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[Simple GLA] Add comments & Fix bad grad
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@yzhangcs
yzhangcs authored Aug 18, 2024
1 parent fd44b54 commit 11c7f66
Showing 1 changed file with 71 additions and 95 deletions.
166 changes: 71 additions & 95 deletions fla/ops/simple_gla/chunk.py
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
# -*- coding: utf-8 -*-
# Copyright (c) 2023, Yu Zhang, Songlin Yang

from typing import Tuple
from typing import Optional, Tuple

import torch
import triton
Expand All @@ -11,23 +11,14 @@
from fla.utils import contiguous


@torch.jit.script
def normalize_output(q, k, o):
k = k.transpose(-2, -1)
k = k.cumsum(-1)
k = k.transpose(-2, -1)
z = (q * k).sum(-1, keepdim=True)
return o / (z + 1e-5)


@triton.jit
def chunk_simple_gla_fwd_kernel_h(
k,
v,
h,
g,
initial_state, # initial state of the chunk [B, H, D_head_K, D_head_V]
final_state, # final state of the chunk [B, H, D_head_K, D_head_V]
h0,
ht,
s_qk_h,
s_qk_t,
s_qk_d,
Expand All @@ -36,7 +27,6 @@ def chunk_simple_gla_fwd_kernel_h(
s_vo_d,
s_h_h,
s_h_t,
H: tl.constexpr,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
Expand All @@ -53,17 +43,13 @@ def chunk_simple_gla_fwd_kernel_h(
b_h = tl.zeros([BK, BV], dtype=tl.float32)

if USE_INITIAL_STATE:
p_h0 = tl.make_block_ptr(initial_state + i_bh * K * V,
(K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_h0 = tl.make_block_ptr(h0 + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
b_h = tl.load(p_h0, boundary_check=(0, 1)).to(tl.float32)

for i_t in range(NT):
p_k = tl.make_block_ptr(
k + i_bh * s_qk_h, (K, T), (s_qk_d, s_qk_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_v = tl.make_block_ptr(
v + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V,
(K, V), (s_h_t, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (K, T), (s_qk_d, s_qk_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))

tl.store(p_h, b_h.to(p_h.dtype.element_ty), boundary_check=(0, 1))
# [BK, BT]
Expand All @@ -72,13 +58,12 @@ def chunk_simple_gla_fwd_kernel_h(
b_v = tl.load(p_v, boundary_check=(0, 1))
# [BK, BV]
b_g_last = tl.load(g + i_bh * T + i_t * BT + BT - 1)
b_h *= tl.math.exp2(b_g_last)
b_h *= tl.exp(b_g_last)
b_g = tl.load(g + i_bh * T + i_t * BT + tl.arange(0, BT))
b_h += tl.dot(b_k, (b_v * tl.math.exp2(b_g_last - b_g)[:, None]).to(b_k.dtype), allow_tf32=False)
b_h += tl.dot(b_k, (b_v * tl.exp(b_g_last - b_g)[:, None]).to(b_k.dtype), allow_tf32=False)

if STORE_FINAL_STATE:
p_ht = tl.make_block_ptr(
final_state + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_ht = tl.make_block_ptr(ht + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
tl.store(p_ht, b_h.to(p_ht.dtype.element_ty), boundary_check=(0, 1))


Expand All @@ -99,7 +84,6 @@ def chunk_simple_gla_fwd_kernel_o(
s_h_h,
s_h_t,
scale,
H: tl.constexpr,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
Expand All @@ -115,12 +99,9 @@ def chunk_simple_gla_fwd_kernel_o(
b_o = tl.zeros([BT, BV], dtype=tl.float32)
b_s = tl.zeros([BT, BT], dtype=tl.float32)
for i_k in range(tl.cdiv(K, BK)):
p_q = tl.make_block_ptr(
q + i_bh * s_qk_h, (T, K), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_k = tl.make_block_ptr(
k + i_bh * s_qk_h, (K, T), (s_qk_d, s_qk_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V,
(K, V), (s_h_t, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_q = tl.make_block_ptr(q + i_bh * s_qk_h, (T, K), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (K, T), (s_qk_d, s_qk_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))

# [BT, BK]
b_q = tl.load(p_q, boundary_check=(0, 1))
Expand All @@ -135,16 +116,14 @@ def chunk_simple_gla_fwd_kernel_o(

p_g = g + i_bh * T + i_t * BT + tl.arange(0, BT)
b_g = tl.load(p_g)
b_o = b_o * tl.math.exp2(b_g)[:, None]
b_s = b_s * tl.math.exp2(b_g[:, None] - b_g[None, :])
b_o = b_o * tl.exp(b_g)[:, None]
b_s = b_s * tl.exp(b_g[:, None] - b_g[None, :])
b_s = tl.where(m_s, b_s, 0)

p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, V),
(s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
b_v = tl.load(p_v, boundary_check=(0, 1))
b_o = (b_o + tl.dot(b_s.to(b_v.dtype), b_v, allow_tf32=False)) * scale
p_o = tl.make_block_ptr(o + i_bh * s_vo_h, (T, V),
(s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_o = tl.make_block_ptr(o + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))


Expand All @@ -163,7 +142,6 @@ def chunk_simple_gla_bwd_kernel_dh(
s_h_h,
s_h_t,
scale,
H: tl.constexpr,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
Expand All @@ -177,22 +155,18 @@ def chunk_simple_gla_bwd_kernel_dh(
# [BK, BV]
b_dh = tl.zeros([BK, BV], dtype=tl.float32)
for i_t in range(NT - 1, -1, -1):
p_q = tl.make_block_ptr(
q + i_bh * s_qk_h, (K, T), (s_qk_d, s_qk_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_do = tl.make_block_ptr(
do + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dh = tl.make_block_ptr(dh + i_bh * s_h_h + i_t * K * V,
(K, V), (s_h_t, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_q = tl.make_block_ptr(q + i_bh * s_qk_h, (K, T), (s_qk_d, s_qk_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_do = tl.make_block_ptr(do + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dh = tl.make_block_ptr(dh + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))

tl.store(p_dh, b_dh.to(p_dh.dtype.element_ty), boundary_check=(0, 1))
# [BK, BT]
b_q = tl.load(p_q, boundary_check=(0, 1))
b_q = (b_q * scale * tl.math.exp2(tl.load(g + i_bh * T +
i_t * BT + tl.arange(0, BT)))[None, :]).to(b_q.dtype)
b_q = (b_q * scale * tl.exp(tl.load(g + i_bh * T + i_t * BT + tl.arange(0, BT)))[None, :]).to(b_q.dtype)
# [BT, V]
b_do = tl.load(p_do, boundary_check=(0, 1))
# [BK, BV]
b_dh *= tl.math.exp2(tl.load(g + i_bh * T + i_t * BT + BT - 1))
b_dh *= tl.exp(tl.load(g + i_bh * T + i_t * BT + BT - 1))
b_dh += tl.dot(b_q, b_do.to(b_q.dtype), allow_tf32=False)


Expand All @@ -217,8 +191,6 @@ def chunk_simple_gla_bwd_kernel_dqkv(
s_h_h,
s_h_t,
scale,
B: tl.constexpr,
H: tl.constexpr,
T: tl.constexpr,
K: tl.constexpr,
V: tl.constexpr,
Expand All @@ -231,35 +203,28 @@ def chunk_simple_gla_bwd_kernel_dqkv(
n_bh = tl.num_programs(2)
o_i = tl.arange(0, BT)

p_q = tl.make_block_ptr(q + i_bh * s_qk_h, (K, T),
(s_qk_d, s_qk_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (T, K),
(s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_q = tl.make_block_ptr(q + i_bh * s_qk_h, (K, T), (s_qk_d, s_qk_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1))
p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (T, K), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))

b_q = tl.load(p_q, boundary_check=(0, 1))
b_k = tl.load(p_k, boundary_check=(0, 1))
b_s = tl.dot(b_k, b_q, allow_tf32=False)
p_g = g + i_bh * T + i_t * BT + tl.arange(0, BT)
b_g = tl.load(p_g)
b_g_last = tl.load(g + i_bh * T + i_t * BT + BT - 1)
mask = tl.math.exp2(b_g[None, :] - b_g[:, None])
mask = tl.exp(b_g[None, :] - b_g[:, None])
mask = tl.where(o_i[:, None] <= o_i[None, :], mask * scale, 0)
b_s = b_s * mask

b_dq = tl.zeros([BT, BK], dtype=tl.float32)
b_dk = tl.zeros([BT, BK], dtype=tl.float32)
b_ds = tl.zeros([BT, BT], dtype=tl.float32)
for i_v in range(tl.cdiv(V, BV)):
p_v = tl.make_block_ptr(
v + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_h = tl.make_block_ptr(h + i_bh * s_h_h, (V, NT * K), (1, s_h_t),
(i_v * BV, i_t * K + i_k * BK), (BV, BK), (0, 1))
p_do = tl.make_block_ptr(
do + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dh = tl.make_block_ptr(dh + i_bh * s_h_h, (NT * K, V),
(s_h_t, 1), (i_t * K + i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_dv = tl.make_block_ptr(dv + (i_k*n_bh+i_bh)*s_vo_h, (T, V),
(s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_h = tl.make_block_ptr(h + i_bh * s_h_h, (V, NT * K), (1, s_h_t), (i_v * BV, i_t * K + i_k * BK), (BV, BK), (0, 1))
p_do = tl.make_block_ptr(do + i_bh * s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
p_dh = tl.make_block_ptr(dh + i_bh * s_h_h, (NT * K, V), (s_h_t, 1), (i_t * K + i_k * BK, i_v * BV), (BK, BV), (1, 0))
p_dv = tl.make_block_ptr(dv + (i_k*n_bh+i_bh)*s_vo_h, (T, V), (s_vo_t, s_vo_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0))
# [BT, BV]
b_v = tl.load(p_v, boundary_check=(0, 1))
b_do = tl.load(p_do, boundary_check=(0, 1))
Expand All @@ -273,21 +238,19 @@ def chunk_simple_gla_bwd_kernel_dqkv(
b_dq += tl.dot(b_do, b_h, allow_tf32=False) * scale
b_dk += tl.dot(b_v, tl.trans(b_dh), allow_tf32=False)
# [BT, BV]
b_dv = tl.dot(b_k, b_dh, allow_tf32=False) * tl.math.exp2(-b_g + b_g_last)[:, None] + \
tl.dot(b_s.to(b_q.dtype), b_do, allow_tf32=False)
b_dv = tl.dot(b_k, b_dh, allow_tf32=False) * tl.exp(-b_g + b_g_last)[:, None]
b_dv += tl.dot(b_s.to(b_q.dtype), b_do, allow_tf32=False)
tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))

b_dq = b_dq * tl.math.exp2(b_g)[:, None]
b_dk = b_dk * tl.math.exp2(-b_g + b_g_last)[:, None]
b_dq = b_dq * tl.exp(b_g)[:, None]
b_dk = b_dk * tl.exp(-b_g + b_g_last)[:, None]
b_ds = b_ds * tl.trans(mask)
b_ds = b_ds.to(b_k.dtype)
# [BT, BK]
b_dq += tl.dot(b_ds, b_k, allow_tf32=False)
b_dk += tl.trans(tl.dot(b_q, b_ds, allow_tf32=False))
p_dq = tl.make_block_ptr(dq + i_bh * s_qk_h, (T, K),
(s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dk = tl.make_block_ptr(dk + i_bh * s_qk_h, (T, K),
(s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dq = tl.make_block_ptr(dq + i_bh * s_qk_h, (T, K), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
p_dk = tl.make_block_ptr(dk + i_bh * s_qk_h, (T, K), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))

Expand All @@ -300,19 +263,14 @@ class SimpleGLAFunction(torch.autograd.Function):
def forward(ctx, q, k, v, g, scale, initial_state, output_final_state):
B, H, T, K, V = *q.shape, v.shape[-1]
BT = 64
BK, BV = min(64, triton.next_power_of_2(K)), min(
64, triton.next_power_of_2(V))
BK, BV = min(64, triton.next_power_of_2(K)), min(64, triton.next_power_of_2(V))
NT, NK, NV = triton.cdiv(T, BT), triton.cdiv(K, BK), triton.cdiv(V, BV)
num_stages = 1
num_warps = 4 if BK == 64 else 2
num_stages = 1

if scale is None:
scale = K ** -0.5

BT = 64
assert T % BT == 0, 'sequence length must be divisible by BT'
g = g.reshape(B, H, -1, BT)
g = g.cumsum(-1) * 1.44269504
g = g.cumsum(-1)
g = g.reshape(B, H, -1)

final_state = None
Expand All @@ -326,7 +284,7 @@ def forward(ctx, q, k, v, g, scale, initial_state, output_final_state):
q.stride(1), q.stride(2), q.stride(3),
v.stride(1), v.stride(2), v.stride(3),
h.stride(1), h.stride(2),
H=H, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT,
T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT,
USE_INITIAL_STATE=initial_state is not None,
STORE_FINAL_STATE=output_final_state,
num_warps=num_warps,
Expand All @@ -340,30 +298,29 @@ def forward(ctx, q, k, v, g, scale, initial_state, output_final_state):
v.stride(1), v.stride(2), v.stride(3),
h.stride(1), h.stride(2),
scale,
H=H, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV,
T=T, K=K, V=V, BT=BT, BK=BK, BV=BV,
num_warps=num_warps,
num_stages=num_stages
)

ctx.save_for_backward(q, k, v, h, g)
ctx.scale = scale
return o.to(q.dtype), final_state

@staticmethod
@custom_bwd
@contiguous
def backward(ctx, do, scale, d_ht=None):
def backward(ctx, do, dht=None):
q, k, v, h, g = ctx.saved_tensors

B, H, T, K, V = *q.shape, v.shape[-1]
BT = 64
BK, BV = min(32 if q.dtype == torch.float32 else 64, triton.next_power_of_2(K)), min(
32 if q.dtype == torch.float32 else 64, triton.next_power_of_2(V))
BK = min(32 if q.dtype == torch.float32 else 64, triton.next_power_of_2(K))
BV = min(32 if q.dtype == torch.float32 else 64, triton.next_power_of_2(V))
NT, NK, NV = triton.cdiv(T, BT), triton.cdiv(K, BK), triton.cdiv(V, BV)
num_stages = 1
num_warps = 4 if BK == 64 else 2

if scale is None:
scale = K ** -0.5
num_stages = 1
scale = ctx.scale

dh = q.new_empty(B, H, NT * K, V)
grid = (NK, NV, B * H)
Expand All @@ -373,7 +330,7 @@ def backward(ctx, do, scale, d_ht=None):
v.stride(1), v.stride(2), v.stride(3),
dh.stride(1), dh.stride(2),
scale,
H=H, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT,
T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT,
num_warps=num_warps,
num_stages=num_stages
)
Expand All @@ -389,7 +346,7 @@ def backward(ctx, do, scale, d_ht=None):
v.stride(1), v.stride(2), v.stride(3),
dh.stride(1), dh.stride(2),
scale,
B=B, H=H, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT,
T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT,
num_warps=num_warps,
num_stages=num_stages
)
Expand All @@ -409,12 +366,31 @@ def chunk_simple_gla(
k: torch.Tensor,
v: torch.Tensor,
g: torch.Tensor, # log decay
scale: float = None,
scale: Optional[float] = None,
initial_state: torch.Tensor = None,
output_final_state: bool = False
) -> Tuple[torch.Tensor, torch.Tensor]:
if initial_state is not None:
initial_state = initial_state.detach()
r"""
Args:
q (torch.Tensor):
queries of shape `(B, H, T, K)`
k (torch.Tensor):
keys of shape `(B, H, T, K)`
v (torch.Tensor):
values of shape `(B, H, T, V)`
g (torch.Tensor):
Forget gates of shape `(B, H, T)` applied to keys.
Compared to GLA, the gating is head-wise instead of elementwise.
scale (Optional[int]):
Scale factor for the attention scores.
If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
initial_state (Optional[torch.Tensor]):
Initial state of shape `(B, H, K, V)`. Default: `None`.
output_final_state (Optional[bool]):
Whether to output the final state of shape `(B, H, K, V)`. Default: `False`.
"""
if scale is None:
scale = k.shape[-1] ** -0.5
g = g.float()
o, final_state = SimpleGLAFunction.apply(q, k, v, g, scale, initial_state, output_final_state)
return o, final_state

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