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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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