#

Transformer XL

This is an implementation of Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context in PyTorch.

Transformer has a limited attention span, equal to the length of the sequence trained in parallel. All these positions have a fixed positional encoding. Transformer XL increases this attention span by letting each of the positions pay attention to precalculated past embeddings. For instance if the context length is $l$ , it will keep the embeddings of all layers for previous batch of length $l$ and feed them to current step. If we use fixed-positional encodings these pre-calculated embeddings will have the same positions as the current context. They introduce relative positional encoding, where the positional encodings are introduced at the attention calculation.

Annotated implementation of relative multi-headed attention is in relative_mha.py .

Here's the training code and a notebook for training a transformer XL model on Tiny Shakespeare dataset.

35from typing import List, Optional
36
37import torch
38import torch.nn as nn
39
40from labml_nn.utils import clone_module_list
41from .relative_mha import RelativeMultiHeadAttention
42from ..feed_forward import FeedForward

#

Transformer XL Layer

The transformer XL model comprises of a number of these layers.

45class TransformerXLLayer(nn.Module):

#

d_model is the token embedding size
self_attn is the self attention module
feed_forward is the feed forward module
dropout_prob is the probability of dropping out after self attention and FFN

51    def __init__(self, *,
52                 d_model: int,
53                 self_attn: RelativeMultiHeadAttention,
54                 feed_forward: FeedForward,
55                 dropout_prob: float):

#

62        super().__init__()
63        self.size = d_model
64        self.self_attn = self_attn
65        self.feed_forward = feed_forward
66        self.dropout = nn.Dropout(dropout_prob)
67        self.norm_self_attn = nn.LayerNorm([d_model])
68        self.norm_ff = nn.LayerNorm([d_model])

#

x is a tensor of the token level feature vectors of shape [seq_len, batch_size, d_model]
mem is a tensor of the past token level feature vectors of shape [mem_len, batch_size, d_model]
mask is a matrix of shape [seq_len, mem_len + seq_len, batch_size] or [seq_len, mem_len + seq_len, 1] . mask[i, j] is true if token at i can see token at j .

70    def forward(self, *,
71                x: torch.Tensor,
72                mem: Optional[torch.Tensor],
73                mask: torch.Tensor):

#

Normalize the vectors before doing self attention

81        z = self.norm_self_attn(x)

#

If there is memory

83        if mem is not None:

#

Normalize it

85            mem = self.norm_self_attn(mem)

#

Concatenate with z

87            m_z = torch.cat((mem, z), dim=0)

#

Ignore if there is no memory

89        else:
90            m_z = z

#

Attention

92        self_attn = self.self_attn(query=z, key=m_z, value=m_z, mask=mask)

#

Add the attention results

94        x = x + self.dropout(self_attn)

#

Normalize for feed-forward

97        z = self.norm_ff(x)

#

Pass through the feed-forward network

99        ff = self.feed_forward(z)

#

Add the feed-forward results back

101        x = x + self.dropout(ff)

#

104        return x

#

Transformer XL Model

This consists of multiple transformer XL layers

107class TransformerXL(nn.Module):

#

114    def __init__(self, layer: TransformerXLLayer, n_layers: int):
115        super().__init__()

#

Make copies of the transformer layer

117        self.layers = clone_module_list(layer, n_layers)

#

Final normalization layer

119        self.norm = nn.LayerNorm([layer.size])

#

x is a tensor of the token embeddings vectors of shape [seq_len, batch_size, d_model]
mem is a list of tensors of the past token level feature vectors of shape [mem_len, batch_size, d_model] for each layer
mask is the masking matrix

121    def forward(self, x: torch.Tensor, mem: List[torch.Tensor], mask: torch.Tensor):

#

List to store token level feature vectors, which will become the memories for the next sequential batch.

130        new_mem = []

#

Run through each transformer layer

132        for i, layer in enumerate(self.layers):

#

Add to the list of feature vectors

134            new_mem.append(x.detach())

#

Memory

136            m = mem[i] if mem else None

#

Run through the transformer XL layer

138            x = layer(x=x, mem=m, mask=mask)

#

Finally, normalize the vectors

140        return self.norm(x), new_mem