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flash_attention_causal.py
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flash_attention_causal.py
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import torch
import torch.nn as nn
import numpy as np
import sys
import time
from einops import rearrange
BLOCK_SIZE = 1024
NEG_INF = -1e10 # -infinity
EPSILON = 1e-10
def normal_attention_causal(Q, K, V):
scale = 1 / np.sqrt(Q.shape[-1])
Q = Q * scale
QKt = torch.einsum('... i d, ... j d -> ... i j', Q, K)
Q_LEN = Q.shape[2]
K_LEN = K.shape[2]
causal_mask = torch.triu(torch.ones((Q_LEN, K_LEN)), K_LEN - Q_LEN + 1)
causal_mask = causal_mask.to(device='cuda')
QKt = torch.where(causal_mask > 0, NEG_INF, QKt)
attn = nn.functional.softmax(QKt, dim=-1)
return attn @ V
def flash_attention_causal_forward(Q, K, V):
O = torch.zeros_like(Q, requires_grad=True)
l = torch.zeros(Q.shape[:-1])[...,None]
m = torch.ones(Q.shape[:-1])[...,None] * NEG_INF
O = O.to(device='cuda')
l = l.to(device='cuda')
m = m.to(device='cuda')
Q_BLOCK_SIZE = min(BLOCK_SIZE, Q.shape[-1])
KV_BLOCK_SIZE = BLOCK_SIZE
Q_BLOCKS = torch.split(Q, Q_BLOCK_SIZE, dim=2)
K_BLOCKS = torch.split(K, KV_BLOCK_SIZE, dim=2)
V_BLOCKS = torch.split(V, KV_BLOCK_SIZE, dim=2)
Tr = len(Q_BLOCKS)
Tc = len(K_BLOCKS)
O_BLOCKS = list(torch.split(O, Q_BLOCK_SIZE, dim=2))
l_BLOCKS = list(torch.split(l, Q_BLOCK_SIZE, dim=2))
m_BLOCKS = list(torch.split(m, Q_BLOCK_SIZE, dim=2))
Q_LEN = Q.shape[2]
K_LEN = K.shape[2]
Q_RANGE = torch.arange(Q_LEN)[:,None] + (K_LEN - Q_LEN)
K_RANGE = torch.arange(K_LEN)[None,:]
Q_RANGE = Q_RANGE.to(device='cuda')
K_RANGE = K_RANGE.to(device='cuda')
Q_RANGE_BLOCKS = torch.split(Q_RANGE, Q_BLOCK_SIZE, dim=0)
K_RANGE_BLOCKS = torch.split(K_RANGE, KV_BLOCK_SIZE, dim=1)
for j in range(Tc):
Kj = K_BLOCKS[j]
Vj = V_BLOCKS[j]
K_RANGE_BLOCKSj = K_RANGE_BLOCKS[j]
for i in range(Tr):
Qi = Q_BLOCKS[i]
Oi = O_BLOCKS[i]
li = l_BLOCKS[i]
mi = m_BLOCKS[i]
Q_RANGE_BLOCKSi = Q_RANGE_BLOCKS[i]
scale = 1 / np.sqrt(Q.shape[-1])
Qi_scaled = Qi * scale
S_ij = torch.einsum('... i d, ... j d -> ... i j', Qi_scaled, Kj)
# Masking
causal_mask = Q_RANGE_BLOCKSi >= K_RANGE_BLOCKSj
S_ij = torch.where(causal_mask > 0, S_ij, NEG_INF)
m_block_ij, _ = torch.max(S_ij, dim=-1, keepdims=True)
P_ij = torch.exp(S_ij - m_block_ij)
# Masking
P_ij = torch.where(causal_mask > 0, P_ij, 0)
l_block_ij = torch.sum(P_ij, dim=-1, keepdims=True) + EPSILON
P_ij_Vj = torch.einsum('... i j, ... j d -> ... i d', P_ij, Vj)
mi_new = torch.maximum(m_block_ij, mi)
li_new = torch.exp(mi - mi_new) * li + torch.exp(m_block_ij - mi_new) * l_block_ij
O_BLOCKS[i] = (li/li_new) * torch.exp(mi - mi_new) * Oi + (torch.exp(m_block_ij - mi_new) / li_new) * P_ij_Vj
l_BLOCKS[i] = li_new
m_BLOCKS[i] = mi_new
O = torch.cat(O_BLOCKS, dim=2)
l = torch.cat(l_BLOCKS, dim=2)
m = torch.cat(m_BLOCKS, dim=2)
return O, l, m
def flash_attention_causal_backward(Q, K, V, O, l, m, dO):
Q_BLOCK_SIZE = min(BLOCK_SIZE, Q.shape[-1])
KV_BLOCK_SIZE = BLOCK_SIZE
Q_BLOCKS = torch.split(Q, Q_BLOCK_SIZE, dim=2)
K_BLOCKS = torch.split(K, KV_BLOCK_SIZE, dim=2)
V_BLOCKS = torch.split(V, KV_BLOCK_SIZE, dim=2)
Tr = len(Q_BLOCKS)
Tc = len(K_BLOCKS)
O_BLOCKS = list(torch.split(O, Q_BLOCK_SIZE, dim=2))
dO_BLOCKS = list(torch.split(dO, Q_BLOCK_SIZE, dim=2))
l_BLOCKS = list(torch.split(l, Q_BLOCK_SIZE, dim=2))
m_BLOCKS = list(torch.split(m, Q_BLOCK_SIZE, dim=2))
dQ = torch.zeros_like(Q, requires_grad=True).to(device='cuda')
dK = torch.zeros_like(K, requires_grad=True).to(device='cuda')
dV = torch.zeros_like(V, requires_grad=True).to(device='cuda')
dQ_BLOCKS = list(torch.split(dQ, Q_BLOCK_SIZE, dim=2))
dK_BLOCKS = list(torch.split(dK, KV_BLOCK_SIZE, dim=2))
dV_BLOCKS = list(torch.split(dV, KV_BLOCK_SIZE, dim=2))
Q_LEN = Q.shape[2]
K_LEN = K.shape[2]
Q_RANGE = torch.arange(Q_LEN)[:,None] + (K_LEN - Q_LEN)
K_RANGE = torch.arange(K_LEN)[None,:]
Q_RANGE = Q_RANGE.to(device='cuda')
K_RANGE = K_RANGE.to(device='cuda')
Q_RANGE_BLOCKS = torch.split(Q_RANGE, Q_BLOCK_SIZE, dim=0)
K_RANGE_BLOCKS = torch.split(K_RANGE, KV_BLOCK_SIZE, dim=1)
for j in range(Tc):
Kj = K_BLOCKS[j]
Vj = V_BLOCKS[j]
K_RANGE_BLOCKSj = K_RANGE_BLOCKS[j]
dKj_block = torch.zeros_like(dK_BLOCKS[j], requires_grad=True).to(device='cuda')
dVj_block = torch.zeros_like(dV_BLOCKS[j], requires_grad=True).to(device='cuda')
for i in range(Tr):
Qi = Q_BLOCKS[i]
Oi = O_BLOCKS[i]
dOi = dO_BLOCKS[i]
li = l_BLOCKS[i]
mi = m_BLOCKS[i]
Q_RANGE_BLOCKSi = Q_RANGE_BLOCKS[i]
scale = 1 / np.sqrt(Q.shape[-1])
Qi_scaled = Qi * scale
S_ij = torch.einsum('... i d, ... j d -> ... i j', Qi_scaled, Kj)
# Masking
causal_mask = Q_RANGE_BLOCKSi >= K_RANGE_BLOCKSj
S_ij = torch.where(causal_mask > 0, S_ij, NEG_INF)
P_ij = (1/li) * torch.exp(S_ij - mi)
# Masking
P_ij = torch.where(causal_mask > 0, P_ij, 0)
dVj_block = dVj_block + torch.einsum('... r c, ... r d -> ... c d', P_ij, dOi)
dP_ij = torch.einsum('... r d, ... c d -> ... r c', dOi, Vj)
Di = torch.sum(dOi * Oi, dim=-1, keepdims=True)
dS_ij = P_ij * (dP_ij - Di)
dQ_BLOCKS[i] = dQ_BLOCKS[i] + scale * torch.einsum('... r c, ... c d -> ... r d', dS_ij, Kj)
dKj_block = dKj_block + scale * torch.einsum('... r c, ... r d -> ... c d', dS_ij, Qi)
dK_BLOCKS[j] = dKj_block
dV_BLOCKS[j] = dVj_block
dQ = torch.cat(dQ_BLOCKS, dim=2)
dK = torch.cat(dK_BLOCKS, dim=2)
dV = torch.cat(dV_BLOCKS, dim=2)
return dQ, dK, dV
def flash_attention_causal(Q, K, V):
out = flash_attention_causal_forward(Q, K, V)
return out[0]
if __name__ == "__main__":
Q = torch.randn(1, 2, 4096, 1024, requires_grad=True).to(device='cuda')
K = torch.randn(1, 2, 4096, 1024, requires_grad=True).to(device='cuda')
V = torch.randn(1, 2, 4096, 1024, requires_grad=True).to(device='cuda')
for i in range(10):
start1 = time.time_ns()
out1 = flash_attention_causal(Q, K, V)
end1 = time.time_ns()
start2 = time.time_ns()
out2 = normal_attention_causal(Q, K, V)
end2 = time.time_ns()
t1 = (end1 - start1) / 1000000
t2 = (end2 - start2) / 1000000
print(f'{t1}ms, {t2}ms')
print(torch.allclose(out1, out2, atol=1e-5))