File size: 7,697 Bytes
fe6327d |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 |
import math
from typing import Any
from einops import rearrange
import torch
from diffusers.models.attention_processor import Attention
# flash attention forwards and backwards
# https://arxiv.org/abs/2205.14135
EPSILON = 1e-6
class FlashAttentionFunction(torch.autograd.function.Function):
@staticmethod
@torch.no_grad()
def forward(ctx, q, k, v, mask, causal, q_bucket_size, k_bucket_size):
"""Algorithm 2 in the paper"""
device = q.device
dtype = q.dtype
max_neg_value = -torch.finfo(q.dtype).max
qk_len_diff = max(k.shape[-2] - q.shape[-2], 0)
o = torch.zeros_like(q)
all_row_sums = torch.zeros((*q.shape[:-1], 1), dtype=dtype, device=device)
all_row_maxes = torch.full(
(*q.shape[:-1], 1), max_neg_value, dtype=dtype, device=device
)
scale = q.shape[-1] ** -0.5
if mask is None:
mask = (None,) * math.ceil(q.shape[-2] / q_bucket_size)
else:
mask = rearrange(mask, "b n -> b 1 1 n")
mask = mask.split(q_bucket_size, dim=-1)
row_splits = zip(
q.split(q_bucket_size, dim=-2),
o.split(q_bucket_size, dim=-2),
mask,
all_row_sums.split(q_bucket_size, dim=-2),
all_row_maxes.split(q_bucket_size, dim=-2),
)
for ind, (qc, oc, row_mask, row_sums, row_maxes) in enumerate(row_splits):
q_start_index = ind * q_bucket_size - qk_len_diff
col_splits = zip(
k.split(k_bucket_size, dim=-2),
v.split(k_bucket_size, dim=-2),
)
for k_ind, (kc, vc) in enumerate(col_splits):
k_start_index = k_ind * k_bucket_size
attn_weights = (
torch.einsum("... i d, ... j d -> ... i j", qc, kc) * scale
)
if row_mask is not None:
attn_weights.masked_fill_(~row_mask, max_neg_value)
if causal and q_start_index < (k_start_index + k_bucket_size - 1):
causal_mask = torch.ones(
(qc.shape[-2], kc.shape[-2]), dtype=torch.bool, device=device
).triu(q_start_index - k_start_index + 1)
attn_weights.masked_fill_(causal_mask, max_neg_value)
block_row_maxes = attn_weights.amax(dim=-1, keepdims=True)
attn_weights -= block_row_maxes
exp_weights = torch.exp(attn_weights)
if row_mask is not None:
exp_weights.masked_fill_(~row_mask, 0.0)
block_row_sums = exp_weights.sum(dim=-1, keepdims=True).clamp(
min=EPSILON
)
new_row_maxes = torch.maximum(block_row_maxes, row_maxes)
exp_values = torch.einsum(
"... i j, ... j d -> ... i d", exp_weights, vc
)
exp_row_max_diff = torch.exp(row_maxes - new_row_maxes)
exp_block_row_max_diff = torch.exp(block_row_maxes - new_row_maxes)
new_row_sums = (
exp_row_max_diff * row_sums
+ exp_block_row_max_diff * block_row_sums
)
oc.mul_((row_sums / new_row_sums) * exp_row_max_diff).add_(
(exp_block_row_max_diff / new_row_sums) * exp_values
)
row_maxes.copy_(new_row_maxes)
row_sums.copy_(new_row_sums)
ctx.args = (causal, scale, mask, q_bucket_size, k_bucket_size)
ctx.save_for_backward(q, k, v, o, all_row_sums, all_row_maxes)
return o
@staticmethod
@torch.no_grad()
def backward(ctx, do):
"""Algorithm 4 in the paper"""
causal, scale, mask, q_bucket_size, k_bucket_size = ctx.args
q, k, v, o, l, m = ctx.saved_tensors
device = q.device
max_neg_value = -torch.finfo(q.dtype).max
qk_len_diff = max(k.shape[-2] - q.shape[-2], 0)
dq = torch.zeros_like(q)
dk = torch.zeros_like(k)
dv = torch.zeros_like(v)
row_splits = zip(
q.split(q_bucket_size, dim=-2),
o.split(q_bucket_size, dim=-2),
do.split(q_bucket_size, dim=-2),
mask,
l.split(q_bucket_size, dim=-2),
m.split(q_bucket_size, dim=-2),
dq.split(q_bucket_size, dim=-2),
)
for ind, (qc, oc, doc, row_mask, lc, mc, dqc) in enumerate(row_splits):
q_start_index = ind * q_bucket_size - qk_len_diff
col_splits = zip(
k.split(k_bucket_size, dim=-2),
v.split(k_bucket_size, dim=-2),
dk.split(k_bucket_size, dim=-2),
dv.split(k_bucket_size, dim=-2),
)
for k_ind, (kc, vc, dkc, dvc) in enumerate(col_splits):
k_start_index = k_ind * k_bucket_size
attn_weights = (
torch.einsum("... i d, ... j d -> ... i j", qc, kc) * scale
)
if causal and q_start_index < (k_start_index + k_bucket_size - 1):
causal_mask = torch.ones(
(qc.shape[-2], kc.shape[-2]), dtype=torch.bool, device=device
).triu(q_start_index - k_start_index + 1)
attn_weights.masked_fill_(causal_mask, max_neg_value)
exp_attn_weights = torch.exp(attn_weights - mc)
if row_mask is not None:
exp_attn_weights.masked_fill_(~row_mask, 0.0)
p = exp_attn_weights / lc
dv_chunk = torch.einsum("... i j, ... i d -> ... j d", p, doc)
dp = torch.einsum("... i d, ... j d -> ... i j", doc, vc)
D = (doc * oc).sum(dim=-1, keepdims=True)
ds = p * scale * (dp - D)
dq_chunk = torch.einsum("... i j, ... j d -> ... i d", ds, kc)
dk_chunk = torch.einsum("... i j, ... i d -> ... j d", ds, qc)
dqc.add_(dq_chunk)
dkc.add_(dk_chunk)
dvc.add_(dv_chunk)
return dq, dk, dv, None, None, None, None
class FlashAttnProcessor:
def __call__(
self,
attn: Attention,
hidden_states,
encoder_hidden_states=None,
attention_mask=None,
) -> Any:
q_bucket_size = 512
k_bucket_size = 1024
h = attn.heads
q = attn.to_q(hidden_states)
encoder_hidden_states = (
encoder_hidden_states
if encoder_hidden_states is not None
else hidden_states
)
encoder_hidden_states = encoder_hidden_states.to(hidden_states.dtype)
if hasattr(attn, "hypernetwork") and attn.hypernetwork is not None:
context_k, context_v = attn.hypernetwork.forward(
hidden_states, encoder_hidden_states
)
context_k = context_k.to(hidden_states.dtype)
context_v = context_v.to(hidden_states.dtype)
else:
context_k = encoder_hidden_states
context_v = encoder_hidden_states
k = attn.to_k(context_k)
v = attn.to_v(context_v)
del encoder_hidden_states, hidden_states
q, k, v = map(lambda t: rearrange(t, "b n (h d) -> b h n d", h=h), (q, k, v))
out = FlashAttentionFunction.apply(
q, k, v, attention_mask, False, q_bucket_size, k_bucket_size
)
out = rearrange(out, "b h n d -> b n (h d)")
out = attn.to_out[0](out)
out = attn.to_out[1](out)
return out
|