import math
import torch
from torch import nn
from torch.nn import functional as F
from TTS.tts.layers.generic.normalization import LayerNorm, LayerNorm2
class RelativePositionMultiHeadAttention(nn.Module):
"""Multi-head attention with Relative Positional embedding.
https://arxiv.org/pdf/1809.04281.pdf
It learns positional embeddings for a window of neighbours. For keys and values,
it learns different set of embeddings. Key embeddings are agregated with the attention
scores and value embeddings are aggregated with the output.
Note:
Example with relative attention window size 2
- input = [a, b, c, d, e]
- rel_attn_embeddings = [e(t-2), e(t-1), e(t+1), e(t+2)]
So it learns 4 embedding vectors (in total 8) separately for key and value vectors.
Considering the input c
- e(t-2) corresponds to c -> a
- e(t-2) corresponds to c -> b
- e(t-2) corresponds to c -> d
- e(t-2) corresponds to c -> e
These embeddings are shared among different time steps. So input a, b, d and e also uses
the same embeddings.
Embeddings are ignored when the relative window is out of limit for the first and the last
n items.
Args:
channels (int): input and inner layer channels.
out_channels (int): output channels.
num_heads (int): number of attention heads.
rel_attn_window_size (int, optional): relation attention window size.
If 4, for each time step next and previous 4 time steps are attended.
If default, relative encoding is disabled and it is a regular transformer.
Defaults to None.
heads_share (bool, optional): [description]. Defaults to True.
dropout_p (float, optional): dropout rate. Defaults to 0..
input_length (int, optional): intput length for positional encoding. Defaults to None.
proximal_bias (bool, optional): enable/disable proximal bias as in the paper. Defaults to False.
proximal_init (bool, optional): enable/disable poximal init as in the paper.
Init key and query layer weights the same. Defaults to False.
"""
def __init__(
self,
channels,
out_channels,
num_heads,
rel_attn_window_size=None,
heads_share=True,
dropout_p=0.0,
input_length=None,
proximal_bias=False,
proximal_init=False,
):
super().__init__()
assert channels % num_heads == 0, " [!] channels should be divisible by num_heads."
# class attributes
self.channels = channels
self.out_channels = out_channels
self.num_heads = num_heads
self.rel_attn_window_size = rel_attn_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
# query, key, value layers
self.k_channels = channels // num_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)
# output layers
self.conv_o = nn.Conv1d(channels, out_channels, 1)
self.dropout = nn.Dropout(dropout_p)
# relative positional encoding layers
if rel_attn_window_size is not None:
n_heads_rel = 1 if heads_share else num_heads
rel_stddev = self.k_channels**-0.5
emb_rel_k = nn.Parameter(
torch.randn(n_heads_rel, rel_attn_window_size * 2 + 1, self.k_channels) * rel_stddev
)
emb_rel_v = nn.Parameter(
torch.randn(n_heads_rel, rel_attn_window_size * 2 + 1, self.k_channels) * rel_stddev
)
self.register_parameter("emb_rel_k", emb_rel_k)
self.register_parameter("emb_rel_v", emb_rel_v)
# init layers
nn.init.xavier_uniform_(self.conv_q.weight)
nn.init.xavier_uniform_(self.conv_k.weight)
# proximal bias
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):
"""
Shapes:
- x: :math:`[B, C, T]`
- c: :math:`[B, C, T]`
- attn_mask: :math:`[B, 1, T, T]`
"""
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.num_heads, self.k_channels, t_t).transpose(2, 3)
key = key.view(b, self.num_heads, self.k_channels, t_s).transpose(2, 3)
value = value.view(b, self.num_heads, self.k_channels, t_s).transpose(2, 3)
# compute raw attention scores
scores = torch.matmul(query, key.transpose(-2, -1)) / math.sqrt(self.k_channels)
# relative positional encoding for scores
if self.rel_attn_window_size is not None:
assert t_s == t_t, "Relative attention is only available for self-attention."
# get relative key embeddings
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
# proximan bias
if self.proximal_bias:
assert t_s == t_t, "Proximal bias is only available for self-attention."
scores = scores + self._attn_proximity_bias(t_s).to(device=scores.device, dtype=scores.dtype)
# attention score masking
if mask is not None:
# add small value to prevent oor error.
scores = scores.masked_fill(mask == 0, -1e4)
if self.input_length is not None:
block_mask = torch.ones_like(scores).triu(-1 * self.input_length).tril(self.input_length)
scores = scores * block_mask + -1e4 * (1 - block_mask)
# attention score normalization
p_attn = F.softmax(scores, dim=-1) # [b, n_h, t_t, t_s]
# apply dropout to attention weights
p_attn = self.dropout(p_attn)
# compute output
output = torch.matmul(p_attn, value)
# relative positional encoding for values
if self.rel_attn_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
@staticmethod
def _matmul_with_relative_values(p_attn, re):
"""
Args:
p_attn (Tensor): attention weights.
re (Tensor): relative value embedding vector. (a_(i,j)^V)
Shapes:
-p_attn: :math:`[B, H, T, V]`
-re: :math:`[H or 1, V, D]`
-logits: :math:`[B, H, T, D]`
"""
logits = torch.matmul(p_attn, re.unsqueeze(0))
return logits
@staticmethod
def _matmul_with_relative_keys(query, re):
"""
Args:
query (Tensor): batch of query vectors. (x*W^Q)
re (Tensor): relative key embedding vector. (a_(i,j)^K)
Shapes:
- query: :math:`[B, H, T, D]`
- re: :math:`[H or 1, V, D]`
- logits: :math:`[B, H, T, V]`
"""
# logits = torch.einsum('bhld, kmd -> bhlm', [query, re.to(query.dtype)])
logits = torch.matmul(query, re.unsqueeze(0).transpose(-2, -1))
return logits
def _get_relative_embeddings(self, relative_embeddings, length):
"""Convert embedding vestors to a tensor of embeddings"""
# Pad first before slice to avoid using cond ops.
pad_length = max(length - (self.rel_attn_window_size + 1), 0)
slice_start_position = max((self.rel_attn_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, [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
@staticmethod
def _relative_position_to_absolute_position(x):
"""Converts tensor from relative to absolute indexing for local attention.
Shapes:
x: :math:`[B, C, T, 2 * T - 1]`
Returns:
A Tensor of shape :math:`[B, C, T, T]`
"""
batch, heads, length, _ = x.size()
# Pad to shift from relative to absolute indexing.
x = F.pad(x, [0, 1, 0, 0, 0, 0, 0, 0])
# Pad 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, [0, length - 1, 0, 0, 0, 0])
# 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
@staticmethod
def _absolute_position_to_relative_position(x):
"""
Shapes:
- x: :math:`[B, C, T, T]`
- ret: :math:`[B, C, T, 2*T-1]`
"""
batch, heads, length, _ = x.size()
# padd along column
x = F.pad(x, [0, length - 1, 0, 0, 0, 0, 0, 0])
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, [length, 0, 0, 0, 0, 0])
x_final = x_flat.view([batch, heads, length, 2 * length])[:, :, :, 1:]
return x_final
@staticmethod
def _attn_proximity_bias(length):
"""Produce an attention mask that discourages distant
attention values.
Args:
length (int): an integer scalar.
Returns:
a Tensor with shape :math:`[1, 1, T, T]`
"""
# L
r = torch.arange(length, dtype=torch.float32)
# L x L
diff = torch.unsqueeze(r, 0) - torch.unsqueeze(r, 1)
# scale mask values
diff = -torch.log1p(torch.abs(diff))
# 1 x 1 x L x L
return diff.unsqueeze(0).unsqueeze(0)
class FeedForwardNetwork(nn.Module):
"""Feed Forward Inner layers for Transformer.
Args:
in_channels (int): input tensor channels.
out_channels (int): output tensor channels.
hidden_channels (int): inner layers hidden channels.
kernel_size (int): conv1d filter kernel size.
dropout_p (float, optional): dropout rate. Defaults to 0.
"""
def __init__(self, in_channels, out_channels, hidden_channels, kernel_size, dropout_p=0.0, causal=False):
super().__init__()
self.in_channels = in_channels
self.out_channels = out_channels
self.hidden_channels = hidden_channels
self.kernel_size = kernel_size
self.dropout_p = dropout_p
if causal:
self.padding = self._causal_padding
else:
self.padding = self._same_padding
self.conv_1 = nn.Conv1d(in_channels, hidden_channels, kernel_size)
self.conv_2 = nn.Conv1d(hidden_channels, out_channels, kernel_size)
self.dropout = nn.Dropout(dropout_p)
def forward(self, x, x_mask):
x = self.conv_1(self.padding(x * x_mask))
x = torch.relu(x)
x = self.dropout(x)
x = self.conv_2(self.padding(x * x_mask))
return x * x_mask
def _causal_padding(self, x):
if self.kernel_size == 1:
return x
pad_l = self.kernel_size - 1
pad_r = 0
padding = [[0, 0], [0, 0], [pad_l, pad_r]]
x = F.pad(x, self._pad_shape(padding))
return x
def _same_padding(self, x):
if self.kernel_size == 1:
return x
pad_l = (self.kernel_size - 1) // 2
pad_r = self.kernel_size // 2
padding = [[0, 0], [0, 0], [pad_l, pad_r]]
x = F.pad(x, self._pad_shape(padding))
return x
@staticmethod
def _pad_shape(padding):
l = padding[::-1]
pad_shape = [item for sublist in l for item in sublist]
return pad_shape
class RelativePositionTransformer(nn.Module):
"""Transformer with Relative Potional Encoding.
https://arxiv.org/abs/1803.02155
Args:
in_channels (int): number of channels of the input tensor.
out_chanels (int): number of channels of the output tensor.
hidden_channels (int): model hidden channels.
hidden_channels_ffn (int): hidden channels of FeedForwardNetwork.
num_heads (int): number of attention heads.
num_layers (int): number of transformer layers.
kernel_size (int, optional): kernel size of feed-forward inner layers. Defaults to 1.
dropout_p (float, optional): dropout rate for self-attention and feed-forward inner layers_per_stack. Defaults to 0.
rel_attn_window_size (int, optional): relation attention window size.
If 4, for each time step next and previous 4 time steps are attended.
If default, relative encoding is disabled and it is a regular transformer.
Defaults to None.
input_length (int, optional): input lenght to limit position encoding. Defaults to None.
layer_norm_type (str, optional): type "1" uses torch tensor operations and type "2" uses torch layer_norm
primitive. Use type "2", type "1: is for backward compat. Defaults to "1".
"""
def __init__(
self,
in_channels: int,
out_channels: int,
hidden_channels: int,
hidden_channels_ffn: int,
num_heads: int,
num_layers: int,
kernel_size=1,
dropout_p=0.0,
rel_attn_window_size: int = None,
input_length: int = None,
layer_norm_type: str = "1",
):
super().__init__()
self.hidden_channels = hidden_channels
self.hidden_channels_ffn = hidden_channels_ffn
self.num_heads = num_heads
self.num_layers = num_layers
self.kernel_size = kernel_size
self.dropout_p = dropout_p
self.rel_attn_window_size = rel_attn_window_size
self.dropout = nn.Dropout(dropout_p)
self.attn_layers = nn.ModuleList()
self.norm_layers_1 = nn.ModuleList()
self.ffn_layers = nn.ModuleList()
self.norm_layers_2 = nn.ModuleList()
for idx in range(self.num_layers):
self.attn_layers.append(
RelativePositionMultiHeadAttention(
hidden_channels if idx != 0 else in_channels,
hidden_channels,
num_heads,
rel_attn_window_size=rel_attn_window_size,
dropout_p=dropout_p,
input_length=input_length,
)
)
if layer_norm_type == "1":
self.norm_layers_1.append(LayerNorm(hidden_channels))
elif layer_norm_type == "2":
self.norm_layers_1.append(LayerNorm2(hidden_channels))
else:
raise ValueError(" [!] Unknown layer norm type")
if hidden_channels != out_channels and (idx + 1) == self.num_layers:
self.proj = nn.Conv1d(hidden_channels, out_channels, 1)
self.ffn_layers.append(
FeedForwardNetwork(
hidden_channels,
hidden_channels if (idx + 1) != self.num_layers else out_channels,
hidden_channels_ffn,
kernel_size,
dropout_p=dropout_p,
)
)
if layer_norm_type == "1":
self.norm_layers_2.append(LayerNorm(hidden_channels if (idx + 1) != self.num_layers else out_channels))
elif layer_norm_type == "2":
self.norm_layers_2.append(LayerNorm2(hidden_channels if (idx + 1) != self.num_layers else out_channels))
else:
raise ValueError(" [!] Unknown layer norm type")
def forward(self, x, x_mask):
"""
Shapes:
- x: :math:`[B, C, T]`
- x_mask: :math:`[B, 1, T]`
"""
attn_mask = x_mask.unsqueeze(2) * x_mask.unsqueeze(-1)
for i in range(self.num_layers):
x = x * x_mask
y = self.attn_layers[i](x, x, attn_mask)
y = self.dropout(y)
x = self.norm_layers_1[i](x + y)
y = self.ffn_layers[i](x, x_mask)
y = self.dropout(y)
if (i + 1) == self.num_layers and hasattr(self, "proj"):
x = self.proj(x)
x = self.norm_layers_2[i](x + y)
x = x * x_mask
return x