636 lines
21 KiB
Python
636 lines
21 KiB
Python
# Copyright (c) 2023, Tri Dao.
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# Implement residual + layer_norm / rms_norm.
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# Based on the Triton LayerNorm tutorial: https://triton-lang.org/main/getting-started/tutorials/05-layer-norm.html
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# For the backward pass, we keep weight_grad and bias_grad in registers and accumulate.
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# This is faster for dimensions up to 8k, but after that it's much slower due to register spilling.
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# The models we train have hidden dim up to 8k anyway (e.g. Llama 70B), so this is fine.
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import math
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import torch
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import torch.nn.functional as F
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from torch.cuda.amp import custom_fwd, custom_bwd
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import triton
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import triton.language as tl
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def layer_norm_ref(x, weight, bias, residual=None, eps=1e-6, prenorm=False, upcast=False):
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dtype = x.dtype
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if upcast:
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weight = weight.float()
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bias = bias.float() if bias is not None else None
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if upcast:
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x = x.float()
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residual = residual.float() if residual is not None else residual
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if residual is not None:
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x = (x + residual).to(x.dtype)
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out = F.layer_norm(x.to(weight.dtype), x.shape[-1:], weight=weight, bias=bias, eps=eps).to(
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dtype
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)
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return out if not prenorm else (out, x)
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def rms_norm_ref(x, weight, bias, residual=None, eps=1e-6, prenorm=False, upcast=False):
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dtype = x.dtype
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if upcast:
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weight = weight.float()
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bias = bias.float() if bias is not None else None
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if upcast:
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x = x.float()
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residual = residual.float() if residual is not None else residual
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if residual is not None:
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x = (x + residual).to(x.dtype)
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rstd = 1 / torch.sqrt((x.square()).mean(dim=-1, keepdim=True) + eps)
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out = (x * rstd * weight) + bias if bias is not None else (x * rstd * weight)
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out = out.to(dtype)
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return out if not prenorm else (out, x)
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@triton.autotune(
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configs=[
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triton.Config({}, num_warps=1),
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triton.Config({}, num_warps=2),
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triton.Config({}, num_warps=4),
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triton.Config({}, num_warps=8),
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triton.Config({}, num_warps=16),
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triton.Config({}, num_warps=32),
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],
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key=["N", "HAS_RESIDUAL", "STORE_RESIDUAL_OUT", "IS_RMS_NORM", "HAS_BIAS"],
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)
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# @triton.heuristics({"HAS_BIAS": lambda args: args["B"] is not None})
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# @triton.heuristics({"HAS_RESIDUAL": lambda args: args["RESIDUAL"] is not None})
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@triton.jit
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def _layer_norm_fwd_1pass_kernel(
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X, # pointer to the input
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Y, # pointer to the output
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W, # pointer to the weights
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B, # pointer to the biases
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RESIDUAL, # pointer to the residual
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RESIDUAL_OUT, # pointer to the residual
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Mean, # pointer to the mean
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Rstd, # pointer to the 1/std
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stride_x_row, # how much to increase the pointer when moving by 1 row
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stride_y_row,
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stride_res_row,
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stride_res_out_row,
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N, # number of columns in X
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eps, # epsilon to avoid division by zero
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IS_RMS_NORM: tl.constexpr,
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BLOCK_N: tl.constexpr,
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HAS_RESIDUAL: tl.constexpr,
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STORE_RESIDUAL_OUT: tl.constexpr,
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HAS_BIAS: tl.constexpr,
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):
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# Map the program id to the row of X and Y it should compute.
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row = tl.program_id(0)
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X += row * stride_x_row
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Y += row * stride_y_row
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if HAS_RESIDUAL:
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RESIDUAL += row * stride_res_row
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if STORE_RESIDUAL_OUT:
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RESIDUAL_OUT += row * stride_res_out_row
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# Compute mean and variance
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cols = tl.arange(0, BLOCK_N)
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x = tl.load(X + cols, mask=cols < N, other=0.0).to(tl.float32)
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if HAS_RESIDUAL:
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residual = tl.load(RESIDUAL + cols, mask=cols < N, other=0.0).to(tl.float32)
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x += residual
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if STORE_RESIDUAL_OUT:
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tl.store(RESIDUAL_OUT + cols, x, mask=cols < N)
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if not IS_RMS_NORM:
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mean = tl.sum(x, axis=0) / N
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tl.store(Mean + row, mean)
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xbar = tl.where(cols < N, x - mean, 0.0)
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var = tl.sum(xbar * xbar, axis=0) / N
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else:
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xbar = tl.where(cols < N, x, 0.0)
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var = tl.sum(xbar * xbar, axis=0) / N
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rstd = 1 / tl.sqrt(var + eps)
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tl.store(Rstd + row, rstd)
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# Normalize and apply linear transformation
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mask = cols < N
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w = tl.load(W + cols, mask=mask).to(tl.float32)
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if HAS_BIAS:
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b = tl.load(B + cols, mask=mask).to(tl.float32)
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x_hat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
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y = x_hat * w + b if HAS_BIAS else x_hat * w
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# Write output
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tl.store(Y + cols, y, mask=mask)
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def _layer_norm_fwd(
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x, weight, bias, eps, residual=None, out_dtype=None, residual_dtype=None, is_rms_norm=False
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):
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if residual is not None:
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residual_dtype = residual.dtype
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M, N = x.shape
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assert x.stride(-1) == 1
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if residual is not None:
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assert residual.stride(-1) == 1
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assert residual.shape == (M, N)
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assert weight.shape == (N,)
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assert weight.stride(-1) == 1
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if bias is not None:
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assert bias.stride(-1) == 1
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assert bias.shape == (N,)
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# allocate output
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y = torch.empty_like(x, dtype=x.dtype if out_dtype is None else out_dtype)
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assert y.stride(-1) == 1
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if residual is not None or (residual_dtype is not None and residual_dtype != x.dtype):
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residual_out = torch.empty(M, N, device=x.device, dtype=residual_dtype)
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assert residual_out.stride(-1) == 1
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else:
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residual_out = None
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mean = torch.empty((M,), dtype=torch.float32, device=x.device) if not is_rms_norm else None
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rstd = torch.empty((M,), dtype=torch.float32, device=x.device)
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# Less than 64KB per feature: enqueue fused kernel
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MAX_FUSED_SIZE = 65536 // x.element_size()
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BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
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if N > BLOCK_N:
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raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
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# heuristics for number of warps
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with torch.cuda.device(x.device.index):
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_layer_norm_fwd_1pass_kernel[(M,)](
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x,
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y,
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weight,
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bias,
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residual,
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residual_out,
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mean,
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rstd,
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x.stride(0),
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y.stride(0),
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residual.stride(0) if residual is not None else 0,
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residual_out.stride(0) if residual_out is not None else 0,
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N,
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eps,
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is_rms_norm,
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BLOCK_N,
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residual is not None,
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residual_out is not None,
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bias is not None,
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)
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# residual_out is None if residual is None and residual_dtype == input_dtype
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return y, mean, rstd, residual_out if residual_out is not None else x
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@triton.autotune(
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configs=[
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triton.Config({}, num_warps=1),
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triton.Config({}, num_warps=2),
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triton.Config({}, num_warps=4),
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triton.Config({}, num_warps=8),
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triton.Config({}, num_warps=16),
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triton.Config({}, num_warps=32),
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],
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key=["N", "HAS_DRESIDUAL", "STORE_DRESIDUAL", "IS_RMS_NORM", "HAS_BIAS"],
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)
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# @triton.heuristics({"HAS_BIAS": lambda args: args["B"] is not None})
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# @triton.heuristics({"HAS_DRESIDUAL": lambda args: args["DRESIDUAL"] is not None})
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# @triton.heuristics({"STORE_DRESIDUAL": lambda args: args["DRESIDUAL_IN"] is not None})
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@triton.heuristics({"RECOMPUTE_OUTPUT": lambda args: args["Y"] is not None})
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@triton.jit
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def _layer_norm_bwd_kernel(
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X, # pointer to the input
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W, # pointer to the weights
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B, # pointer to the biases
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Y, # pointer to the output to be recomputed
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DY, # pointer to the output gradient
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DX, # pointer to the input gradient
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DW, # pointer to the partial sum of weights gradient
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DB, # pointer to the partial sum of biases gradient
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DRESIDUAL,
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DRESIDUAL_IN,
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Mean, # pointer to the mean
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Rstd, # pointer to the 1/std
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stride_x_row, # how much to increase the pointer when moving by 1 row
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stride_y_row,
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stride_dy_row,
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stride_dx_row,
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stride_dres_row,
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stride_dres_in_row,
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M, # number of rows in X
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N, # number of columns in X
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eps, # epsilon to avoid division by zero
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rows_per_program,
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IS_RMS_NORM: tl.constexpr,
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BLOCK_N: tl.constexpr,
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HAS_DRESIDUAL: tl.constexpr,
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STORE_DRESIDUAL: tl.constexpr,
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HAS_BIAS: tl.constexpr,
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RECOMPUTE_OUTPUT: tl.constexpr,
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):
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# Map the program id to the elements of X, DX, and DY it should compute.
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row_block_id = tl.program_id(0)
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row_start = row_block_id * rows_per_program
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cols = tl.arange(0, BLOCK_N)
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mask = cols < N
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X += row_start * stride_x_row
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if HAS_DRESIDUAL:
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DRESIDUAL += row_start * stride_dres_row
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if STORE_DRESIDUAL:
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DRESIDUAL_IN += row_start * stride_dres_in_row
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DY += row_start * stride_dy_row
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DX += row_start * stride_dx_row
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if RECOMPUTE_OUTPUT:
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Y += row_start * stride_y_row
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w = tl.load(W + cols, mask=mask).to(tl.float32)
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if RECOMPUTE_OUTPUT and HAS_BIAS:
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b = tl.load(B + cols, mask=mask, other=0.0).to(tl.float32)
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dw = tl.zeros((BLOCK_N,), dtype=tl.float32)
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if HAS_BIAS:
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db = tl.zeros((BLOCK_N,), dtype=tl.float32)
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row_end = min((row_block_id + 1) * rows_per_program, M)
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for row in range(row_start, row_end):
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# Load data to SRAM
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x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)
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dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32)
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if not IS_RMS_NORM:
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mean = tl.load(Mean + row)
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rstd = tl.load(Rstd + row)
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# Compute dx
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xhat = (x - mean) * rstd if not IS_RMS_NORM else x * rstd
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xhat = tl.where(mask, xhat, 0.0)
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if RECOMPUTE_OUTPUT:
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y = xhat * w + b if HAS_BIAS else xhat * w
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tl.store(Y + cols, y, mask=mask)
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wdy = w * dy
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dw += dy * xhat
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if HAS_BIAS:
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db += dy
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if not IS_RMS_NORM:
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c1 = tl.sum(xhat * wdy, axis=0) / N
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c2 = tl.sum(wdy, axis=0) / N
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dx = (wdy - (xhat * c1 + c2)) * rstd
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else:
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c1 = tl.sum(xhat * wdy, axis=0) / N
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dx = (wdy - xhat * c1) * rstd
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if HAS_DRESIDUAL:
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dres = tl.load(DRESIDUAL + cols, mask=mask, other=0).to(tl.float32)
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dx += dres
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# Write dx
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if STORE_DRESIDUAL:
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tl.store(DRESIDUAL_IN + cols, dx, mask=mask)
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tl.store(DX + cols, dx, mask=mask)
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X += stride_x_row
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if HAS_DRESIDUAL:
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DRESIDUAL += stride_dres_row
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if STORE_DRESIDUAL:
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DRESIDUAL_IN += stride_dres_in_row
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if RECOMPUTE_OUTPUT:
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Y += stride_y_row
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DY += stride_dy_row
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DX += stride_dx_row
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tl.store(DW + row_block_id * N + cols, dw, mask=mask)
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if HAS_BIAS:
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tl.store(DB + row_block_id * N + cols, db, mask=mask)
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def _layer_norm_bwd(
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dy,
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x,
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weight,
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bias,
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eps,
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mean,
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rstd,
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dresidual=None,
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has_residual=False,
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is_rms_norm=False,
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x_dtype=None,
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recompute_output=False,
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):
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M, N = x.shape
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assert x.stride(-1) == 1
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assert dy.stride(-1) == 1
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assert dy.shape == (M, N)
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if dresidual is not None:
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assert dresidual.stride(-1) == 1
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assert dresidual.shape == (M, N)
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assert weight.shape == (N,)
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assert weight.stride(-1) == 1
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if bias is not None:
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assert bias.stride(-1) == 1
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assert bias.shape == (N,)
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# allocate output
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dx = (
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torch.empty_like(x)
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if x_dtype is None
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else torch.empty(M, N, dtype=x_dtype, device=x.device)
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)
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dresidual_in = torch.empty_like(x) if has_residual and dx.dtype != x.dtype else None
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y = torch.empty(M, N, dtype=dy.dtype, device=dy.device) if recompute_output else None
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# Less than 64KB per feature: enqueue fused kernel
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MAX_FUSED_SIZE = 65536 // x.element_size()
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BLOCK_N = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
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if N > BLOCK_N:
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raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
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sm_count = torch.cuda.get_device_properties(x.device).multi_processor_count
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_dw = torch.empty((sm_count, N), dtype=torch.float32, device=weight.device)
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_db = (
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torch.empty((sm_count, N), dtype=torch.float32, device=bias.device)
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if bias is not None
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else None
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)
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rows_per_program = math.ceil(M / sm_count)
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grid = (sm_count,)
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with torch.cuda.device(x.device.index):
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_layer_norm_bwd_kernel[grid](
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x,
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weight,
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bias,
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y,
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dy,
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dx,
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_dw,
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_db,
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dresidual,
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dresidual_in,
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mean,
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rstd,
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x.stride(0),
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0 if not recompute_output else y.stride(0),
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dy.stride(0),
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dx.stride(0),
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dresidual.stride(0) if dresidual is not None else 0,
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dresidual_in.stride(0) if dresidual_in is not None else 0,
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M,
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N,
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eps,
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rows_per_program,
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is_rms_norm,
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BLOCK_N,
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dresidual is not None,
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dresidual_in is not None,
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bias is not None,
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)
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dw = _dw.sum(0).to(weight.dtype)
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db = _db.sum(0).to(bias.dtype) if bias is not None else None
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# Don't need to compute dresidual_in separately in this case
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if has_residual and dx.dtype == x.dtype:
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dresidual_in = dx
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return (dx, dw, db, dresidual_in) if not recompute_output else (dx, dw, db, dresidual_in, y)
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class LayerNormFn(torch.autograd.Function):
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@staticmethod
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def forward(
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ctx,
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x,
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weight,
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bias,
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residual=None,
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eps=1e-6,
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prenorm=False,
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residual_in_fp32=False,
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is_rms_norm=False,
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):
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x_shape_og = x.shape
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# reshape input data into 2D tensor
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x = x.reshape(-1, x.shape[-1])
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if x.stride(-1) != 1:
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x = x.contiguous()
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if residual is not None:
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assert residual.shape == x_shape_og
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residual = residual.reshape(-1, residual.shape[-1])
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if residual.stride(-1) != 1:
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residual = residual.contiguous()
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weight = weight.contiguous()
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if bias is not None:
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bias = bias.contiguous()
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residual_dtype = (
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residual.dtype
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if residual is not None
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else (torch.float32 if residual_in_fp32 else None)
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)
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y, mean, rstd, residual_out = _layer_norm_fwd(
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x, weight, bias, eps, residual, residual_dtype=residual_dtype, is_rms_norm=is_rms_norm
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)
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ctx.save_for_backward(residual_out, weight, bias, mean, rstd)
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ctx.x_shape_og = x_shape_og
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ctx.eps = eps
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ctx.is_rms_norm = is_rms_norm
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ctx.has_residual = residual is not None
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ctx.prenorm = prenorm
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ctx.x_dtype = x.dtype
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y = y.reshape(x_shape_og)
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return y if not prenorm else (y, residual_out.reshape(x_shape_og))
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@staticmethod
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def backward(ctx, dy, *args):
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x, weight, bias, mean, rstd = ctx.saved_tensors
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dy = dy.reshape(-1, dy.shape[-1])
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if dy.stride(-1) != 1:
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dy = dy.contiguous()
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assert dy.shape == x.shape
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if ctx.prenorm:
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dresidual = args[0]
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dresidual = dresidual.reshape(-1, dresidual.shape[-1])
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if dresidual.stride(-1) != 1:
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dresidual = dresidual.contiguous()
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assert dresidual.shape == x.shape
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else:
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dresidual = None
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dx, dw, db, dresidual_in = _layer_norm_bwd(
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dy,
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x,
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weight,
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bias,
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ctx.eps,
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mean,
|
|
rstd,
|
|
dresidual,
|
|
ctx.has_residual,
|
|
ctx.is_rms_norm,
|
|
x_dtype=ctx.x_dtype,
|
|
)
|
|
return (
|
|
dx.reshape(ctx.x_shape_og),
|
|
dw,
|
|
db,
|
|
dresidual_in.reshape(ctx.x_shape_og) if ctx.has_residual else None,
|
|
None,
|
|
None,
|
|
None,
|
|
None,
|
|
)
|
|
|
|
|
|
def layer_norm_fn(
|
|
x,
|
|
weight,
|
|
bias,
|
|
residual=None,
|
|
eps=1e-6,
|
|
prenorm=False,
|
|
residual_in_fp32=False,
|
|
is_rms_norm=False,
|
|
):
|
|
return LayerNormFn.apply(x, weight, bias, residual, eps, prenorm, residual_in_fp32, is_rms_norm)
|
|
|
|
|
|
def rms_norm_fn(x, weight, bias, residual=None, prenorm=False, residual_in_fp32=False, eps=1e-6):
|
|
return LayerNormFn.apply(x, weight, bias, residual, eps, prenorm, residual_in_fp32, True)
|
|
|
|
|
|
class RMSNorm(torch.nn.Module):
|
|
def __init__(self, hidden_size, eps=1e-5, device=None, dtype=None):
|
|
factory_kwargs = {"device": device, "dtype": dtype}
|
|
super().__init__()
|
|
self.eps = eps
|
|
self.weight = torch.nn.Parameter(torch.empty(hidden_size, **factory_kwargs))
|
|
self.register_parameter("bias", None)
|
|
self.reset_parameters()
|
|
|
|
def reset_parameters(self):
|
|
torch.nn.init.ones_(self.weight)
|
|
|
|
def forward(self, x, residual=None, prenorm=False, residual_in_fp32=False):
|
|
return rms_norm_fn(
|
|
x,
|
|
self.weight,
|
|
self.bias,
|
|
residual=residual,
|
|
eps=self.eps,
|
|
prenorm=prenorm,
|
|
residual_in_fp32=residual_in_fp32,
|
|
)
|
|
|
|
|
|
class LayerNormLinearFn(torch.autograd.Function):
|
|
@staticmethod
|
|
@custom_fwd
|
|
def forward(
|
|
ctx,
|
|
x,
|
|
norm_weight,
|
|
norm_bias,
|
|
linear_weight,
|
|
linear_bias,
|
|
residual=None,
|
|
eps=1e-6,
|
|
prenorm=False,
|
|
residual_in_fp32=False,
|
|
is_rms_norm=False,
|
|
):
|
|
x_shape_og = x.shape
|
|
# reshape input data into 2D tensor
|
|
x = x.reshape(-1, x.shape[-1])
|
|
if x.stride(-1) != 1:
|
|
x = x.contiguous()
|
|
if residual is not None:
|
|
assert residual.shape == x_shape_og
|
|
residual = residual.reshape(-1, residual.shape[-1])
|
|
if residual.stride(-1) != 1:
|
|
residual = residual.contiguous()
|
|
norm_weight = norm_weight.contiguous()
|
|
if norm_bias is not None:
|
|
norm_bias = norm_bias.contiguous()
|
|
residual_dtype = (
|
|
residual.dtype
|
|
if residual is not None
|
|
else (torch.float32 if residual_in_fp32 else None)
|
|
)
|
|
y, mean, rstd, residual_out = _layer_norm_fwd(
|
|
x,
|
|
norm_weight,
|
|
norm_bias,
|
|
eps,
|
|
residual,
|
|
out_dtype=None if not torch.is_autocast_enabled() else torch.get_autocast_gpu_dtype(),
|
|
residual_dtype=residual_dtype,
|
|
is_rms_norm=is_rms_norm,
|
|
)
|
|
y = y.reshape(x_shape_og)
|
|
dtype = torch.get_autocast_gpu_dtype() if torch.is_autocast_enabled() else y.dtype
|
|
linear_weight = linear_weight.to(dtype)
|
|
linear_bias = linear_bias.to(dtype) if linear_bias is not None else None
|
|
out = F.linear(y.to(linear_weight.dtype), linear_weight, linear_bias)
|
|
# We don't store y, will be recomputed in the backward pass to save memory
|
|
ctx.save_for_backward(residual_out, norm_weight, norm_bias, linear_weight, mean, rstd)
|
|
ctx.x_shape_og = x_shape_og
|
|
ctx.eps = eps
|
|
ctx.is_rms_norm = is_rms_norm
|
|
ctx.has_residual = residual is not None
|
|
ctx.prenorm = prenorm
|
|
ctx.x_dtype = x.dtype
|
|
ctx.linear_bias_is_none = linear_bias is None
|
|
return out if not prenorm else (out, residual_out.reshape(x_shape_og))
|
|
|
|
@staticmethod
|
|
@custom_bwd
|
|
def backward(ctx, dout, *args):
|
|
x, norm_weight, norm_bias, linear_weight, mean, rstd = ctx.saved_tensors
|
|
dout = dout.reshape(-1, dout.shape[-1])
|
|
dy = F.linear(dout, linear_weight.t())
|
|
dlinear_bias = None if ctx.linear_bias_is_none else dout.sum(0)
|
|
if dy.stride(-1) != 1:
|
|
dy = dy.contiguous()
|
|
assert dy.shape == x.shape
|
|
if ctx.prenorm:
|
|
dresidual = args[0]
|
|
dresidual = dresidual.reshape(-1, dresidual.shape[-1])
|
|
if dresidual.stride(-1) != 1:
|
|
dresidual = dresidual.contiguous()
|
|
assert dresidual.shape == x.shape
|
|
else:
|
|
dresidual = None
|
|
dx, dnorm_weight, dnorm_bias, dresidual_in, y = _layer_norm_bwd(
|
|
dy,
|
|
x,
|
|
norm_weight,
|
|
norm_bias,
|
|
ctx.eps,
|
|
mean,
|
|
rstd,
|
|
dresidual,
|
|
ctx.has_residual,
|
|
ctx.is_rms_norm,
|
|
x_dtype=ctx.x_dtype,
|
|
recompute_output=True,
|
|
)
|
|
dlinear_weight = torch.einsum("bo,bi->oi", dout, y)
|
|
return (
|
|
dx.reshape(ctx.x_shape_og),
|
|
dnorm_weight,
|
|
dnorm_bias,
|
|
dlinear_weight,
|
|
dlinear_bias,
|
|
dresidual_in.reshape(ctx.x_shape_og) if ctx.has_residual else None,
|
|
None,
|
|
None,
|
|
None,
|
|
None,
|
|
)
|
|
|
|
|
|
def layer_norm_linear_fn(
|
|
x,
|
|
norm_weight,
|
|
norm_bias,
|
|
linear_weight,
|
|
linear_bias,
|
|
residual=None,
|
|
eps=1e-6,
|
|
prenorm=False,
|
|
residual_in_fp32=False,
|
|
is_rms_norm=False,
|
|
):
|
|
return LayerNormLinearFn.apply(
|
|
x,
|
|
norm_weight,
|
|
norm_bias,
|
|
linear_weight,
|
|
linear_bias,
|
|
residual,
|
|
eps,
|
|
prenorm,
|
|
residual_in_fp32,
|
|
is_rms_norm,
|
|
)
|