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flash attention v1 v2 in numpy
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import numpy as np | |
N_inp = 64 | |
N_out = 64 | |
d = 128 | |
Q = np.random.randn(N_out, d) | |
K = np.random.randn(N_inp, d) | |
V = np.random.randn(N_inp, d) | |
O = np.random.randn(N_out, d) | |
Bc = 16 | |
Br = 16 | |
Tc = (N_inp + Bc - 1) // Bc | |
Tr = (N_out + Br - 1) // Br | |
scale_factor = 1 / np.sqrt(Q.shape[-1]) | |
L = np.zeros((N_out, 1)) | |
M = np.full((N_out, 1), -np.inf) | |
for j in range(Tc): | |
Kj = K[j * Bc: (j + 1) * Bc] | |
Vj = V[j * Bc: (j + 1) * Bc] | |
for i in range(Tr): | |
Oi = O[i * Br: (i + 1) * Br] | |
li = L[i * Br: (i + 1) * Br] | |
mi = M[i * Br: (i + 1) * Br] | |
Qi = Q[i * Br: (i + 1) * Br] | |
Sij = scale_factor * (Qi @ Kj.T) | |
mij = np.max(Sij, axis=1, keepdims=True) | |
Pij = np.exp(Sij - mij) | |
lij = np.sum(Pij, axis=1, keepdims=True) | |
mi_new = np.maximum(mi, mij) | |
li_new = np.exp(mi - mi_new) * li + np.exp(mij - mi_new) * lij | |
Oi = (1.0 / li_new) * (li * np.exp(mi - mi_new) * Oi + np.exp(mij - mi_new) * (Pij @ Vj)) | |
O[i * Br: (i + 1) * Br] = Oi | |
L[i * Br: (i + 1) * Br] = li_new | |
M[i * Br: (i + 1) * Br] = mi_new | |
S_ = scale_factor * Q @ K.T | |
P_ = np.exp(S_ - np.max(S_, axis=1, keepdims=True)) | |
O_ = (P_ / np.sum(P_, axis=1, keepdims=True)) @ V | |
assert(np.allclose(O, O_)) |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
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import numpy as np | |
N_inp = 64 | |
N_out = 64 | |
d = 128 | |
Q = np.random.randn(N_out, d) | |
K = np.random.randn(N_inp, d) | |
V = np.random.randn(N_inp, d) | |
O = np.random.randn(N_out, d) | |
L = np.zeros((N_out, 1)) | |
Bc = 16 | |
Br = 16 | |
Tc = (N_inp + Bc - 1) // Bc | |
Tr = (N_out + Br - 1) // Br | |
scale_factor = 1 / np.sqrt(Q.shape[-1]) | |
for i in range(Tr): | |
Qi = Q[i * Br: (i + 1) * Br] | |
Oi = np.zeros((Br, d)) | |
li = np.zeros((Br, 1)) | |
mi = np.full((Br, 1), -np.inf) | |
last_mi = mi | |
for j in range(Tc): | |
Kj = K[j * Bc: (j + 1) * Bc] | |
Vj = V[j * Bc: (j + 1) * Bc] | |
Si = scale_factor * (Qi @ Kj.T) | |
mi = np.maximum(mi, np.max(Si, axis=1, keepdims=True)) | |
Pi = np.exp(Si - mi) | |
li = np.exp(last_mi - mi) * li + np.sum(Pi, axis=1, keepdims=True) | |
Oi = np.exp(last_mi - mi) * Oi + Pi @ Vj | |
last_mi = mi | |
Oi = Oi / li | |
O[i * Br: (i + 1) * Br] = Oi | |
L[i * Br: (i + 1) * Br] = li | |
S_ = scale_factor * Q @ K.T | |
P_ = np.exp(S_ - np.max(S_, axis=1, keepdims=True)) | |
O_ = (P_ / np.sum(P_, axis=1, keepdims=True)) @ V | |
assert(np.allclose(O, O_)) |
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