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# Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved.
import torch
###### BIAS GELU FUSION/ NO AUTOGRAD ################
# 1/sqrt(2*pi)-> 0.3989423
# 1/sqrt(2) -> 0.70710678
# sqrt(2/pi) -> 0.79788456
# this function is tanh approximation of gelu
# actual gelu is:
# x * 0.5 * (1.0 + torch.erf(x * 0.70710678))
@torch.jit.script
def bias_gelu(bias, y):
x = bias + y
return x * 0.5 * (1.0 + torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x)))
# gradient of tanh approximation of gelu
# gradient of actual gelu is:
# 0.5 * (1. + torch.erf(x * 0.70710678)) + 0.3989423 * x * torch.exp(-0.5 * x * x)
@torch.jit.script
def bias_gelu_back(g, bias, y):
x = bias + y
tanh_out = torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x))
# sqrt(2/pi) * 3 * 0.044715 -> 0.1070322243
ff = 0.5 * x * ((1 - tanh_out * tanh_out) * (0.79788456 + 0.1070322243 * x * x)) + 0.5 * (1 + tanh_out)
return ff*g
class GeLUFunction(torch.autograd.Function):
@staticmethod
# bias is an optional argument
def forward(ctx, input, bias):
ctx.save_for_backward(input, bias)
return bias_gelu(bias, input)
@staticmethod
def backward(ctx, grad_output):
input, bias = ctx.saved_tensors
tmp = bias_gelu_back(grad_output, bias, input)
return tmp, tmp
bias_gelu_impl = GeLUFunction.apply
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