import copy import math import numpy as np import torch from torch import nn from torch.nn import functional as F def convert_pad_shape(pad_shape): l = pad_shape[::-1] pad_shape = [item for sublist in l for item in sublist] return pad_shape class MultiHeadAttention(nn.Module): def __init__(self, channels, out_channels, n_heads, window_size=None, heads_share=True, dropout_p=0., input_length=None, proximal_bias=False, proximal_init=False): super().__init__() assert channels % n_heads == 0 self.channels = channels self.out_channels = out_channels self.n_heads = n_heads self.window_size = window_size self.heads_share = heads_share self.input_length = input_length self.proximal_bias = proximal_bias self.dropout_p = dropout_p self.attn = None self.k_channels = channels // n_heads self.conv_q = nn.Conv1d(channels, channels, 1) self.conv_k = nn.Conv1d(channels, channels, 1) self.conv_v = nn.Conv1d(channels, channels, 1) if window_size is not None: n_heads_rel = 1 if heads_share else n_heads rel_stddev = self.k_channels**-0.5 self.emb_rel_k = nn.Parameter( torch.randn(n_heads_rel, window_size * 2 + 1, self.k_channels) * rel_stddev) self.emb_rel_v = nn.Parameter( torch.randn(n_heads_rel, window_size * 2 + 1, self.k_channels) * rel_stddev) self.conv_o = nn.Conv1d(channels, out_channels, 1) self.drop = nn.Dropout(dropout_p) nn.init.xavier_uniform_(self.conv_q.weight) nn.init.xavier_uniform_(self.conv_k.weight) if proximal_init: self.conv_k.weight.data.copy_(self.conv_q.weight.data) self.conv_k.bias.data.copy_(self.conv_q.bias.data) nn.init.xavier_uniform_(self.conv_v.weight) def forward(self, x, c, attn_mask=None): q = self.conv_q(x) k = self.conv_k(c) v = self.conv_v(c) x, self.attn = self.attention(q, k, v, mask=attn_mask) x = self.conv_o(x) return x def attention(self, query, key, value, mask=None): # reshape [b, d, t] -> [b, n_h, t, d_k] b, d, t_s, t_t = (*key.size(), query.size(2)) query = query.view(b, self.n_heads, self.k_channels, t_t).transpose(2, 3) key = key.view(b, self.n_heads, self.k_channels, t_s).transpose(2, 3) value = value.view(b, self.n_heads, self.k_channels, t_s).transpose(2, 3) scores = torch.matmul(query, key.transpose(-2, -1)) / math.sqrt( self.k_channels) if self.window_size is not None: assert t_s == t_t, "Relative attention is only available for self-attention." key_relative_embeddings = self._get_relative_embeddings( self.emb_rel_k, t_s) rel_logits = self._matmul_with_relative_keys( query, key_relative_embeddings) rel_logits = self._relative_position_to_absolute_position( rel_logits) scores_local = rel_logits / math.sqrt(self.k_channels) scores = scores + scores_local if self.proximal_bias: assert t_s == t_t, "Proximal bias is only available for self-attention." scores = scores + self._attention_bias_proximal(t_s).to( device=scores.device, dtype=scores.dtype) if mask is not None: scores = scores.masked_fill(mask == 0, -1e4) if self.input_length is not None: block_mask = torch.ones_like(scores).triu( -self.input_length).tril(self.input_length) scores = scores * block_mask + -1e4 * (1 - block_mask) p_attn = F.softmax(scores, dim=-1) # [b, n_h, t_t, t_s] p_attn = self.drop(p_attn) output = torch.matmul(p_attn, value) if self.window_size is not None: relative_weights = self._absolute_position_to_relative_position( p_attn) value_relative_embeddings = self._get_relative_embeddings( self.emb_rel_v, t_s) output = output + self._matmul_with_relative_values( relative_weights, value_relative_embeddings) output = output.transpose(2, 3).contiguous().view( b, d, t_t) # [b, n_h, t_t, d_k] -> [b, d, t_t] return output, p_attn def _matmul_with_relative_values(self, x, y): """ x: [b, h, l, m] y: [h or 1, m, d] ret: [b, h, l, d] """ ret = torch.matmul(x, y.unsqueeze(0)) return ret def _matmul_with_relative_keys(self, x, y): """ x: [b, h, l, d] y: [h or 1, m, d] ret: [b, h, l, m] """ ret = torch.matmul(x, y.unsqueeze(0).transpose(-2, -1)) return ret def _get_relative_embeddings(self, relative_embeddings, length): max_relative_position = 2 * self.window_size + 1 # Pad first before slice to avoid using cond ops. pad_length = max(length - (self.window_size + 1), 0) slice_start_position = max((self.window_size + 1) - length, 0) slice_end_position = slice_start_position + 2 * length - 1 if pad_length > 0: padded_relative_embeddings = F.pad( relative_embeddings, convert_pad_shape([[0, 0], [pad_length, pad_length], [0, 0]])) else: padded_relative_embeddings = relative_embeddings used_relative_embeddings = padded_relative_embeddings[:, slice_start_position: slice_end_position] return used_relative_embeddings def _relative_position_to_absolute_position(self, x): """ x: [b, h, l, 2*l-1] ret: [b, h, l, l] """ batch, heads, length, _ = x.size() # Concat columns of pad to shift from relative to absolute indexing. x = F.pad(x, convert_pad_shape([[0, 0], [0, 0], [0, 0], [0, 1]])) # Concat extra elements so to add up to shape (len+1, 2*len-1). x_flat = x.view([batch, heads, length * 2 * length]) x_flat = F.pad( x_flat, convert_pad_shape([[0, 0], [0, 0], [0, length - 1]])) # Reshape and slice out the padded elements. x_final = x_flat.view([batch, heads, length + 1, 2 * length - 1])[:, :, :length, length - 1:] return x_final def _absolute_position_to_relative_position(self, x): """ x: [b, h, l, l] ret: [b, h, l, 2*l-1] """ batch, heads, length, _ = x.size() # padd along column x = F.pad( x, convert_pad_shape([[0, 0], [0, 0], [0, 0], [0, length - 1]])) x_flat = x.view([batch, heads, length**2 + length * (length - 1)]) # add 0's in the beginning that will skew the elements after reshape x_flat = F.pad( x_flat, convert_pad_shape([[0, 0], [0, 0], [length, 0]])) x_final = x_flat.view([batch, heads, length, 2 * length])[:, :, :, 1:] return x_final def _attention_bias_proximal(self, length): """Bias for self-attention to encourage attention to close positions. Args: length: an integer scalar. Returns: a Tensor with shape [1, 1, length, length] """ r = torch.arange(length, dtype=torch.float32) diff = torch.unsqueeze(r, 0) - torch.unsqueeze(r, 1) return torch.unsqueeze( torch.unsqueeze(-torch.log1p(torch.abs(diff)), 0), 0)