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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Copyright 2019 Shigeki Karita
# Apache 2.0 (http://www.apache.org/licenses/LICENSE-2.0)
"""Multi-Head Attention layer definition."""
import math
import numpy
import torch
from torch import nn
class MultiHeadedAttention(nn.Module):
"""Multi-Head Attention layer.
Args:
n_head (int): The number of heads.
n_feat (int): The number of features.
dropout_rate (float): Dropout rate.
"""
def __init__(self, n_head, n_feat, dropout_rate):
"""Construct an MultiHeadedAttention object."""
super(MultiHeadedAttention, self).__init__()
assert n_feat % n_head == 0
# We assume d_v always equals d_k
self.d_k = n_feat // n_head
self.h = n_head
self.linear_q = nn.Linear(n_feat, n_feat)
self.linear_k = nn.Linear(n_feat, n_feat)
self.linear_v = nn.Linear(n_feat, n_feat)
self.linear_out = nn.Linear(n_feat, n_feat)
self.attn = None
self.dropout = nn.Dropout(p=dropout_rate)
def forward_qkv(self, query, key, value):
"""Transform query, key and value.
Args:
query (torch.Tensor): Query tensor (#batch, time1, size).
key (torch.Tensor): Key tensor (#batch, time2, size).
value (torch.Tensor): Value tensor (#batch, time2, size).
Returns:
torch.Tensor: Transformed query tensor (#batch, n_head, time1, d_k).
torch.Tensor: Transformed key tensor (#batch, n_head, time2, d_k).
torch.Tensor: Transformed value tensor (#batch, n_head, time2, d_k).
"""
n_batch = query.size(0)
q = self.linear_q(query).view(n_batch, -1, self.h, self.d_k)
k = self.linear_k(key).view(n_batch, -1, self.h, self.d_k)
v = self.linear_v(value).view(n_batch, -1, self.h, self.d_k)
q = q.transpose(1, 2) # (batch, head, time1, d_k)
k = k.transpose(1, 2) # (batch, head, time2, d_k)
v = v.transpose(1, 2) # (batch, head, time2, d_k)
return q, k, v
def forward_attention(self, value, scores, mask):
"""Compute attention context vector.
Args:
value (torch.Tensor): Transformed value (#batch, n_head, time2, d_k).
scores (torch.Tensor): Attention score (#batch, n_head, time1, time2).
mask (torch.Tensor): Mask (#batch, 1, time2) or (#batch, time1, time2).
Returns:
torch.Tensor: Transformed value (#batch, time1, d_model)
weighted by the attention score (#batch, time1, time2).
"""
n_batch = value.size(0)
if mask is not None:
mask = mask.unsqueeze(1).eq(0) # (batch, 1, *, time2)
min_value = float(
numpy.finfo(torch.tensor(0, dtype=scores.dtype).numpy().dtype).min
)
scores = scores.masked_fill(mask, min_value)
self.attn = torch.softmax(scores, dim=-1).masked_fill(
mask, 0.0
) # (batch, head, time1, time2)
else:
self.attn = torch.softmax(scores, dim=-1) # (batch, head, time1, time2)
p_attn = self.dropout(self.attn)
x = torch.matmul(p_attn, value) # (batch, head, time1, d_k)
x = (
x.transpose(1, 2).contiguous().view(n_batch, -1, self.h * self.d_k)
) # (batch, time1, d_model)
return self.linear_out(x) # (batch, time1, d_model)
def forward(self, query, key, value, mask):
"""Compute scaled dot product attention.
Args:
query (torch.Tensor): Query tensor (#batch, time1, size).
key (torch.Tensor): Key tensor (#batch, time2, size).
value (torch.Tensor): Value tensor (#batch, time2, size).
mask (torch.Tensor): Mask tensor (#batch, 1, time2) or
(#batch, time1, time2).
Returns:
torch.Tensor: Output tensor (#batch, time1, d_model).
"""
q, k, v = self.forward_qkv(query, key, value)
scores = torch.matmul(q, k.transpose(-2, -1)) / math.sqrt(self.d_k)
return self.forward_attention(v, scores, mask)
class RelPositionMultiHeadedAttention(MultiHeadedAttention):
"""Multi-Head Attention layer with relative position encoding.
Paper: https://arxiv.org/abs/1901.02860
Args:
n_head (int): The number of heads.
n_feat (int): The number of features.
dropout_rate (float): Dropout rate.
"""
def __init__(self, n_head, n_feat, dropout_rate):
"""Construct an RelPositionMultiHeadedAttention object."""
super().__init__(n_head, n_feat, dropout_rate)
# linear transformation for positional ecoding
self.linear_pos = nn.Linear(n_feat, n_feat, bias=False)
# these two learnable bias are used in matrix c and matrix d
# as described in https://arxiv.org/abs/1901.02860 Section 3.3
self.pos_bias_u = nn.Parameter(torch.Tensor(self.h, self.d_k))
self.pos_bias_v = nn.Parameter(torch.Tensor(self.h, self.d_k))
torch.nn.init.xavier_uniform_(self.pos_bias_u)
torch.nn.init.xavier_uniform_(self.pos_bias_v)
def rel_shift(self, x, zero_triu=False):
"""Compute relative positinal encoding.
Args:
x (torch.Tensor): Input tensor (batch, time, size).
zero_triu (bool): If true, return the lower triangular part of the matrix.
Returns:
torch.Tensor: Output tensor.
"""
zero_pad = torch.zeros((*x.size()[:3], 1), device=x.device, dtype=x.dtype)
x_padded = torch.cat([zero_pad, x], dim=-1)
x_padded = x_padded.view(*x.size()[:2], x.size(3) + 1, x.size(2))
x = x_padded[:, :, 1:].view_as(x)
if zero_triu:
ones = torch.ones((x.size(2), x.size(3)))
x = x * torch.tril(ones, x.size(3) - x.size(2))[None, None, :, :]
return x
def forward(self, query, key, value, pos_emb, mask):
"""Compute 'Scaled Dot Product Attention' with rel. positional encoding.
Args:
query (torch.Tensor): Query tensor (#batch, time1, size).
key (torch.Tensor): Key tensor (#batch, time2, size).
value (torch.Tensor): Value tensor (#batch, time2, size).
pos_emb (torch.Tensor): Positional embedding tensor (#batch, time2, size).
mask (torch.Tensor): Mask tensor (#batch, 1, time2) or
(#batch, time1, time2).
Returns:
torch.Tensor: Output tensor (#batch, time1, d_model).
"""
q, k, v = self.forward_qkv(query, key, value)
q = q.transpose(1, 2) # (batch, time1, head, d_k)
n_batch_pos = pos_emb.size(0)
p = self.linear_pos(pos_emb).view(n_batch_pos, -1, self.h, self.d_k)
p = p.transpose(1, 2) # (batch, head, time1, d_k)
# (batch, head, time1, d_k)
q_with_bias_u = (q + self.pos_bias_u).transpose(1, 2)
# (batch, head, time1, d_k)
q_with_bias_v = (q + self.pos_bias_v).transpose(1, 2)
# compute attention score
# first compute matrix a and matrix c
# as described in https://arxiv.org/abs/1901.02860 Section 3.3
# (batch, head, time1, time2)
matrix_ac = torch.matmul(q_with_bias_u, k.transpose(-2, -1))
# compute matrix b and matrix d
# (batch, head, time1, time2)
matrix_bd = torch.matmul(q_with_bias_v, p.transpose(-2, -1))
matrix_bd = self.rel_shift(matrix_bd)
scores = (matrix_ac + matrix_bd) / math.sqrt(
self.d_k
) # (batch, head, time1, time2)
return self.forward_attention(v, scores, mask)
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