Modules/GeneralLayers/PositionalEncoding.py

"""
Taken from ESPNet
"""

import math

import torch


class PositionalEncoding(torch.nn.Module):
    """
    Positional encoding.

    Args:
        d_model (int): Embedding dimension.
        dropout_rate (float): Dropout rate.
        max_len (int): Maximum input length.
        reverse (bool): Whether to reverse the input position.
    """

    def __init__(self, d_model, dropout_rate, max_len=5000, reverse=False):
        """
        Construct an PositionalEncoding object.
        """
        super(PositionalEncoding, self).__init__()
        self.d_model = d_model
        self.reverse = reverse
        self.xscale = math.sqrt(self.d_model)
        self.dropout = torch.nn.Dropout(p=dropout_rate)
        self.pe = None
        self.extend_pe(torch.tensor(0.0, device=d_model.device).expand(1, max_len))

    def extend_pe(self, x):
        """
        Reset the positional encodings.
        """
        if self.pe is not None:
            if self.pe.size(1) >= x.size(1):
                if self.pe.dtype != x.dtype or self.pe.device != x.device:
                    self.pe = self.pe.to(dtype=x.dtype, device=x.device)
                return
        pe = torch.zeros(x.size(1), self.d_model)
        if self.reverse:
            position = torch.arange(x.size(1) - 1, -1, -1.0, dtype=torch.float32).unsqueeze(1)
        else:
            position = torch.arange(0, x.size(1), dtype=torch.float32).unsqueeze(1)
        div_term = torch.exp(torch.arange(0, self.d_model, 2, dtype=torch.float32) * -(math.log(10000.0) / self.d_model))
        pe[:, 0::2] = torch.sin(position * div_term)
        pe[:, 1::2] = torch.cos(position * div_term)
        pe = pe.unsqueeze(0)
        self.pe = pe.to(device=x.device, dtype=x.dtype)

    def forward(self, x):
        """
        Add positional encoding.

        Args:
            x (torch.Tensor): Input tensor (batch, time, `*`).

        Returns:
            torch.Tensor: Encoded tensor (batch, time, `*`).
        """
        self.extend_pe(x)
        x = x * self.xscale + self.pe[:, : x.size(1)]
        return self.dropout(x)


class RelPositionalEncoding(torch.nn.Module):
    """
    Relative positional encoding module (new implementation).
    Details can be found in https://github.com/espnet/espnet/pull/2816.
    See : Appendix B in https://arxiv.org/abs/1901.02860
    Args:
        d_model (int): Embedding dimension.
        dropout_rate (float): Dropout rate.
        max_len (int): Maximum input length.
    """

    def __init__(self, d_model, dropout_rate, max_len=5000):
        """
        Construct an PositionalEncoding object.
        """
        super(RelPositionalEncoding, self).__init__()
        self.d_model = d_model
        self.xscale = math.sqrt(self.d_model)
        self.dropout = torch.nn.Dropout(p=dropout_rate)
        self.pe = None
        self.extend_pe(torch.tensor(0.0).expand(1, max_len))

    def extend_pe(self, x):
        """Reset the positional encodings."""
        if self.pe is not None:
            # self.pe contains both positive and negative parts
            # the length of self.pe is 2 * input_len - 1
            if self.pe.size(1) >= x.size(1) * 2 - 1:
                if self.pe.dtype != x.dtype or self.pe.device != x.device:
                    self.pe = self.pe.to(dtype=x.dtype, device=x.device)
                return
        # Suppose `i` means to the position of query vecotr and `j` means the
        # position of key vector. We use position relative positions when keys
        # are to the left (i>j) and negative relative positions otherwise (i<j).
        pe_positive = torch.zeros(x.size(1), self.d_model, device=x.device)
        pe_negative = torch.zeros(x.size(1), self.d_model, device=x.device)
        position = torch.arange(0, x.size(1), dtype=torch.float32, device=x.device).unsqueeze(1)
        div_term = torch.exp(torch.arange(0, self.d_model, 2, dtype=torch.float32, device=x.device) * -(math.log(10000.0) / self.d_model))
        pe_positive[:, 0::2] = torch.sin(position * div_term)
        pe_positive[:, 1::2] = torch.cos(position * div_term)
        pe_negative[:, 0::2] = torch.sin(-1 * position * div_term)
        pe_negative[:, 1::2] = torch.cos(-1 * position * div_term)

        # Reserve the order of positive indices and concat both positive and
        # negative indices. This is used to support the shifting trick
        # as in https://arxiv.org/abs/1901.02860
        pe_positive = torch.flip(pe_positive, [0]).unsqueeze(0)
        pe_negative = pe_negative[1:].unsqueeze(0)
        pe = torch.cat([pe_positive, pe_negative], dim=1)
        self.pe = pe.to(dtype=x.dtype)

    def forward(self, x):
        """
        Add positional encoding.
        Args:
            x (torch.Tensor): Input tensor (batch, time, `*`).
        Returns:
            torch.Tensor: Encoded tensor (batch, time, `*`).
        """
        self.extend_pe(x)
        x = x * self.xscale
        pos_emb = self.pe[:, self.pe.size(1) // 2 - x.size(1) + 1: self.pe.size(1) // 2 + x.size(1), ]
        return self.dropout(x), self.dropout(pos_emb)


class ScaledPositionalEncoding(PositionalEncoding):
    """
    Scaled positional encoding module.

    See Sec. 3.2  https://arxiv.org/abs/1809.08895

    Args:
        d_model (int): Embedding dimension.
        dropout_rate (float): Dropout rate.
        max_len (int): Maximum input length.

    """

    def __init__(self, d_model, dropout_rate, max_len=5000):
        super().__init__(d_model=d_model, dropout_rate=dropout_rate, max_len=max_len)
        self.alpha = torch.nn.Parameter(torch.tensor(1.0))

    def reset_parameters(self):
        self.alpha.data = torch.tensor(1.0)

    def forward(self, x):
        """
        Add positional encoding.

        Args:
            x (torch.Tensor): Input tensor (batch, time, `*`).

        Returns:
            torch.Tensor: Encoded tensor (batch, time, `*`).

        """
        self.extend_pe(x)
        x = x + self.alpha * self.pe[:, : x.size(1)]
        return self.dropout(x)