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# Copyright (c) OpenMMLab. All rights reserved.
import torch
import triton
import triton.language as tl
@triton.jit
def _rms_norm_fwd_fused(
X, # pointer to the input
Y, # pointer to the output
W, # pointer to the weights
Rstd, # pointer to the 1/std
stride, # how much to increase the pointer when moving by 1 row
N, # number of columns in X
eps, # epsilon to avoid division by zero
BLOCK_SIZE: tl.constexpr,
):
# Map the program id to the row of X and Y it should compute.
row = tl.program_id(0)
Y += row * stride
X += row * stride
# Compute variance
_var = tl.zeros([BLOCK_SIZE], dtype=tl.float32)
for off in range(0, N, BLOCK_SIZE):
cols = off + tl.arange(0, BLOCK_SIZE)
x = tl.load(X + cols, mask=cols < N, other=0.).to(tl.float32)
_var += x * x
var = tl.sum(_var, axis=0) / N
rstd = 1 / tl.sqrt(var + eps)
# Write rstd
tl.store(Rstd + row, rstd)
# Normalize and apply linear transformation
for off in range(0, N, BLOCK_SIZE):
cols = off + tl.arange(0, BLOCK_SIZE)
mask = cols < N
w = tl.load(W + cols, mask=mask)
x = tl.load(X + cols, mask=mask, other=0.).to(tl.float32)
x_hat = x * rstd
y = x_hat * w
# Write output
tl.store(Y + cols, y, mask=mask)
@triton.jit
def _rms_norm_bwd_dx_fused(
DX, # pointer to the input gradient
DY, # pointer to the output gradient
DW, # pointer to the partial sum of weights gradient
X, # pointer to the input
W, # pointer to the weights
Rstd, # pointer to the 1/std
Lock, # pointer to the lock
stride, # how much to increase the pointer when moving by 1 row
N, # number of columns in X
eps, # epsilon to avoid division by zero
GROUP_SIZE_M: tl.constexpr,
BLOCK_SIZE_N: tl.constexpr):
# Map the program id to the elements of X, DX, and DY it should compute.
row = tl.program_id(0)
cols = tl.arange(0, BLOCK_SIZE_N)
mask = cols < N
X += row * stride
DY += row * stride
DX += row * stride
# Offset locks and weights/biases gradient pointer for parallel reduction
lock_id = row % GROUP_SIZE_M
Lock += lock_id
Count = Lock + GROUP_SIZE_M
DW = DW + lock_id * N + cols
# Load data to SRAM
x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)
dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32)
w = tl.load(W + cols, mask=mask).to(tl.float32)
rstd = tl.load(Rstd + row)
# Compute dx
xhat = x * rstd
wdy = w * dy
xhat = tl.where(mask, xhat, 0.)
wdy = tl.where(mask, wdy, 0.)
c1 = tl.sum(xhat * wdy, axis=0) / N
dx = (wdy - (xhat * c1)) * rstd
# Write dx
tl.store(DX + cols, dx, mask=mask)
# Accumulate partial sums for dw/db
partial_dw = (dy * xhat).to(w.dtype)
while tl.atomic_cas(Lock, 0, 1) == 1:
pass
count = tl.load(Count)
# First store doesn't accumulate
if count == 0:
tl.atomic_xchg(Count, 1)
else:
partial_dw += tl.load(DW, mask=mask)
tl.store(DW, partial_dw, mask=mask)
# Release the lock
tl.atomic_xchg(Lock, 0)
@triton.jit
def _rms_norm_bwd_dwdb(
DW, # pointer to the partial sum of weights gradient
FINAL_DW, # pointer to the weights gradient
M, # GROUP_SIZE_M
N, # number of columns
BLOCK_SIZE_M: tl.constexpr,
BLOCK_SIZE_N: tl.constexpr):
# Map the program id to the elements of DW and DB it should compute.
pid = tl.program_id(0)
cols = pid * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
dw = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
# Iterate through the rows of DW and DB to sum the partial sums.
for i in range(0, M, BLOCK_SIZE_M):
rows = i + tl.arange(0, BLOCK_SIZE_M)
mask = (rows[:, None] < M) & (cols[None, :] < N)
offs = rows[:, None] * N + cols[None, :]
dw += tl.load(DW + offs, mask=mask, other=0.)
# Write the final sum to the output.
sum_dw = tl.sum(dw, axis=0)
tl.store(FINAL_DW + cols, sum_dw, mask=cols < N)
class RMSNorm(torch.autograd.Function):
@staticmethod
def forward(ctx, x, weight, eps):
# allocate output
y = torch.empty_like(x)
# reshape input data into 2D tensor
x_arg = x.reshape(-1, x.shape[-1])
M, N = x_arg.shape
rstd = torch.empty((M, ), dtype=torch.float32, device='cuda')
# Less than 64KB per feature: enqueue fused kernel
MAX_FUSED_SIZE = 65536 // x.element_size()
BLOCK_SIZE = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
if N > BLOCK_SIZE:
raise RuntimeError(
"This rms norm doesn't support feature dim >= 64KB.")
# heuristics for number of warps
num_warps = min(max(BLOCK_SIZE // 256, 1), 8)
# enqueue kernel
_rms_norm_fwd_fused[(M, )](
x_arg,
y,
weight,
rstd,
x_arg.stride(0),
N,
eps,
BLOCK_SIZE=BLOCK_SIZE,
num_warps=num_warps,
)
ctx.save_for_backward(x, weight, rstd)
ctx.BLOCK_SIZE = BLOCK_SIZE
ctx.num_warps = num_warps
ctx.eps = eps
return y
@staticmethod
def backward(ctx, dy):
x, w, v = ctx.saved_tensors
# heuristics for amount of parallel reduction stream for DW/DB
N = w.shape[0]
GROUP_SIZE_M = 64
if N <= 8192:
GROUP_SIZE_M = 96
if N <= 4096:
GROUP_SIZE_M = 128
if N <= 1024:
GROUP_SIZE_M = 256
# allocate output
locks = torch.zeros(2 * GROUP_SIZE_M, dtype=torch.int32, device='cuda')
_dw = torch.empty((GROUP_SIZE_M, w.shape[0]),
dtype=x.dtype,
device=w.device)
dw = torch.empty((w.shape[0], ), dtype=w.dtype, device=w.device)
dx = torch.empty_like(dy)
# enqueue kernel using forward pass heuristics
# also compute partial sums for DW and DB
x_arg = x.reshape(-1, x.shape[-1])
M, N = x_arg.shape
_rms_norm_bwd_dx_fused[(M, )](
dx,
dy,
_dw,
x,
w,
v,
locks,
x_arg.stride(0),
N,
ctx.eps,
BLOCK_SIZE_N=ctx.BLOCK_SIZE,
GROUP_SIZE_M=GROUP_SIZE_M,
num_warps=ctx.num_warps)
def grid(meta):
return [triton.cdiv(N, meta['BLOCK_SIZE_N'])]
# accumulate partial sums in separate kernel
_rms_norm_bwd_dwdb[grid](
_dw,
dw,
GROUP_SIZE_M,
N,
BLOCK_SIZE_M=32,
BLOCK_SIZE_N=128,
)
return dx, dw, None
rms_norm = RMSNorm.apply
def rms_norm_forward(self, hidden_states):
if (hidden_states.device == torch.device('cpu')
or self.weight.device == torch.device('cpu')):
raise RuntimeError(
'Can not use triton kernels on cpu. Please set `USE_TRITON_KERNEL`'
' environment variable to 0 before training.')
return rms_norm(hidden_states, self.weight, self.variance_epsilon)
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