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pkgs/xformers/_flash_attn/ops/activations.py

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+# Copied from https://github.com/mlcommons/training_results_v1.1/blob/main/NVIDIA/benchmarks/bert/implementations/pytorch/model/layers/activations.py
+import math
+
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+
+
+# 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(y, bias):
+    x = bias + y
+    return (x * 0.5 * (1.0 + torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x)))).to(dtype=y.dtype)
+
+# 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, y, bias):
+    """Assume that y has shape (B, D) and bias has shape (D)
+    """
+    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)
+    grad_y = ff * g
+    return grad_y.to(dtype=y.dtype), grad_y.sum(dim=(0), dtype=bias.dtype)
+
+
+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(input, bias)
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        input, bias = ctx.saved_tensors
+        tmp = bias_gelu_back(grad_output, input, bias)
+        return tmp, tmp
+
+
+bias_gelu_impl = GeLUFunction.apply
+
+# this function is tanh approximation of gelu
+# actual gelu is:
+# x * 0.5 * (1.0 + torch.erf(x * 0.70710678))
+@torch.jit.script
+def gelu_fwd(x):
+    return (x * 0.5 * (1.0 + torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x)))).to(dtype=x.dtype)
+
+# 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 gelu_bwd(g, x):
+    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).to(dtype=x.dtype)
+
+
+class FastGeLUFunction(torch.autograd.Function):
+    @staticmethod
+    # bias is an optional argument
+    def forward(ctx, input):
+        ctx.save_for_backward(input)
+        return gelu_fwd(input)
+
+    @staticmethod
+    def backward(ctx, grad_output):
+        input, = ctx.saved_tensors
+        tmp = gelu_bwd(grad_output, input)
+        return tmp
+
+fast_gelu_impl = FastGeLUFunction.apply
+
+
+@torch.jit.script
+def relu_bwd(g, x):
+    return torch.where(x >= 0, g, 0.0).to(dtype=x.dtype)
+
+
+@torch.jit.script
+def sqrelu_fwd(x):
+    r = F.relu(x)
+    return (r * r).to(dtype=x.dtype)
+
+
+@torch.jit.script
+def sqrelu_bwd(g, x):
+    return (2.0 * g * F.relu(x)).to(dtype=x.dtype)