flash-attention/flash_attn/ops/activations.py

# 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)


swiglu_fwd_codestring = """
template <typename T> T swiglu_fwd(T x, T y) {
    return float(x) * float(y) / (1.0f + ::exp(-float(x)));
}
"""
swiglu_bwd_codestring = """
template <typename T> void swiglu_bwd(T x, T y, T g, T& dx, T& dy) {
    float x_sigmoid = 1.0f / (1.0f + ::exp(-float(x)));
    dx = x_sigmoid * (1 + float(x) * (1.0f - x_sigmoid)) * float(g) * float(y);
    dy = float(x) * x_sigmoid * float(g);
}
"""
swiglu_fwd = torch.cuda.jiterator._create_jit_fn(swiglu_fwd_codestring)
swiglu_bwd = torch.cuda.jiterator._create_multi_output_jit_fn(swiglu_bwd_codestring, num_outputs=2)


class SwiGLUFunction(torch.autograd.Function):

    @staticmethod
    def forward(ctx, x, y):
        ctx.save_for_backward(x, y)
        return swiglu_fwd(x, y)

    @staticmethod
    def backward(ctx, dout):
        x, y = ctx.saved_tensors
        return swiglu_bwd(x, y, dout)

swiglu = SwiGLUFunction.apply