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--- |
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library_name: transformers |
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tags: [] |
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--- |
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<!-- Provide a quick summary of what the model is/does. --> |
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Foundation Neural-Network Quantum State trained on the two-dimension \\(J_1\\)- \\(J_2\\) Heisenberg on a \\(10\times 10\\) square lattice. |
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The system is described by the following Hamiltonian (with periodic boundary conditions): |
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$$ |
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\hat{H} = J_1\!\!\sum_{\langle {\boldsymbol{r}},{\boldsymbol{r'}} \rangle} \hat{\boldsymbol{S}}_{\boldsymbol{r}}\cdot\hat{\boldsymbol{S}}_{\boldsymbol{r'}} |
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+ J_2 \!\!\!\!\sum_{\langle \langle {\boldsymbol{r}},{\boldsymbol{r'}} \rangle \rangle} \!\!\!\hat{\boldsymbol{S}}_{\boldsymbol{r}}\cdot\hat{\boldsymbol{S}}_{\boldsymbol{r'}} \ . |
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$$ |
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The architecture has been trained on \\(R=100\\) different couplings \\(J_2\\) equispaced in the interval \\(J_2 \in [0.4, 0.6]\\), |
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using a total batch size of \\(M=16000\\) samples. |
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The computation has been distributed over 4 A100-64GB GPUs for few hours. |
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## How to Get Started with the Model |
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Use the code below to get started with the model. In particular, we sample the architecture for a fixed value of the coupling \\(J_2\\) using NetKet. |
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```python |
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from functools import partial |
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import numpy as np |
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import jax |
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import jax.numpy as jnp |
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import netket as nk |
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from huggingface_hub import hf_hub_download |
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import flax |
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from flax.training import checkpoints |
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flax.config.update('flax_use_orbax_checkpointing', False) |
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lattice = nk.graph.Hypercube(length=10, n_dim=2, pbc=True, max_neighbor_order=2) |
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J2 = 0.5 |
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assert J2 >= 0.4 and J2 <= 0.6 #* the model has been trained on this interval |
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from transformers import FlaxAutoModel |
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wf = FlaxAutoModel.from_pretrained("nqs-models/j1j2_square_fnqs", trust_remote_code=True) |
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N_params = nk.jax.tree_size(wf.params) |
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print('Number of parameters = ', N_params, flush=True) |
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hilbert = nk.hilbert.Spin(s=1/2, N=lattice.n_nodes, total_sz=0) |
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hamiltonian = nk.operator.Heisenberg(hilbert=hilbert, |
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graph=lattice, |
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J=[1.0, J2], |
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sign_rule=[False, False]).to_jax_operator() # No Marshall sign rule |
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sampler = nk.sampler.MetropolisExchange(hilbert=hilbert, |
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graph=lattice, |
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d_max=2, |
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n_chains=16000, |
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sweep_size=lattice.n_nodes) |
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key = jax.random.PRNGKey(0) |
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key, subkey = jax.random.split(key, 2) |
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vstate = nk.vqs.MCState(sampler=sampler, |
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apply_fun=partial(wf.__call__, coups=J2), |
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sampler_seed=subkey, |
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n_samples=16000, |
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n_discard_per_chain=0, |
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variables=wf.params, |
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chunk_size=16000) |
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# Overwrite samples with already thermalized ones |
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path = hf_hub_download(repo_id="nqs-models/j1j2_square_fnqs", filename="spins") |
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samples = checkpoints.restore_checkpoint(ckpt_dir=path, prefix="spins", target=None) |
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samples = jnp.array(samples, dtype='int8') |
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vstate.sampler_state = vstate.sampler_state.replace(σ = samples) |
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import time |
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# Sample the model |
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for _ in range(10): |
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start = time.time() |
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E = vstate.expect(hamiltonian) |
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vstate.sample() |
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print("Mean: ", E.mean.real / lattice.n_nodes / 4, "\t time=", time.time()-start) |
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``` |
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The time per sweep is 21s, evaluated on a single A100-40GB GPU. |
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### Extract hidden representation |
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The hidden representation associated to the input batch of configurations can be extracted as: |
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```python |
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wf = FlaxAutoModel.from_pretrained("nqs-models/j1j2_square_fnqs", trust_remote_code=True, return_z=True) |
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z = wf(wf.params, samples, J2) |
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``` |
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#### Training Hyperparameters |
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Number of layers: 4 |
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Embedding dimension: 72 |
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Hidden dimension: 288 |
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Number of heads: 12 |
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Patch size: 2x2 |
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Total number of parameters: 223,104 |
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## Model Card Contact |
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Riccardo Rende ([email protected]) |
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Luciano Loris Viteritti ([email protected]) |
