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import math |
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from typing import Any |
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from einops import rearrange |
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import torch |
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from diffusers.models.attention_processor import Attention |
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EPSILON = 1e-6 |
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class FlashAttentionFunction(torch.autograd.function.Function): |
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@staticmethod |
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@torch.no_grad() |
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def forward(ctx, q, k, v, mask, causal, q_bucket_size, k_bucket_size): |
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"""Algorithm 2 in the paper""" |
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device = q.device |
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dtype = q.dtype |
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max_neg_value = -torch.finfo(q.dtype).max |
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qk_len_diff = max(k.shape[-2] - q.shape[-2], 0) |
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o = torch.zeros_like(q) |
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all_row_sums = torch.zeros((*q.shape[:-1], 1), dtype=dtype, device=device) |
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all_row_maxes = torch.full( |
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(*q.shape[:-1], 1), max_neg_value, dtype=dtype, device=device |
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) |
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scale = q.shape[-1] ** -0.5 |
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if mask is None: |
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mask = (None,) * math.ceil(q.shape[-2] / q_bucket_size) |
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else: |
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mask = rearrange(mask, "b n -> b 1 1 n") |
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mask = mask.split(q_bucket_size, dim=-1) |
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row_splits = zip( |
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q.split(q_bucket_size, dim=-2), |
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o.split(q_bucket_size, dim=-2), |
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mask, |
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all_row_sums.split(q_bucket_size, dim=-2), |
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all_row_maxes.split(q_bucket_size, dim=-2), |
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) |
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for ind, (qc, oc, row_mask, row_sums, row_maxes) in enumerate(row_splits): |
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q_start_index = ind * q_bucket_size - qk_len_diff |
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col_splits = zip( |
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k.split(k_bucket_size, dim=-2), |
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v.split(k_bucket_size, dim=-2), |
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) |
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for k_ind, (kc, vc) in enumerate(col_splits): |
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k_start_index = k_ind * k_bucket_size |
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attn_weights = ( |
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torch.einsum("... i d, ... j d -> ... i j", qc, kc) * scale |
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) |
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if row_mask is not None: |
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attn_weights.masked_fill_(~row_mask, max_neg_value) |
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if causal and q_start_index < (k_start_index + k_bucket_size - 1): |
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causal_mask = torch.ones( |
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(qc.shape[-2], kc.shape[-2]), dtype=torch.bool, device=device |
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).triu(q_start_index - k_start_index + 1) |
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attn_weights.masked_fill_(causal_mask, max_neg_value) |
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block_row_maxes = attn_weights.amax(dim=-1, keepdims=True) |
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attn_weights -= block_row_maxes |
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exp_weights = torch.exp(attn_weights) |
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if row_mask is not None: |
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exp_weights.masked_fill_(~row_mask, 0.0) |
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block_row_sums = exp_weights.sum(dim=-1, keepdims=True).clamp( |
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min=EPSILON |
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) |
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new_row_maxes = torch.maximum(block_row_maxes, row_maxes) |
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exp_values = torch.einsum( |
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"... i j, ... j d -> ... i d", exp_weights, vc |
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) |
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exp_row_max_diff = torch.exp(row_maxes - new_row_maxes) |
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exp_block_row_max_diff = torch.exp(block_row_maxes - new_row_maxes) |
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new_row_sums = ( |
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exp_row_max_diff * row_sums |
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+ exp_block_row_max_diff * block_row_sums |
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) |
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oc.mul_((row_sums / new_row_sums) * exp_row_max_diff).add_( |
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(exp_block_row_max_diff / new_row_sums) * exp_values |
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) |
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row_maxes.copy_(new_row_maxes) |
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row_sums.copy_(new_row_sums) |
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ctx.args = (causal, scale, mask, q_bucket_size, k_bucket_size) |
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ctx.save_for_backward(q, k, v, o, all_row_sums, all_row_maxes) |
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return o |
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@staticmethod |
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@torch.no_grad() |
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def backward(ctx, do): |
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"""Algorithm 4 in the paper""" |
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causal, scale, mask, q_bucket_size, k_bucket_size = ctx.args |
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q, k, v, o, l, m = ctx.saved_tensors |
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device = q.device |
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max_neg_value = -torch.finfo(q.dtype).max |
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qk_len_diff = max(k.shape[-2] - q.shape[-2], 0) |
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dq = torch.zeros_like(q) |
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dk = torch.zeros_like(k) |
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dv = torch.zeros_like(v) |
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row_splits = zip( |
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q.split(q_bucket_size, dim=-2), |
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o.split(q_bucket_size, dim=-2), |
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do.split(q_bucket_size, dim=-2), |
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mask, |
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l.split(q_bucket_size, dim=-2), |
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m.split(q_bucket_size, dim=-2), |
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dq.split(q_bucket_size, dim=-2), |
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) |
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for ind, (qc, oc, doc, row_mask, lc, mc, dqc) in enumerate(row_splits): |
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q_start_index = ind * q_bucket_size - qk_len_diff |
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col_splits = zip( |
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k.split(k_bucket_size, dim=-2), |
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v.split(k_bucket_size, dim=-2), |
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dk.split(k_bucket_size, dim=-2), |
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dv.split(k_bucket_size, dim=-2), |
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) |
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for k_ind, (kc, vc, dkc, dvc) in enumerate(col_splits): |
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k_start_index = k_ind * k_bucket_size |
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attn_weights = ( |
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torch.einsum("... i d, ... j d -> ... i j", qc, kc) * scale |
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) |
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if causal and q_start_index < (k_start_index + k_bucket_size - 1): |
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causal_mask = torch.ones( |
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(qc.shape[-2], kc.shape[-2]), dtype=torch.bool, device=device |
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).triu(q_start_index - k_start_index + 1) |
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attn_weights.masked_fill_(causal_mask, max_neg_value) |
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exp_attn_weights = torch.exp(attn_weights - mc) |
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if row_mask is not None: |
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exp_attn_weights.masked_fill_(~row_mask, 0.0) |
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p = exp_attn_weights / lc |
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dv_chunk = torch.einsum("... i j, ... i d -> ... j d", p, doc) |
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dp = torch.einsum("... i d, ... j d -> ... i j", doc, vc) |
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D = (doc * oc).sum(dim=-1, keepdims=True) |
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ds = p * scale * (dp - D) |
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dq_chunk = torch.einsum("... i j, ... j d -> ... i d", ds, kc) |
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dk_chunk = torch.einsum("... i j, ... i d -> ... j d", ds, qc) |
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dqc.add_(dq_chunk) |
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dkc.add_(dk_chunk) |
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dvc.add_(dv_chunk) |
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return dq, dk, dv, None, None, None, None |
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class FlashAttnProcessor: |
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def __call__( |
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self, |
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attn: Attention, |
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hidden_states, |
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encoder_hidden_states=None, |
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attention_mask=None, |
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) -> Any: |
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q_bucket_size = 512 |
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k_bucket_size = 1024 |
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h = attn.heads |
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q = attn.to_q(hidden_states) |
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encoder_hidden_states = ( |
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encoder_hidden_states |
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if encoder_hidden_states is not None |
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else hidden_states |
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) |
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encoder_hidden_states = encoder_hidden_states.to(hidden_states.dtype) |
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if hasattr(attn, "hypernetwork") and attn.hypernetwork is not None: |
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context_k, context_v = attn.hypernetwork.forward( |
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hidden_states, encoder_hidden_states |
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) |
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context_k = context_k.to(hidden_states.dtype) |
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context_v = context_v.to(hidden_states.dtype) |
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else: |
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context_k = encoder_hidden_states |
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context_v = encoder_hidden_states |
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k = attn.to_k(context_k) |
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v = attn.to_v(context_v) |
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del encoder_hidden_states, hidden_states |
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q, k, v = map(lambda t: rearrange(t, "b n (h d) -> b h n d", h=h), (q, k, v)) |
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out = FlashAttentionFunction.apply( |
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q, k, v, attention_mask, False, q_bucket_size, k_bucket_size |
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) |
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out = rearrange(out, "b h n d -> b n (h d)") |
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out = attn.to_out[0](out) |
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out = attn.to_out[1](out) |
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return out |
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