_ratio)
+    return -t1 + t2 + t3 - (0.5 * (1 + math.log(2 * math.pi)))
+
+
+@register_kl(Normal, Laplace)
+def _kl_normal_laplace(p, q):
+    loc_diff = p.loc - q.loc
+    scale_ratio = p.scale / q.scale
+    loc_diff_scale_ratio = loc_diff / p.scale
+    t1 = torch.log(scale_ratio)
+    t2 = (
+        math.sqrt(2 / math.pi) * p.scale * torch.exp(-0.5 * loc_diff_scale_ratio.pow(2))
+    )
+    t3 = loc_diff * torch.erf(math.sqrt(0.5) * loc_diff_scale_ratio)
+    return -t1 + (t2 + t3) / q.scale - (0.5 * (1 + math.log(0.5 * math.pi)))
+
+
+@register_kl(Pareto, Beta)
+@register_kl(Pareto, ContinuousBernoulli)
+@register_kl(Pareto, Uniform)
+def _kl_pareto_infinity(p, q):
+    return _infinite_like(p.scale)
+
+
+@register_kl(Pareto, Exponential)
+def _kl_pareto_exponential(p, q):
+    scale_rate_prod = p.scale * q.rate
+    t1 = (p.alpha / scale_rate_prod).log()
+    t2 = p.alpha.reciprocal()
+    t3 = p.alpha * scale_rate_prod / (p.alpha - 1)
+    result = t1 - t2 + t3 - 1
+    result[p.alpha <= 1] = inf
+    return result
+
+
+@register_kl(Pareto, Gamma)
+def _kl_pareto_gamma(p, q):
+    common_term = p.scale.log() + p.alpha.reciprocal()
+    t1 = p.alpha.log() - common_term
+    t2 = q.concentration.lgamma() - q.concentration * q.rate.log()
+    t3 = (1 - q.concentration) * common_term
+    t4 = q.rate * p.alpha * p.scale / (p.alpha - 1)
+    result = t1 + t2 + t3 + t4 - 1
+    result[p.alpha <= 1] = inf
+    return result
+
+
+# TODO: Add Pareto-Laplace KL Divergence
+
+
+@register_kl(Pareto, Normal)
+def _kl_pareto_normal(p, q):
+    var_normal = 2 * q.scale.pow(2)
+    common_term = p.scale / (p.alpha - 1)
+    t1 = (math.sqrt(2 * math.pi) * q.scale * p.alpha / p.scale).log()
+    t2 = p.alpha.reciprocal()
+    t3 = p.alpha * common_term.pow(2) / (p.alpha - 2)
+    t4 = (p.alpha * common_term - q.loc).pow(2)
+    result = t1 - t2 + (t3 + t4) / var_normal - 1
+    result[p.alpha <= 2] = inf
+    return result
+
+
+@register_kl(Poisson, Bernoulli)
+@register_kl(Poisson, Binomial)
+def _kl_poisson_infinity(p, q):
+    return _infinite_like(p.rate)
+
+
+@register_kl(Uniform, Beta)
+def _kl_uniform_beta(p, q):
+    common_term = p.high - p.low
+    t1 = torch.log(common_term)
+    t2 = (
+        (q.concentration1 - 1)
+        * (_x_log_x(p.high) - _x_log_x(p.low) - common_term)
+        / common_term
+    )
+    t3 = (
+        (q.concentration0 - 1)
+        * (_x_log_x(1 - p.high) - _x_log_x(1 - p.low) + common_term)
+        / common_term
+    )
+    t4 = (
+        q.concentration1.lgamma()
+        + q.concentration0.lgamma()
+        - (q.concentration1 + q.concentration0).lgamma()
+    )
+    result = t3 + t4 - t1 - t2
+    result[(p.high > q.support.upper_bound) | (p.low < q.support.lower_bound)] = inf
+    return result
+
+
+@register_kl(Uniform, ContinuousBernoulli)
+def _kl_uniform_continuous_bernoulli(p, q):
+    result = (
+        -p.entropy()
+        - p.mean * q.logits
+        - torch.log1p(-q.probs)
+        - q._cont_bern_log_norm()
+    )
+    return torch.where(
+        torch.max(
+            torch.ge(p.high, q.support.upper_bound),
+            torch.le(p.low, q.support.lower_bound),
+        ),
+        torch.ones_like(result) * inf,
+        result,
+    )
+
+
+@register_kl(Uniform, Exponential)
+def _kl_uniform_exponetial(p, q):
+    result = q.rate * (p.high + p.low) / 2 - ((p.high - p.low) * q.rate).log()
+    result[p.low < q.support.lower_bound] = inf
+    return result
+
+
+@register_kl(Uniform, Gamma)
+def _kl_uniform_gamma(p, q):
+    common_term = p.high - p.low
+    t1 = common_term.log()
+    t2 = q.concentration.lgamma() - q.concentration * q.rate.log()
+    t3 = (
+        (1 - q.concentration)
+        * (_x_log_x(p.high) - _x_log_x(p.low) - common_term)
+        / common_term
+    )
+    t4 = q.rate * (p.high + p.low) / 2
+    result = -t1 + t2 + t3 + t4
+    result[p.low < q.support.lower_bound] = inf
+    return result
+
+
+@register_kl(Uniform, Gumbel)
+def _kl_uniform_gumbel(p, q):
+    common_term = q.scale / (p.high - p.low)
+    high_loc_diff = (p.high - q.loc) / q.scale
+    low_loc_diff = (p.low - q.loc) / q.scale
+    t1 = common_term.log() + 0.5 * (high_loc_diff + low_loc_diff)
+    t2 = common_term * (torch.exp(-high_loc_diff) - torch.exp(-low_loc_diff))
+    return t1 - t2
+
+
+# TODO: Uniform-Laplace KL Divergence
+
+
+@register_kl(Uniform, Normal)
+def _kl_uniform_normal(p, q):
+    common_term = p.high - p.low
+    t1 = (math.sqrt(math.pi * 2) * q.scale / common_term).log()
+    t2 = (common_term).pow(2) / 12
+    t3 = ((p.high + p.low - 2 * q.loc) / 2).pow(2)
+    return t1 + 0.5 * (t2 + t3) / q.scale.pow(2)
+
+
+@register_kl(Uniform, Pareto)
+def _kl_uniform_pareto(p, q):
+    support_uniform = p.high - p.low
+    t1 = (q.alpha * q.scale.pow(q.alpha) * (support_uniform)).log()
+    t2 = (_x_log_x(p.high) - _x_log_x(p.low) - support_uniform) / support_uniform
+    result = t2 * (q.alpha + 1) - t1
+    result[p.low < q.support.lower_bound] = inf
+    return result
+
+
+@register_kl(Independent, Independent)
+def _kl_independent_independent(p, q):
+    if p.reinterpreted_batch_ndims != q.reinterpreted_batch_ndims:
+        raise NotImplementedError
+    result = kl_divergence(p.base_dist, q.base_dist)
+    return _sum_rightmost(result, p.reinterpreted_batch_ndims)
+
+
+@register_kl(Cauchy, Cauchy)
+def _kl_cauchy_cauchy(p, q):
+    # From https://arxiv.org/abs/1905.10965
+    t1 = ((p.scale + q.scale).pow(2) + (p.loc - q.loc).pow(2)).log()
+    t2 = (4 * p.scale * q.scale).log()
+    return t1 - t2
+
+
+def _add_kl_info():
+    """Appends a list of implemented KL functions to the doc for kl_divergence."""
+    rows = [
+        "KL divergence is currently implemented for the following distribution pairs:"
+    ]
+    for p, q in sorted(
+        _KL_REGISTRY, key=lambda p_q: (p_q[0].__name__, p_q[1].__name__)
+    ):
+        rows.append(
+            f"* :class:`~torch.distributions.{p.__name__}` and :class:`~torch.distributions.{q.__name__}`"
+        )
+    kl_info = "\n\t".join(rows)
+    if kl_divergence.__doc__:
+        kl_divergence.__doc__ += kl_info  # type: ignore[operator]

venv/lib/python3.10/site-packages/torch/distributions/kumaraswamy.py

@@ -0,0 +1,97 @@
+import torch
+from torch import nan
+from torch.distributions import constraints
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import AffineTransform, PowerTransform
+from torch.distributions.uniform import Uniform
+from torch.distributions.utils import broadcast_all, euler_constant
+
+__all__ = ["Kumaraswamy"]
+
+
+def _moments(a, b, n):
+    """
+    Computes nth moment of Kumaraswamy using using torch.lgamma
+    """
+    arg1 = 1 + n / a
+    log_value = torch.lgamma(arg1) + torch.lgamma(b) - torch.lgamma(arg1 + b)
+    return b * torch.exp(log_value)
+
+
+class Kumaraswamy(TransformedDistribution):
+    r"""
+    Samples from a Kumaraswamy distribution.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Kumaraswamy(torch.tensor([1.0]), torch.tensor([1.0]))
+        >>> m.sample()  # sample from a Kumaraswamy distribution with concentration alpha=1 and beta=1
+        tensor([ 0.1729])
+
+    Args:
+        concentration1 (float or Tensor): 1st concentration parameter of the distribution
+            (often referred to as alpha)
+        concentration0 (float or Tensor): 2nd concentration parameter of the distribution
+            (often referred to as beta)
+    """
+    arg_constraints = {
+        "concentration1": constraints.positive,
+        "concentration0": constraints.positive,
+    }
+    support = constraints.unit_interval
+    has_rsample = True
+
+    def __init__(self, concentration1, concentration0, validate_args=None):
+        self.concentration1, self.concentration0 = broadcast_all(
+            concentration1, concentration0
+        )
+        finfo = torch.finfo(self.concentration0.dtype)
+        base_dist = Uniform(
+            torch.full_like(self.concentration0, 0),
+            torch.full_like(self.concentration0, 1),
+            validate_args=validate_args,
+        )
+        transforms = [
+            PowerTransform(exponent=self.concentration0.reciprocal()),
+            AffineTransform(loc=1.0, scale=-1.0),
+            PowerTransform(exponent=self.concentration1.reciprocal()),
+        ]
+        super().__init__(base_dist, transforms, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Kumaraswamy, _instance)
+        new.concentration1 = self.concentration1.expand(batch_shape)
+        new.concentration0 = self.concentration0.expand(batch_shape)
+        return super().expand(batch_shape, _instance=new)
+
+    @property
+    def mean(self):
+        return _moments(self.concentration1, self.concentration0, 1)
+
+    @property
+    def mode(self):
+        # Evaluate in log-space for numerical stability.
+        log_mode = (
+            self.concentration0.reciprocal() * (-self.concentration0).log1p()
+            - (-self.concentration0 * self.concentration1).log1p()
+        )
+        log_mode[(self.concentration0 < 1) | (self.concentration1 < 1)] = nan
+        return log_mode.exp()
+
+    @property
+    def variance(self):
+        return _moments(self.concentration1, self.concentration0, 2) - torch.pow(
+            self.mean, 2
+        )
+
+    def entropy(self):
+        t1 = 1 - self.concentration1.reciprocal()
+        t0 = 1 - self.concentration0.reciprocal()
+        H0 = torch.digamma(self.concentration0 + 1) + euler_constant
+        return (
+            t0
+            + t1 * H0
+            - torch.log(self.concentration1)
+            - torch.log(self.concentration0)
+        )

venv/lib/python3.10/site-packages/torch/distributions/logistic_normal.py

@@ -0,0 +1,54 @@
+from torch.distributions import constraints
+from torch.distributions.normal import Normal
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import StickBreakingTransform
+
+__all__ = ["LogisticNormal"]
+
+
+class LogisticNormal(TransformedDistribution):
+    r"""
+    Creates a logistic-normal distribution parameterized by :attr:`loc` and :attr:`scale`
+    that define the base `Normal` distribution transformed with the
+    `StickBreakingTransform` such that::
+
+        X ~ LogisticNormal(loc, scale)
+        Y = log(X / (1 - X.cumsum(-1)))[..., :-1] ~ Normal(loc, scale)
+
+    Args:
+        loc (float or Tensor): mean of the base distribution
+        scale (float or Tensor): standard deviation of the base distribution
+
+    Example::
+
+        >>> # logistic-normal distributed with mean=(0, 0, 0) and stddev=(1, 1, 1)
+        >>> # of the base Normal distribution
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = LogisticNormal(torch.tensor([0.0] * 3), torch.tensor([1.0] * 3))
+        >>> m.sample()
+        tensor([ 0.7653,  0.0341,  0.0579,  0.1427])
+
+    """
+    arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
+    support = constraints.simplex
+    has_rsample = True
+
+    def __init__(self, loc, scale, validate_args=None):
+        base_dist = Normal(loc, scale, validate_args=validate_args)
+        if not base_dist.batch_shape:
+            base_dist = base_dist.expand([1])
+        super().__init__(
+            base_dist, StickBreakingTransform(), validate_args=validate_args
+        )
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(LogisticNormal, _instance)
+        return super().expand(batch_shape, _instance=new)
+
+    @property
+    def loc(self):
+        return self.base_dist.base_dist.loc
+
+    @property
+    def scale(self):
+        return self.base_dist.base_dist.scale

venv/lib/python3.10/site-packages/torch/distributions/mixture_same_family.py

@@ -0,0 +1,214 @@
+from typing import Dict
+
+import torch
+from torch.distributions import Categorical, constraints
+from torch.distributions.distribution import Distribution
+
+__all__ = ["MixtureSameFamily"]
+
+
+class MixtureSameFamily(Distribution):
+    r"""
+    The `MixtureSameFamily` distribution implements a (batch of) mixture
+    distribution where all component are from different parameterizations of
+    the same distribution type. It is parameterized by a `Categorical`
+    "selecting distribution" (over `k` component) and a component
+    distribution, i.e., a `Distribution` with a rightmost batch shape
+    (equal to `[k]`) which indexes each (batch of) component.
+
+    Examples::
+
+        >>> # xdoctest: +SKIP("undefined vars")
+        >>> # Construct Gaussian Mixture Model in 1D consisting of 5 equally
+        >>> # weighted normal distributions
+        >>> mix = D.Categorical(torch.ones(5,))
+        >>> comp = D.Normal(torch.randn(5,), torch.rand(5,))
+        >>> gmm = MixtureSameFamily(mix, comp)
+
+        >>> # Construct Gaussian Mixture Model in 2D consisting of 5 equally
+        >>> # weighted bivariate normal distributions
+        >>> mix = D.Categorical(torch.ones(5,))
+        >>> comp = D.Independent(D.Normal(
+        ...          torch.randn(5,2), torch.rand(5,2)), 1)
+        >>> gmm = MixtureSameFamily(mix, comp)
+
+        >>> # Construct a batch of 3 Gaussian Mixture Models in 2D each
+        >>> # consisting of 5 random weighted bivariate normal distributions
+        >>> mix = D.Categorical(torch.rand(3,5))
+        >>> comp = D.Independent(D.Normal(
+        ...         torch.randn(3,5,2), torch.rand(3,5,2)), 1)
+        >>> gmm = MixtureSameFamily(mix, comp)
+
+    Args:
+        mixture_distribution: `torch.distributions.Categorical`-like
+            instance. Manages the probability of selecting component.
+            The number of categories must match the rightmost batch
+            dimension of the `component_distribution`. Must have either
+            scalar `batch_shape` or `batch_shape` matching
+            `component_distribution.batch_shape[:-1]`
+        component_distribution: `torch.distributions.Distribution`-like
+            instance. Right-most batch dimension indexes component.
+    """
+    arg_constraints: Dict[str, constraints.Constraint] = {}
+    has_rsample = False
+
+    def __init__(
+        self, mixture_distribution, component_distribution, validate_args=None
+    ):
+        self._mixture_distribution = mixture_distribution
+        self._component_distribution = component_distribution
+
+        if not isinstance(self._mixture_distribution, Categorical):
+            raise ValueError(
+                " The Mixture distribution needs to be an "
+                " instance of torch.distributions.Categorical"
+            )
+
+        if not isinstance(self._component_distribution, Distribution):
+            raise ValueError(
+                "The Component distribution need to be an "
+                "instance of torch.distributions.Distribution"
+            )
+
+        # Check that batch size matches
+        mdbs = self._mixture_distribution.batch_shape
+        cdbs = self._component_distribution.batch_shape[:-1]
+        for size1, size2 in zip(reversed(mdbs), reversed(cdbs)):
+            if size1 != 1 and size2 != 1 and size1 != size2:
+                raise ValueError(
+                    f"`mixture_distribution.batch_shape` ({mdbs}) is not "
+                    "compatible with `component_distribution."
+                    f"batch_shape`({cdbs})"
+                )
+
+        # Check that the number of mixture component matches
+        km = self._mixture_distribution.logits.shape[-1]
+        kc = self._component_distribution.batch_shape[-1]
+        if km is not None and kc is not None and km != kc:
+            raise ValueError(
+                f"`mixture_distribution component` ({km}) does not"
+                " equal `component_distribution.batch_shape[-1]`"
+                f" ({kc})"
+            )
+        self._num_component = km
+
+        event_shape = self._component_distribution.event_shape
+        self._event_ndims = len(event_shape)
+        super().__init__(
+            batch_shape=cdbs, event_shape=event_shape, validate_args=validate_args
+        )
+
+    def expand(self, batch_shape, _instance=None):
+        batch_shape = torch.Size(batch_shape)
+        batch_shape_comp = batch_shape + (self._num_component,)
+        new = self._get_checked_instance(MixtureSameFamily, _instance)
+        new._component_distribution = self._component_distribution.expand(
+            batch_shape_comp
+        )
+        new._mixture_distribution = self._mixture_distribution.expand(batch_shape)
+        new._num_component = self._num_component
+        new._event_ndims = self._event_ndims
+        event_shape = new._component_distribution.event_shape
+        super(MixtureSameFamily, new).__init__(
+            batch_shape=batch_shape, event_shape=event_shape, validate_args=False
+        )
+        new._validate_args = self._validate_args
+        return new
+
+    @constraints.dependent_property
+    def support(self):
+        # FIXME this may have the wrong shape when support contains batched
+        # parameters
+        return self._component_distribution.support
+
+    @property
+    def mixture_distribution(self):
+        return self._mixture_distribution
+
+    @property
+    def component_distribution(self):
+        return self._component_distribution
+
+    @property
+    def mean(self):
+        probs = self._pad_mixture_dimensions(self.mixture_distribution.probs)
+        return torch.sum(
+            probs * self.component_distribution.mean, dim=-1 - self._event_ndims
+        )  # [B, E]
+
+    @property
+    def variance(self):
+        # Law of total variance: Var(Y) = E[Var(Y|X)] + Var(E[Y|X])
+        probs = self._pad_mixture_dimensions(self.mixture_distribution.probs)
+        mean_cond_var = torch.sum(
+            probs * self.component_distribution.variance, dim=-1 - self._event_ndims
+        )
+        var_cond_mean = torch.sum(
+            probs * (self.component_distribution.mean - self._pad(self.mean)).pow(2.0),
+            dim=-1 - self._event_ndims,
+        )
+        return mean_cond_var + var_cond_mean
+
+    def cdf(self, x):
+        x = self._pad(x)
+        cdf_x = self.component_distribution.cdf(x)
+        mix_prob = self.mixture_distribution.probs
+
+        return torch.sum(cdf_x * mix_prob, dim=-1)
+
+    def log_prob(self, x):
+        if self._validate_args:
+            self._validate_sample(x)
+        x = self._pad(x)
+        log_prob_x = self.component_distribution.log_prob(x)  # [S, B, k]
+        log_mix_prob = torch.log_softmax(
+            self.mixture_distribution.logits, dim=-1
+        )  # [B, k]
+        return torch.logsumexp(log_prob_x + log_mix_prob, dim=-1)  # [S, B]
+
+    def sample(self, sample_shape=torch.Size()):
+        with torch.no_grad():
+            sample_len = len(sample_shape)
+            batch_len = len(self.batch_shape)
+            gather_dim = sample_len + batch_len
+            es = self.event_shape
+
+            # mixture samples [n, B]
+            mix_sample = self.mixture_distribution.sample(sample_shape)
+            mix_shape = mix_sample.shape
+
+            # component samples [n, B, k, E]
+            comp_samples = self.component_distribution.sample(sample_shape)
+
+            # Gather along the k dimension
+            mix_sample_r = mix_sample.reshape(
+                mix_shape + torch.Size([1] * (len(es) + 1))
+            )
+            mix_sample_r = mix_sample_r.repeat(
+                torch.Size([1] * len(mix_shape)) + torch.Size([1]) + es
+            )
+
+            samples = torch.gather(comp_samples, gather_dim, mix_sample_r)
+            return samples.squeeze(gather_dim)
+
+    def _pad(self, x):
+        return x.unsqueeze(-1 - self._event_ndims)
+
+    def _pad_mixture_dimensions(self, x):
+        dist_batch_ndims = len(self.batch_shape)
+        cat_batch_ndims = len(self.mixture_distribution.batch_shape)
+        pad_ndims = 0 if cat_batch_ndims == 1 else dist_batch_ndims - cat_batch_ndims
+        xs = x.shape
+        x = x.reshape(
+            xs[:-1]
+            + torch.Size(pad_ndims * [1])
+            + xs[-1:]
+            + torch.Size(self._event_ndims * [1])
+        )
+        return x
+
+    def __repr__(self):
+        args_string = (
+            f"\n  {self.mixture_distribution},\n  {self.component_distribution}"
+        )
+        return "MixtureSameFamily" + "(" + args_string + ")"

venv/lib/python3.10/site-packages/torch/distributions/multivariate_normal.py

@@ -0,0 +1,262 @@
+import math
+
+import torch
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import _standard_normal, lazy_property
+
+__all__ = ["MultivariateNormal"]
+
+
+def _batch_mv(bmat, bvec):
+    r"""
+    Performs a batched matrix-vector product, with compatible but different batch shapes.
+
+    This function takes as input `bmat`, containing :math:`n \times n` matrices, and
+    `bvec`, containing length :math:`n` vectors.
+
+    Both `bmat` and `bvec` may have any number of leading dimensions, which correspond
+    to a batch shape. They are not necessarily assumed to have the same batch shape,
+    just ones which can be broadcasted.
+    """
+    return torch.matmul(bmat, bvec.unsqueeze(-1)).squeeze(-1)
+
+
+def _batch_mahalanobis(bL, bx):
+    r"""
+    Computes the squared Mahalanobis distance :math:`\mathbf{x}^\top\mathbf{M}^{-1}\mathbf{x}`
+    for a factored :math:`\mathbf{M} = \mathbf{L}\mathbf{L}^\top`.
+
+    Accepts batches for both bL and bx. They are not necessarily assumed to have the same batch
+    shape, but `bL` one should be able to broadcasted to `bx` one.
+    """
+    n = bx.size(-1)
+    bx_batch_shape = bx.shape[:-1]
+
+    # Assume that bL.shape = (i, 1, n, n), bx.shape = (..., i, j, n),
+    # we are going to make bx have shape (..., 1, j,  i, 1, n) to apply batched tri.solve
+    bx_batch_dims = len(bx_batch_shape)
+    bL_batch_dims = bL.dim() - 2
+    outer_batch_dims = bx_batch_dims - bL_batch_dims
+    old_batch_dims = outer_batch_dims + bL_batch_dims
+    new_batch_dims = outer_batch_dims + 2 * bL_batch_dims
+    # Reshape bx with the shape (..., 1, i, j, 1, n)
+    bx_new_shape = bx.shape[:outer_batch_dims]
+    for sL, sx in zip(bL.shape[:-2], bx.shape[outer_batch_dims:-1]):
+        bx_new_shape += (sx // sL, sL)
+    bx_new_shape += (n,)
+    bx = bx.reshape(bx_new_shape)
+    # Permute bx to make it have shape (..., 1, j, i, 1, n)
+    permute_dims = (
+        list(range(outer_batch_dims))
+        + list(range(outer_batch_dims, new_batch_dims, 2))
+        + list(range(outer_batch_dims + 1, new_batch_dims, 2))
+        + [new_batch_dims]
+    )
+    bx = bx.permute(permute_dims)
+
+    flat_L = bL.reshape(-1, n, n)  # shape = b x n x n
+    flat_x = bx.reshape(-1, flat_L.size(0), n)  # shape = c x b x n
+    flat_x_swap = flat_x.permute(1, 2, 0)  # shape = b x n x c
+    M_swap = (
+        torch.linalg.solve_triangular(flat_L, flat_x_swap, upper=False).pow(2).sum(-2)
+    )  # shape = b x c
+    M = M_swap.t()  # shape = c x b
+
+    # Now we revert the above reshape and permute operators.
+    permuted_M = M.reshape(bx.shape[:-1])  # shape = (..., 1, j, i, 1)
+    permute_inv_dims = list(range(outer_batch_dims))
+    for i in range(bL_batch_dims):
+        permute_inv_dims += [outer_batch_dims + i, old_batch_dims + i]
+    reshaped_M = permuted_M.permute(permute_inv_dims)  # shape = (..., 1, i, j, 1)
+    return reshaped_M.reshape(bx_batch_shape)
+
+
+def _precision_to_scale_tril(P):
+    # Ref: https://nbviewer.jupyter.org/gist/fehiepsi/5ef8e09e61604f10607380467eb82006#Precision-to-scale_tril
+    Lf = torch.linalg.cholesky(torch.flip(P, (-2, -1)))
+    L_inv = torch.transpose(torch.flip(Lf, (-2, -1)), -2, -1)
+    Id = torch.eye(P.shape[-1], dtype=P.dtype, device=P.device)
+    L = torch.linalg.solve_triangular(L_inv, Id, upper=False)
+    return L
+
+
+class MultivariateNormal(Distribution):
+    r"""
+    Creates a multivariate normal (also called Gaussian) distribution
+    parameterized by a mean vector and a covariance matrix.
+
+    The multivariate normal distribution can be parameterized either
+    in terms of a positive definite covariance matrix :math:`\mathbf{\Sigma}`
+    or a positive definite precision matrix :math:`\mathbf{\Sigma}^{-1}`
+    or a lower-triangular matrix :math:`\mathbf{L}` with positive-valued
+    diagonal entries, such that
+    :math:`\mathbf{\Sigma} = \mathbf{L}\mathbf{L}^\top`. This triangular matrix
+    can be obtained via e.g. Cholesky decomposition of the covariance.
+
+    Example:
+
+        >>> # xdoctest: +REQUIRES(env:TORCH_DOCTEST_LAPACK)
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = MultivariateNormal(torch.zeros(2), torch.eye(2))
+        >>> m.sample()  # normally distributed with mean=`[0,0]` and covariance_matrix=`I`
+        tensor([-0.2102, -0.5429])
+
+    Args:
+        loc (Tensor): mean of the distribution
+        covariance_matrix (Tensor): positive-definite covariance matrix
+        precision_matrix (Tensor): positive-definite precision matrix
+        scale_tril (Tensor): lower-triangular factor of covariance, with positive-valued diagonal
+
+    Note:
+        Only one of :attr:`covariance_matrix` or :attr:`precision_matrix` or
+        :attr:`scale_tril` can be specified.
+
+        Using :attr:`scale_tril` will be more efficient: all computations internally
+        are based on :attr:`scale_tril`. If :attr:`covariance_matrix` or
+        :attr:`precision_matrix` is passed instead, it is only used to compute
+        the corresponding lower triangular matrices using a Cholesky decomposition.
+    """
+    arg_constraints = {
+        "loc": constraints.real_vector,
+        "covariance_matrix": constraints.positive_definite,
+        "precision_matrix": constraints.positive_definite,
+        "scale_tril": constraints.lower_cholesky,
+    }
+    support = constraints.real_vector
+    has_rsample = True
+
+    def __init__(
+        self,
+        loc,
+        covariance_matrix=None,
+        precision_matrix=None,
+        scale_tril=None,
+        validate_args=None,
+    ):
+        if loc.dim() < 1:
+            raise ValueError("loc must be at least one-dimensional.")
+        if (covariance_matrix is not None) + (scale_tril is not None) + (
+            precision_matrix is not None
+        ) != 1:
+            raise ValueError(
+                "Exactly one of covariance_matrix or precision_matrix or scale_tril may be specified."
+            )
+
+        if scale_tril is not None:
+            if scale_tril.dim() < 2:
+                raise ValueError(
+                    "scale_tril matrix must be at least two-dimensional, "
+                    "with optional leading batch dimensions"
+                )
+            batch_shape = torch.broadcast_shapes(scale_tril.shape[:-2], loc.shape[:-1])
+            self.scale_tril = scale_tril.expand(batch_shape + (-1, -1))
+        elif covariance_matrix is not None:
+            if covariance_matrix.dim() < 2:
+                raise ValueError(
+                    "covariance_matrix must be at least two-dimensional, "
+                    "with optional leading batch dimensions"
+                )
+            batch_shape = torch.broadcast_shapes(
+                covariance_matrix.shape[:-2], loc.shape[:-1]
+            )
+            self.covariance_matrix = covariance_matrix.expand(batch_shape + (-1, -1))
+        else:
+            if precision_matrix.dim() < 2:
+                raise ValueError(
+                    "precision_matrix must be at least two-dimensional, "
+                    "with optional leading batch dimensions"
+                )
+            batch_shape = torch.broadcast_shapes(
+                precision_matrix.shape[:-2], loc.shape[:-1]
+            )
+            self.precision_matrix = precision_matrix.expand(batch_shape + (-1, -1))
+        self.loc = loc.expand(batch_shape + (-1,))
+
+        event_shape = self.loc.shape[-1:]
+        super().__init__(batch_shape, event_shape, validate_args=validate_args)
+
+        if scale_tril is not None:
+            self._unbroadcasted_scale_tril = scale_tril
+        elif covariance_matrix is not None:
+            self._unbroadcasted_scale_tril = torch.linalg.cholesky(covariance_matrix)
+        else:  # precision_matrix is not None
+            self._unbroadcasted_scale_tril = _precision_to_scale_tril(precision_matrix)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(MultivariateNormal, _instance)
+        batch_shape = torch.Size(batch_shape)
+        loc_shape = batch_shape + self.event_shape
+        cov_shape = batch_shape + self.event_shape + self.event_shape
+        new.loc = self.loc.expand(loc_shape)
+        new._unbroadcasted_scale_tril = self._unbroadcasted_scale_tril
+        if "covariance_matrix" in self.__dict__:
+            new.covariance_matrix = self.covariance_matrix.expand(cov_shape)
+        if "scale_tril" in self.__dict__:
+            new.scale_tril = self.scale_tril.expand(cov_shape)
+        if "precision_matrix" in self.__dict__:
+            new.precision_matrix = self.precision_matrix.expand(cov_shape)
+        super(MultivariateNormal, new).__init__(
+            batch_shape, self.event_shape, validate_args=False
+        )
+        new._validate_args = self._validate_args
+        return new
+
+    @lazy_property
+    def scale_tril(self):
+        return self._unbroadcasted_scale_tril.expand(
+            self._batch_shape + self._event_shape + self._event_shape
+        )
+
+    @lazy_property
+    def covariance_matrix(self):
+        return torch.matmul(
+            self._unbroadcasted_scale_tril, self._unbroadcasted_scale_tril.mT
+        ).expand(self._batch_shape + self._event_shape + self._event_shape)
+
+    @lazy_property
+    def precision_matrix(self):
+        return torch.cholesky_inverse(self._unbroadcasted_scale_tril).expand(
+            self._batch_shape + self._event_shape + self._event_shape
+        )
+
+    @property
+    def mean(self):
+        return self.loc
+
+    @property
+    def mode(self):
+        return self.loc
+
+    @property
+    def variance(self):
+        return (
+            self._unbroadcasted_scale_tril.pow(2)
+            .sum(-1)
+            .expand(self._batch_shape + self._event_shape)
+        )
+
+    def rsample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        eps = _standard_normal(shape, dtype=self.loc.dtype, device=self.loc.device)
+        return self.loc + _batch_mv(self._unbroadcasted_scale_tril, eps)
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        diff = value - self.loc
+        M = _batch_mahalanobis(self._unbroadcasted_scale_tril, diff)
+        half_log_det = (
+            self._unbroadcasted_scale_tril.diagonal(dim1=-2, dim2=-1).log().sum(-1)
+        )
+        return -0.5 * (self._event_shape[0] * math.log(2 * math.pi) + M) - half_log_det
+
+    def entropy(self):
+        half_log_det = (
+            self._unbroadcasted_scale_tril.diagonal(dim1=-2, dim2=-1).log().sum(-1)
+        )
+        H = 0.5 * self._event_shape[0] * (1.0 + math.log(2 * math.pi)) + half_log_det
+        if len(self._batch_shape) == 0:
+            return H
+        else:
+            return H.expand(self._batch_shape)

venv/lib/python3.10/site-packages/torch/distributions/negative_binomial.py

@@ -0,0 +1,133 @@
+import torch
+import torch.nn.functional as F
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import (
+    broadcast_all,
+    lazy_property,
+    logits_to_probs,
+    probs_to_logits,
+)
+
+__all__ = ["NegativeBinomial"]
+
+
+class NegativeBinomial(Distribution):
+    r"""
+    Creates a Negative Binomial distribution, i.e. distribution
+    of the number of successful independent and identical Bernoulli trials
+    before :attr:`total_count` failures are achieved. The probability
+    of success of each Bernoulli trial is :attr:`probs`.
+
+    Args:
+        total_count (float or Tensor): non-negative number of negative Bernoulli
+            trials to stop, although the distribution is still valid for real
+            valued count
+        probs (Tensor): Event probabilities of success in the half open interval [0, 1)
+        logits (Tensor): Event log-odds for probabilities of success
+    """
+    arg_constraints = {
+        "total_count": constraints.greater_than_eq(0),
+        "probs": constraints.half_open_interval(0.0, 1.0),
+        "logits": constraints.real,
+    }
+    support = constraints.nonnegative_integer
+
+    def __init__(self, total_count, probs=None, logits=None, validate_args=None):
+        if (probs is None) == (logits is None):
+            raise ValueError(
+                "Either `probs` or `logits` must be specified, but not both."
+            )
+        if probs is not None:
+            (
+                self.total_count,
+                self.probs,
+            ) = broadcast_all(total_count, probs)
+            self.total_count = self.total_count.type_as(self.probs)
+        else:
+            (
+                self.total_count,
+                self.logits,
+            ) = broadcast_all(total_count, logits)
+            self.total_count = self.total_count.type_as(self.logits)
+
+        self._param = self.probs if probs is not None else self.logits
+        batch_shape = self._param.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(NegativeBinomial, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.total_count = self.total_count.expand(batch_shape)
+        if "probs" in self.__dict__:
+            new.probs = self.probs.expand(batch_shape)
+            new._param = new.probs
+        if "logits" in self.__dict__:
+            new.logits = self.logits.expand(batch_shape)
+            new._param = new.logits
+        super(NegativeBinomial, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def _new(self, *args, **kwargs):
+        return self._param.new(*args, **kwargs)
+
+    @property
+    def mean(self):
+        return self.total_count * torch.exp(self.logits)
+
+    @property
+    def mode(self):
+        return ((self.total_count - 1) * self.logits.exp()).floor().clamp(min=0.0)
+
+    @property
+    def variance(self):
+        return self.mean / torch.sigmoid(-self.logits)
+
+    @lazy_property
+    def logits(self):
+        return probs_to_logits(self.probs, is_binary=True)
+
+    @lazy_property
+    def probs(self):
+        return logits_to_probs(self.logits, is_binary=True)
+
+    @property
+    def param_shape(self):
+        return self._param.size()
+
+    @lazy_property
+    def _gamma(self):
+        # Note we avoid validating because self.total_count can be zero.
+        return torch.distributions.Gamma(
+            concentration=self.total_count,
+            rate=torch.exp(-self.logits),
+            validate_args=False,
+        )
+
+    def sample(self, sample_shape=torch.Size()):
+        with torch.no_grad():
+            rate = self._gamma.sample(sample_shape=sample_shape)
+            return torch.poisson(rate)
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+
+        log_unnormalized_prob = self.total_count * F.logsigmoid(
+            -self.logits
+        ) + value * F.logsigmoid(self.logits)
+
+        log_normalization = (
+            -torch.lgamma(self.total_count + value)
+            + torch.lgamma(1.0 + value)
+            + torch.lgamma(self.total_count)
+        )
+        # The case self.total_count == 0 and value == 0 has probability 1 but
+        # lgamma(0) is infinite. Handle this case separately using a function
+        # that does not modify tensors in place to allow Jit compilation.
+        log_normalization = log_normalization.masked_fill(
+            self.total_count + value == 0.0, 0.0
+        )
+
+        return log_unnormalized_prob - log_normalization