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norms.py
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norms.py
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# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the BSD-style license found in the
# LICENSE file in the root directory of this source tree.
import math
from functools import partial
import torch
import torch.nn as nn
import triton
import triton.language as tl
from torch.distributed._tensor import Partial, Replicate, Shard
from torch.distributed._tensor.experimental import local_map
def build_norm(norm_type: str, dim: int, eps: float = 1e-6):
"""
Builds the specified normalization layer based on the norm_type.
Args:
norm_type (str): The type of normalization layer to build.
Supported types: layernorm, np_layernorm, rmsnorm, fused_rmsnorm
dim (int): The dimension of the normalization layer.
eps (float, optional): The epsilon value for numerical stability. Defaults to 1e-6.
Returns:
The built normalization layer.
Raises:
NotImplementedError: If an unknown norm_type is provided.
"""
norm_type = norm_type.lower() # Normalize to lowercase
if norm_type == "layernorm":
return nn.LayerNorm(dim, eps=eps, bias=False)
elif norm_type == "np_layernorm":
return nn.LayerNorm(dim, eps=eps, elementwise_affine=False, bias=False)
elif norm_type == "rmsnorm":
return RMSNorm(dim, eps=eps)
elif norm_type == "fused_rmsnorm":
return FusedRMSNorm(dim, eps=eps)
else:
raise NotImplementedError(f"Unknown norm_type: '{norm_type}'")
class FusedRMSNorm(nn.Module):
"""Fused RMS Norm, wraps a fused Triton Kernel"""
def __init__(
self,
dim: int,
eps: float = 1e-6,
):
super().__init__()
self.eps = eps
self.weight = nn.Parameter(torch.ones(dim))
self.fused_rms_norm_fn = fused_rms_norm_fn
def forward(self, x: torch.Tensor) -> torch.Tensor:
"""leverages Triton Fused RMS Norm kernel"""
return self.fused_rms_norm_fn(
x,
self.weight,
eps=self.eps,
)
def reset_parameters(self):
torch.nn.init.ones_(self.weight) # type: ignore
class RMSNorm(nn.Module):
"""
Initialize the RMSNorm normalization layer.
Args:
dim (int): The dimension of the input tensor.
eps (float, optional): A small value added to the denominator for numerical stability. Default is 1e-6.
Attributes:
eps (float): A small value added to the denominator for numerical stability.
weight (nn.Parameter): Learnable scaling parameter.
"""
def __init__(self, dim: int, eps: float = 1e-6):
super().__init__()
self.eps = eps
self.weight = nn.Parameter(torch.ones(dim))
def _norm(self, x: torch.Tensor):
return x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps)
def forward(self, x: torch.Tensor):
output = self._norm(x.float()).type_as(x)
return output * self.weight
def reset_parameters(self):
torch.nn.init.ones_(self.weight) # type: ignore
# FusedRMSNorm in Triton
# Credit
# Tri Dao's Triton LayerNorm: https://github.com/Dao-AILab/flash-attention/blob/main/flash_attn/ops/triton/layer_norm.py
# Triton LayerNorm tutorial: https://triton-lang.org/main/getting-started/tutorials/05-layer-norm.html
@triton.autotune(
configs=[
triton.Config({}, num_warps=1),
triton.Config({}, num_warps=2),
triton.Config({}, num_warps=4),
triton.Config({}, num_warps=8),
triton.Config({}, num_warps=16),
triton.Config({}, num_warps=32),
],
key=["N"],
)
@triton.jit
def _rms_norm_fwd_kernel(
X,
stride_x,
Y,
stride_y,
W,
Rstd,
eps,
M, # num rows
N, # num cols
block_N: tl.constexpr,
):
row = tl.program_id(0)
cols = tl.arange(0, block_N)
# Load input data and weights
mask = cols < N
x = tl.load(X + row * stride_x + cols, mask=mask, other=0.0).to(tl.float32)
w = tl.load(W + cols, mask=mask, other=0.0).to(tl.float32)
# Compute mean and variance
xbar = tl.where(cols < N, x, 0.0)
var = tl.sum(xbar * xbar, axis=0) / N
rstd = 1 / tl.sqrt(var + eps)
# Store the reciprocal standard deviation
tl.store(Rstd + row, rstd)
# Normalize and apply linear transformation
x_hat = x * rstd
y = x_hat * w
# Write output
tl.store(Y + row * stride_y + cols, y, mask=mask)
@triton.autotune(
configs=[
triton.Config({}, num_warps=1),
triton.Config({}, num_warps=2),
triton.Config({}, num_warps=4),
triton.Config({}, num_warps=8),
triton.Config({}, num_warps=16),
triton.Config({}, num_warps=32),
],
key=["N"],
)
@triton.jit
def _rms_norm_bwd_kernel_sm(
X,
stride_x,
W,
DY,
stride_dy,
DX,
stride_dx,
Rstd,
DW,
eps,
M, # num rows
N, # num cols
rows_per_program,
block_N: tl.constexpr,
):
row_block_id = tl.program_id(0)
row_start = row_block_id * rows_per_program
cols = tl.arange(0, block_N)
mask = cols < N
# Load weights
w = tl.load(W + cols, mask=mask, other=0.0).to(tl.float32)
# Accumulate gradients for weights
dw = tl.zeros((block_N,), dtype=tl.float32)
row_end = min(row_start + rows_per_program, M)
for row in range(row_start, row_end):
# Load input, output gradient, and reciprocal standard deviation
x = tl.load(X + row * stride_x + cols, mask=mask, other=0.0).to(tl.float32)
dy = tl.load(DY + row * stride_dy + cols, mask=mask, other=0.0).to(tl.float32)
rstd = tl.load(Rstd + row)
# Compute normalized input and gradients
x_hat = x * rstd
wdy = w * dy
dw += dy * x_hat
c1 = tl.sum(x_hat * wdy, axis=0) / N
dx = (wdy - x_hat * c1) * rstd
# Store input gradient
tl.store(DX + row * stride_dx + cols, dx, mask=mask)
# Store weight gradients
tl.store(DW + row_block_id * N + cols, dw, mask=mask)
class TritonFusedRMSNorm(torch.autograd.Function):
@partial(
local_map,
out_placements=[Shard(1)],
in_placements=(None, [Shard(1)], [Replicate()], None),
)
@staticmethod
def forward(ctx, x, weight, eps):
x_shape_start = x.shape
# Flatten input
x = x.view(-1, x.shape[-1])
if x.stride(-1) != 1:
x = x.contiguous()
if weight.stride(-1) != 1:
weight = weight.contiguous()
M, N = x.shape
y = torch.empty_like(x)
rstd = torch.empty((M,), dtype=torch.float32, device=x.device)
max_size = 65536 // x.element_size()
block_N = min(max_size, triton.next_power_of_2(N))
if N > block_N:
raise ValueError(f"N {N} must be <= {block_N=}")
grid = lambda meta: (M,)
_rms_norm_fwd_kernel[grid](
x,
x.stride(0),
y,
y.stride(0),
weight,
rstd,
eps,
M,
N,
block_N,
)
ctx.eps = eps
ctx.save_for_backward(x, weight, rstd)
ctx.x_shape_start = x_shape_start
y = y.reshape(x_shape_start)
return y
@partial(
local_map,
out_placements=([Shard(1)], [Partial()], None),
in_placements=(None, [Shard(1)]),
)
@staticmethod
def backward(ctx, dy):
x, weight, rstd = ctx.saved_tensors
eps = ctx.eps
x_shape_start = ctx.x_shape_start
# Flatten input and output gradients
dy = dy.view(-1, dy.shape[-1])
if dy.stride(-1) != 1:
dy = dy.contiguous()
M, N = dy.shape
dx = torch.empty_like(x)
sm_count = torch.cuda.get_device_properties(x.device).multi_processor_count
_dw = torch.empty((sm_count, N), dtype=torch.float32, device=weight.device)
max_size = 65536 // x.element_size()
block_N = min(max_size, triton.next_power_of_2(N))
rows_per_sm = math.ceil(M / sm_count)
if N > block_N:
raise ValueError(f"N {N} must be <= {block_N=}")
grid = lambda meta: (sm_count,)
_rms_norm_bwd_kernel_sm[grid](
x,
x.stride(0),
weight,
dy,
dy.stride(0),
dx,
dx.stride(0),
rstd,
_dw,
eps,
M,
N,
rows_per_sm,
block_N,
)
dw = _dw.sum(0).to(weight.dtype)
dx = dx.view(x_shape_start)
return dx, dw, None
# expose fusedRMSNorm as a function
def fused_rms_norm_fn(
x,
weight,
eps=1e-6,
):
return TritonFusedRMSNorm.apply(
x,
weight,
eps,
)