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