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 LayerNorm(nn.Module): def __init__(self, channels, eps=1e-4): """Layer norm for the 2nd dimension of the input. Args: channels (int): number of channels (2nd dimension) of the input. eps (float): to prevent 0 division Shapes: - input: (B, C, T) - output: (B, C, T) """ super().__init__() self.channels = channels self.eps = eps self.gamma = nn.Parameter(torch.ones(1, channels, 1) * 0.1) self.beta = nn.Parameter(torch.zeros(1, channels, 1)) def forward(self, x): mean = torch.mean(x, 1, keepdim=True) variance = torch.mean((x - mean) ** 2, 1, keepdim=True) x = (x - mean) * torch.rsqrt(variance + self.eps) x = x * self.gamma + self.beta return x class LayerNorm2(nn.Module): """Layer norm for the 2nd dimension of the input using torch primitive. Args: channels (int): number of channels (2nd dimension) of the input. eps (float): to prevent 0 division Shapes: - input: (B, C, T) - output: (B, C, T) """ def __init__(self, channels, eps=1e-5): super().__init__() self.channels = channels self.eps = eps self.gamma = nn.Parameter(torch.ones(channels)) self.beta = nn.Parameter(torch.zeros(channels)) def forward(self, x): x = x.transpose(1, -1) x = torch.nn.functional.layer_norm(x, (self.channels,), self.gamma, self.beta, self.eps) return x.transpose(1, -1) 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.out_channels = out_channels 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) if self.out_channels!=1 or i!=(self.num_layers-1): x = self.norm_layers_2[i](x + y) x = x * x_mask return x