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# this function implements the chunkwise form of HGRN, inspired by
# [Volodymyr Kyrylov in his blog post](https://proger.github.io/posts/scan/chunk.html)
# also refer to the `accelerated-scan` lib: https://github.com/proger/accelerated-scan
# from tests on H800, with B, D = 16, 128, we see that the chunk can be greatly faster than the recurrent:
#
# Performance:
# seq_len chunk recurrent chunk_bwd recurrent_bwd
# 0 128.0 0.039360 0.061056 0.312160 0.205008
# 1 256.0 0.045824 0.123712 0.308784 0.297696
# 2 512.0 0.058688 0.241952 0.310720 0.626528
# 3 1024.0 0.088288 0.476992 0.313184 1.333152
# 4 2048.0 0.169472 0.943264 0.452464 2.724864
# 5 4096.0 0.329920 1.886144 0.881600 5.551520
# 6 8192.0 0.647872 3.755040 1.740496 11.117184
# 7 16384.0 1.272064 7.520576 3.446608 22.362528
import torch
import triton
import triton.language as tl
from fla.ops.utils.op import exp
from fla.utils import autotune_cache_kwargs, input_guard
@triton.autotune(
configs=[
triton.Config({'BD': 32}, num_warps=1),
triton.Config({'BD': 32}, num_warps=2),
triton.Config({'BD': 32}, num_warps=4),
triton.Config({'BD': 32}, num_warps=8),
triton.Config({'BD': 64}, num_warps=1),
triton.Config({'BD': 64}, num_warps=2),
triton.Config({'BD': 64}, num_warps=4),
triton.Config({'BD': 64}, num_warps=8),
triton.Config({'BD': 128}, num_warps=1),
triton.Config({'BD': 128}, num_warps=2),
triton.Config({'BD': 128}, num_warps=4),
triton.Config({'BD': 128}, num_warps=8),
],
key=['D'],
**autotune_cache_kwargs,
)
@triton.jit(do_not_specialize=['T'])
def chunk_hgrn_fwd_kernel_h(
x,
g,
gc,
o,
h0,
T,
D: tl.constexpr,
BT: tl.constexpr,
BD: tl.constexpr,
USE_INITIAL_STATE: tl.constexpr,
):
i_d, i_t, i_b = tl.program_id(0), tl.program_id(1), tl.program_id(2)
o_d = i_d * BD + tl.arange(0, BD)
mask = o_d < D
p_x = x + i_b * T * D + i_t * BT * D + o_d
p_g = g + i_b * T * D + i_t * BT * D + o_d
p_gc = gc + i_b * T * D + i_t * BT * D + o_d
p_o = o + i_b * T * D + i_t * BT * D + o_d
b_h = tl.zeros([BD], dtype=tl.float32)
b_gc = tl.zeros([BD], dtype=tl.float32)
if USE_INITIAL_STATE:
if i_t == 0:
b_h += tl.load(h0 + i_b * D + o_d, mask=mask, other=0).to(tl.float32)
for i in range(0, BT):
mask_t = mask & ((i_t * BT + i) < T)
b_x = tl.load(p_x, mask=mask_t, other=0).to(tl.float32)
b_g = tl.load(p_g, mask=mask_t, other=0).to(tl.float32)
b_h = exp(b_g) * b_h + b_x
b_gc = b_gc + b_g
tl.store(p_gc, b_gc.to(p_o.dtype.element_ty), mask=mask_t)
tl.store(p_o, b_h.to(p_o.dtype.element_ty), mask=mask_t)
p_x += D
p_g += D
p_gc += D
p_o += D
@triton.jit(do_not_specialize=['T'])
def chunk_hgrn_fwd_kernel_o(
gc,
o,
s_b,
s_t,
s_d,
T,
D: tl.constexpr,
BT: tl.constexpr,
BD: tl.constexpr,
):
i_d, i_b = tl.program_id(0), tl.program_id(1)
o_d = i_d * BD + tl.arange(0, BD)
mask = o_d < D
for i_t in range(1, tl.cdiv(T, BT)):
p_gc = tl.make_block_ptr(gc + i_b * s_b, (T, D), (s_t, s_d), (i_t * BT, i_d * BD), (BT, BD), (1, 0))
p_o = tl.make_block_ptr(o + i_b * s_b, (T, D), (s_t, s_d), (i_t * BT, i_d * BD), (BT, BD), (1, 0))
# [BD,]
b_h0 = tl.load(o + i_b * T * D + i_t * BT * D - D + o_d, mask=mask, other=0).to(tl.float32)
# [BT, BD]
b_gc = tl.load(p_gc, boundary_check=(0, 1)).to(tl.float32)
b_o = tl.load(p_o, boundary_check=(0, 1)).to(tl.float32)
b_o = b_o + exp(b_gc) * b_h0[None, :]
tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
@triton.autotune(
configs=[
triton.Config({'BD': BD}, num_warps=num_warps)
for BD in [32, 64, 128]
for num_warps in [1, 2, 4, 8]
],
key=['D'],
**autotune_cache_kwargs,
)
@triton.jit(do_not_specialize=['T'])
def chunk_hgrn_bwd_kernel_h(
g,
gc,
dx,
do,
T,
D: tl.constexpr,
BT: tl.constexpr,
BD: tl.constexpr,
):
i_d, i_t, i_b = tl.program_id(0), tl.program_id(1), tl.program_id(2)
o_d = i_d * BD + tl.arange(0, BD)
mask = o_d < D
BC = min(BT, T - i_t * BT)
NT = tl.num_programs(1)
p_g = g + (i_b * T + i_t * BT + BC - 1) * D + o_d
p_gc = gc + (i_b * T + i_t * BT + BC - 1) * D + o_d
p_dx = dx + (i_b * T + i_t * BT + BC - 1) * D + o_d
p_do = do + (i_b * T + i_t * BT + BC - 1) * D + o_d
if i_t == NT - 1:
b_gc = tl.zeros([BD], dtype=tl.float32)
else:
b_gc = tl.load(g + (i_b * T + i_t * BT + BT) * D + o_d, mask=mask, other=0).to(tl.float32)
b_dh = tl.zeros([BD], dtype=tl.float32)
for _ in range(BC - 1, -1, -1):
tl.store(p_gc, b_gc.to(p_gc.dtype.element_ty), mask=mask)
b_g = tl.load(p_g, mask=mask, other=0).to(tl.float32)
b_do = tl.load(p_do, mask=mask, other=0).to(tl.float32)
b_gc = b_gc + b_g
b_dh = b_dh + b_do
b_dx = b_dh
b_dh = b_dh * exp(b_g)
tl.store(p_dx, b_dx.to(p_dx.dtype.element_ty), mask=mask)
p_g -= D
p_gc -= D
p_dx -= D
p_do -= D
@triton.jit(do_not_specialize=['T'])
def chunk_hgrn_bwd_kernel_o(
g,
gc,
o,
dx,
dg,
s_b,
s_t,
s_d,
T,
D: tl.constexpr,
BT: tl.constexpr,
BD: tl.constexpr,
):
i_d, i_b = tl.program_id(0), tl.program_id(1)
o_d = i_d * BD + tl.arange(0, BD)
mask = o_d < D
for i_t in range(tl.cdiv(T, BT) - 1, -1, -1):
p_g = tl.make_block_ptr(g + i_b * s_b, (T, D), (s_t, s_d), (i_t * BT, i_d * BD), (BT, BD), (1, 0))
p_gc = tl.make_block_ptr(gc + i_b * s_b, (T, D), (s_t, s_d), (i_t * BT, i_d * BD), (BT, BD), (1, 0))
p_o = tl.make_block_ptr(o + i_b * s_b, (T, D), (s_t, s_d), (i_t * BT - 1, i_d * BD), (BT, BD), (1, 0))
p_dx = tl.make_block_ptr(dx + i_b * s_b, (T, D), (s_t, s_d), (i_t * BT, i_d * BD), (BT, BD), (1, 0))
p_dg = tl.make_block_ptr(dg + i_b * s_b, (T, D), (s_t, s_d), (i_t * BT, i_d * BD), (BT, BD), (1, 0))
# [BD,]
mask_t = mask & ((i_t + 1) * BT < T)
b_ht = tl.load(dx + i_b * T * D + (i_t + 1) * BT * D + o_d, mask=mask_t, other=0).to(tl.float32)
# [BT, BD]
b_g = tl.load(p_g, boundary_check=(0, 1)).to(tl.float32)
b_gc = tl.load(p_gc, boundary_check=(0, 1)).to(tl.float32)
b_o = tl.load(p_o, boundary_check=(0, 1)).to(tl.float32)
b_dx = tl.load(p_dx, boundary_check=(0, 1)).to(tl.float32)
b_dx = b_dx + exp(b_gc) * b_ht[None, :]
b_dg = b_o * b_dx * exp(b_g)
tl.store(p_dx, b_dx.to(p_dx.dtype.element_ty), boundary_check=(0, 1))
tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0, 1))
class ChunkHGRNFunction(torch.autograd.Function):
@staticmethod
@input_guard
def forward(ctx, x, g, initial_state=None, output_final_state=False):
B, T, D = x.shape
BT, BD = 128, min(64, triton.next_power_of_2(D))
num_warps = 8 if BD == 64 else 4
gc = torch.empty_like(g, dtype=torch.float)
o = torch.empty_like(x, dtype=torch.float)
def grid(meta): return (triton.cdiv(D, meta['BD']), triton.cdiv(T, meta['BT']), B)
chunk_hgrn_fwd_kernel_h[grid](
x, g, gc, o, initial_state,
T=T, D=D, BT=BT,
USE_INITIAL_STATE=initial_state is not None,
)
def grid(meta): return (triton.cdiv(D, meta['BD']), B)
chunk_hgrn_fwd_kernel_o[grid](
gc, o,
o.stride(-3), o.stride(-2), o.stride(-1),
T=T, D=D, BT=BT, BD=BD,
num_warps=num_warps,
)
final_state = None
if output_final_state:
final_state = o[:, -1].clone()
o = o.to(x.dtype)
ctx.save_for_backward(g, o, initial_state)
return o, final_state
@staticmethod
@input_guard
def backward(ctx, do, dht=None):
g, o, initial_state = ctx.saved_tensors
B, T, D = do.shape
BT, BD = 128, min(64, triton.next_power_of_2(D))
num_warps = 8 if BD == 64 else 4
gc = torch.empty_like(g, dtype=torch.float)
dx = torch.empty_like(o, dtype=torch.float)
def grid(meta): return (triton.cdiv(D, meta['BD']), triton.cdiv(T, meta['BT']), B)
chunk_hgrn_bwd_kernel_h[grid](
g, gc, dx, do,
T=T, D=D, BT=BT,
)
dg = torch.empty_like(g, dtype=torch.float)
def grid(meta): return (triton.cdiv(D, meta['BD']), B)
chunk_hgrn_bwd_kernel_o[grid](
g, gc, o, dx, dg,
o.stride(-3), o.stride(-2), o.stride(-1),
T=T, D=D, BT=BT, BD=BD,
num_warps=num_warps,
)
if initial_state is not None:
dg[:, 0] = (initial_state * dx[:, 0] * g[:, 0].float().exp()).to(dg.dtype)
return dx.to(o.dtype), dg, None, None
@torch.compiler.disable
def chunk_hgrn(
x: torch.Tensor,
g: torch.Tensor,
initial_state: torch.Tensor = None,
output_final_state: bool = False,
) -> tuple[torch.Tensor, torch.Tensor]:
return ChunkHGRNFunction.apply(x, g, initial_state, output_final_state)
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