11.7. The Transformer Architecture¶ Open the notebook in SageMaker Studio Lab
We have compared CNNs, RNNs, and self-attention in Section 11.6.2. Notably, self-attention enjoys both parallel computation and the shortest maximum path length. Therefore, it is appealing to design deep architectures by using self-attention. Unlike earlier self-attention models that still rely on RNNs for input representations (Cheng et al., 2016, Lin et al., 2017, Paulus et al., 2017), the Transformer model is solely based on attention mechanisms without any convolutional or recurrent layer (Vaswani et al., 2017). Though originally proposed for sequence-to-sequence learning on text data, Transformers have been pervasive in a wide range of modern deep learning applications, such as in areas to do with language, vision, speech, and reinforcement learning.
import math
import pandas as pd
import torch
from torch import nn
from d2l import torch as d2l
import math
import pandas as pd
from mxnet import autograd, init, np, npx
from mxnet.gluon import nn
from d2l import mxnet as d2l
npx.set_np()
import math
import jax
import pandas as pd
from flax import linen as nn
from jax import numpy as jnp
from d2l import jax as d2l
import numpy as np
import pandas as pd
import tensorflow as tf
from d2l import tensorflow as d2l
11.7.1. Model¶
As an instance of the encoder–decoder architecture, the overall architecture of the Transformer is presented in Fig. 11.7.1. As we can see, the Transformer is composed of an encoder and a decoder. In contrast to Bahdanau attention for sequence-to-sequence learning in Fig. 11.4.2, the input (source) and output (target) sequence embeddings are added with positional encoding before being fed into the encoder and the decoder that stack modules based on self-attention.
Fig. 11.7.1 The Transformer architecture.¶
Now we provide an overview of the Transformer architecture in Fig. 11.7.1. At a high level, the Transformer encoder is a stack of multiple identical layers, where each layer has two sublayers (either is denoted as \(\textrm{sublayer}\)). The first is a multi-head self-attention pooling and the second is a positionwise feed-forward network. Specifically, in the encoder self-attention, queries, keys, and values are all from the outputs of the previous encoder layer. Inspired by the ResNet design of Section 8.6, a residual connection is employed around both sublayers. In the Transformer, for any input \(\mathbf{x} \in \mathbb{R}^d\) at any position of the sequence, we require that \(\textrm{sublayer}(\mathbf{x}) \in \mathbb{R}^d\) so that the residual connection \(\mathbf{x} + \textrm{sublayer}(\mathbf{x}) \in \mathbb{R}^d\) is feasible. This addition from the residual connection is immediately followed by layer normalization (Ba et al., 2016). As a result, the Transformer encoder outputs a \(d\)-dimensional vector representation for each position of the input sequence.
The Transformer decoder is also a stack of multiple identical layers with residual connections and layer normalizations. As well as the two sublayers described in the encoder, the decoder inserts a third sublayer, known as the encoder–decoder attention, between these two. In the encoder–decoder attention, queries are from the outputs of the decoder’s self-attention sublayer, and the keys and values are from the Transformer encoder outputs. In the decoder self-attention, queries, keys, and values are all from the outputs of the previous decoder layer. However, each position in the decoder is allowed only to attend to all positions in the decoder up to that position. This masked attention preserves the autoregressive property, ensuring that the prediction only depends on those output tokens that have been generated.
We have already described and implemented multi-head attention based on scaled dot products in Section 11.5 and positional encoding in Section 11.6.3. In the following, we will implement the rest of the Transformer model.
11.7.2. Positionwise Feed-Forward Networks¶
The positionwise feed-forward network transforms the representation at
all the sequence positions using the same MLP. This is why we call it
positionwise. In the implementation below, the input X with shape
(batch size, number of time steps or sequence length in tokens, number
of hidden units or feature dimension) will be transformed by a two-layer
MLP into an output tensor of shape (batch size, number of time steps,
ffn_num_outputs).
class PositionWiseFFN(nn.Module): #@save
"""The positionwise feed-forward network."""
def __init__(self, ffn_num_hiddens, ffn_num_outputs):
super().__init__()
self.dense1 = nn.LazyLinear(ffn_num_hiddens)
self.relu = nn.ReLU()
self.dense2 = nn.LazyLinear(ffn_num_outputs)
def forward(self, X):
return self.dense2(self.relu(self.dense1(X)))
class PositionWiseFFN(nn.Block): #@save
"""The positionwise feed-forward network."""
def __init__(self, ffn_num_hiddens, ffn_num_outputs):
super().__init__()
self.dense1 = nn.Dense(ffn_num_hiddens, flatten=False,
activation='relu')
self.dense2 = nn.Dense(ffn_num_outputs, flatten=False)
def forward(self, X):
return self.dense2(self.dense1(X))
class PositionWiseFFN(nn.Module): #@save
"""The positionwise feed-forward network."""
ffn_num_hiddens: int
ffn_num_outputs: int
def setup(self):
self.dense1 = nn.Dense(self.ffn_num_hiddens)
self.dense2 = nn.Dense(self.ffn_num_outputs)
def __call__(self, X):
return self.dense2(nn.relu(self.dense1(X)))
class PositionWiseFFN(tf.keras.layers.Layer): #@save
"""The positionwise feed-forward network."""
def __init__(self, ffn_num_hiddens, ffn_num_outputs):
super().__init__()
self.dense1 = tf.keras.layers.Dense(ffn_num_hiddens)
self.relu = tf.keras.layers.ReLU()
self.dense2 = tf.keras.layers.Dense(ffn_num_outputs)
def call(self, X):
return self.dense2(self.relu(self.dense1(X)))
The following example shows that the innermost dimension of a tensor changes to the number of outputs in the positionwise feed-forward network. Since the same MLP transforms at all the positions, when the inputs at all these positions are the same, their outputs are also identical.
ffn = PositionWiseFFN(4, 8)
ffn.eval()
ffn(torch.ones((2, 3, 4)))[0]
tensor([[ 0.6300, 0.7739, 0.0278, 0.2508, -0.0519, 0.4881, -0.4105, 0.5163],
[ 0.6300, 0.7739, 0.0278, 0.2508, -0.0519, 0.4881, -0.4105, 0.5163],
[ 0.6300, 0.7739, 0.0278, 0.2508, -0.0519, 0.4881, -0.4105, 0.5163]],
grad_fn=<SelectBackward0>)
ffn = PositionWiseFFN(4, 8)
ffn.initialize()
ffn(np.ones((2, 3, 4)))[0]
[22:58:52] ../src/storage/storage.cc:196: Using Pooled (Naive) StorageManager for CPU
array([[ 0.00239431, 0.00927085, -0.00021069, -0.00923989, -0.0082903 ,
-0.00162741, 0.00659031, 0.00023905],
[ 0.00239431, 0.00927085, -0.00021069, -0.00923989, -0.0082903 ,
-0.00162741, 0.00659031, 0.00023905],
[ 0.00239431, 0.00927085, -0.00021069, -0.00923989, -0.0082903 ,
-0.00162741, 0.00659031, 0.00023905]])
ffn = PositionWiseFFN(4, 8)
ffn.init_with_output(d2l.get_key(), jnp.ones((2, 3, 4)))[0][0]
Array([[ 0.18922476, -0.17692721, -0.01605045, 0.00809076, 0.34023476,
0.1972927 , -0.00320223, 0.07913349],
[ 0.18922476, -0.17692721, -0.01605045, 0.00809076, 0.34023476,
0.1972927 , -0.00320223, 0.07913349],
[ 0.18922476, -0.17692721, -0.01605045, 0.00809076, 0.34023476,
0.1972927 , -0.00320223, 0.07913349]], dtype=float32)
ffn = PositionWiseFFN(4, 8)
ffn(tf.ones((2, 3, 4)))[0]
<tf.Tensor: shape=(3, 8), dtype=float32, numpy=
array([[ 0.44900823, -0.3150453 , -0.2648125 , -0.28306794, -0.33855066,
-0.4591836 , -0.656264 , -0.81445634],
[ 0.44900823, -0.3150453 , -0.2648125 , -0.28306794, -0.33855066,
-0.4591836 , -0.656264 , -0.81445634],
[ 0.44900823, -0.3150453 , -0.2648125 , -0.28306794, -0.33855066,
-0.4591836 , -0.656264 , -0.81445634]], dtype=float32)>
11.7.3. Residual Connection and Layer Normalization¶
Now let’s focus on the “add & norm” component in Fig. 11.7.1. As we described at the beginning of this section, this is a residual connection immediately followed by layer normalization. Both are key to effective deep architectures.
In Section 8.5, we explained how batch normalization recenters and rescales across the examples within a minibatch. As discussed in Section 8.5.2.3, layer normalization is the same as batch normalization except that the former normalizes across the feature dimension, thus enjoying benefits of scale independence and batch size independence. Despite its pervasive applications in computer vision, batch normalization is usually empirically less effective than layer normalization in natural language processing tasks, where the inputs are often variable-length sequences.
The following code snippet compares the normalization across different dimensions by layer normalization and batch normalization.
ln = nn.LayerNorm(2)
bn = nn.LazyBatchNorm1d()
X = torch.tensor([[1, 2], [2, 3]], dtype=torch.float32)
# Compute mean and variance from X in the training mode
print('layer norm:', ln(X), '\nbatch norm:', bn(X))
layer norm: tensor([[-1.0000, 1.0000],
[-1.0000, 1.0000]], grad_fn=<NativeLayerNormBackward0>)
batch norm: tensor([[-1.0000, -1.0000],
[ 1.0000, 1.0000]], grad_fn=<NativeBatchNormBackward0>)
ln = nn.LayerNorm()
ln.initialize()
bn = nn.BatchNorm()
bn.initialize()
X = np.array([[1, 2], [2, 3]])
# Compute mean and variance from X in the training mode
with autograd.record():
print('layer norm:', ln(X), '\nbatch norm:', bn(X))
layer norm: [[-0.99998 0.99998]
[-0.99998 0.99998]]
batch norm: [[-0.99998 -0.99998]
[ 0.99998 0.99998]]
ln = nn.LayerNorm()
bn = nn.BatchNorm()
X = jnp.array([[1, 2], [2, 3]], dtype=jnp.float32)
# Compute mean and variance from X in the training mode
print('layer norm:', ln.init_with_output(d2l.get_key(), X)[0],
'\nbatch norm:', bn.init_with_output(d2l.get_key(), X,
use_running_average=False)[0])
layer norm: [[-0.9999979 0.9999979]
[-0.9999979 0.9999979]]
batch norm: [[-0.9999799 -0.9999799]
[ 0.9999799 0.9999799]]
ln = tf.keras.layers.LayerNormalization()
bn = tf.keras.layers.BatchNormalization()
X = tf.constant([[1, 2], [2, 3]], dtype=tf.float32)
print('layer norm:', ln(X), '\nbatch norm:', bn(X, training=True))
layer norm: tf.Tensor(
[[-0.998006 0.9980061]
[-0.9980061 0.998006 ]], shape=(2, 2), dtype=float32)
batch norm: tf.Tensor(
[[-0.998006 -0.9980061 ]
[ 0.9980061 0.99800587]], shape=(2, 2), dtype=float32)
Now we can implement the AddNorm class using a residual connection
followed by layer normalization. Dropout is also applied for
regularization.
class AddNorm(nn.Module): #@save
"""The residual connection followed by layer normalization."""
def __init__(self, norm_shape, dropout):
super().__init__()
self.dropout = nn.Dropout(dropout)
self.ln = nn.LayerNorm(norm_shape)
def forward(self, X, Y):
return self.ln(self.dropout(Y) + X)
class AddNorm(nn.Block): #@save
"""The residual connection followed by layer normalization."""
def __init__(self, dropout):
super().__init__()
self.dropout = nn.Dropout(dropout)
self.ln = nn.LayerNorm()
def forward(self, X, Y):
return self.ln(self.dropout(Y) + X)
class AddNorm(nn.Module): #@save
"""The residual connection followed by layer normalization."""
dropout: int
@nn.compact
def __call__(self, X, Y, training=False):
return nn.LayerNorm()(
nn.Dropout(self.dropout)(Y, deterministic=not training) + X)
class AddNorm(tf.keras.layers.Layer): #@save
"""The residual connection followed by layer normalization."""
def __init__(self, norm_shape, dropout):
super().__init__()
self.dropout = tf.keras.layers.Dropout(dropout)
self.ln = tf.keras.layers.LayerNormalization(norm_shape)
def call(self, X, Y, **kwargs):
return self.ln(self.dropout(Y, **kwargs) + X)
The residual connection requires that the two inputs are of the same shape so that the output tensor also has the same shape after the addition operation.
add_norm = AddNorm(4, 0.5)
shape = (2, 3, 4)
d2l.check_shape(add_norm(torch.ones(shape), torch.ones(shape)), shape)
add_norm = AddNorm(0.5)
add_norm.initialize()
shape = (2, 3, 4)
d2l.check_shape(add_norm(np.ones(shape), np.ones(shape)), shape)
add_norm = AddNorm(0.5)
shape = (2, 3, 4)
output, _ = add_norm.init_with_output(d2l.get_key(), jnp.ones(shape),
jnp.ones(shape))
d2l.check_shape(output, shape)
# Normalized_shape is: [i for i in range(len(input.shape))][1:]
add_norm = AddNorm([1, 2], 0.5)
shape = (2, 3, 4)
d2l.check_shape(add_norm(tf.ones(shape), tf.ones(shape), training=False),
shape)
11.7.4. Encoder¶
With all the essential components to assemble the Transformer encoder,
let’s start by implementing a single layer within the encoder. The
following TransformerEncoderBlock class contains two sublayers:
multi-head self-attention and positionwise feed-forward networks, where
a residual connection followed by layer normalization is employed around
both sublayers.
class TransformerEncoderBlock(nn.Module): #@save
"""The Transformer encoder block."""
def __init__(self, num_hiddens, ffn_num_hiddens, num_heads, dropout,
use_bias=False):
super().__init__()
self.attention = d2l.MultiHeadAttention(num_hiddens, num_heads,
dropout, use_bias)
self.addnorm1 = AddNorm(num_hiddens, dropout)
self.ffn = PositionWiseFFN(ffn_num_hiddens, num_hiddens)
self.addnorm2 = AddNorm(num_hiddens, dropout)
def forward(self, X, valid_lens):
Y = self.addnorm1(X, self.attention(X, X, X, valid_lens))
return self.addnorm2(Y, self.ffn(Y))
class TransformerEncoderBlock(nn.Block): #@save
"""The Transformer encoder block."""
def __init__(self, num_hiddens, ffn_num_hiddens, num_heads, dropout,
use_bias=False):
super().__init__()
self.attention = d2l.MultiHeadAttention(
num_hiddens, num_heads, dropout, use_bias)
self.addnorm1 = AddNorm(dropout)
self.ffn = PositionWiseFFN(ffn_num_hiddens, num_hiddens)
self.addnorm2 = AddNorm(dropout)
def forward(self, X, valid_lens):
Y = self.addnorm1(X, self.attention(X, X, X, valid_lens))
return self.addnorm2(Y, self.ffn(Y))
class TransformerEncoderBlock(nn.Module): #@save
"""The Transformer encoder block."""
num_hiddens: int
ffn_num_hiddens: int
num_heads: int
dropout: float
use_bias: bool = False
def setup(self):
self.attention = d2l.MultiHeadAttention(self.num_hiddens, self.num_heads,
self.dropout, self.use_bias)
self.addnorm1 = AddNorm(self.dropout)
self.ffn = PositionWiseFFN(self.ffn_num_hiddens, self.num_hiddens)
self.addnorm2 = AddNorm(self.dropout)
def __call__(self, X, valid_lens, training=False):
output, attention_weights = self.attention(X, X, X, valid_lens,
training=training)
Y = self.addnorm1(X, output, training=training)
return self.addnorm2(Y, self.ffn(Y), training=training), attention_weights
class TransformerEncoderBlock(tf.keras.layers.Layer): #@save
"""The Transformer encoder block."""
def __init__(self, key_size, query_size, value_size, num_hiddens,
norm_shape, ffn_num_hiddens, num_heads, dropout, bias=False):
super().__init__()
self.attention = d2l.MultiHeadAttention(
key_size, query_size, value_size, num_hiddens, num_heads, dropout,
bias)
self.addnorm1 = AddNorm(norm_shape, dropout)
self.ffn = PositionWiseFFN(ffn_num_hiddens, num_hiddens)
self.addnorm2 = AddNorm(norm_shape, dropout)
def call(self, X, valid_lens, **kwargs):
Y = self.addnorm1(X, self.attention(X, X, X, valid_lens, **kwargs),
**kwargs)
return self.addnorm2(Y, self.ffn(Y), **kwargs)
As we can see, no layer in the Transformer encoder changes the shape of its input.
X = torch.ones((2, 100, 24))
valid_lens = torch.tensor([3, 2])
encoder_blk = TransformerEncoderBlock(24, 48, 8, 0.5)
encoder_blk.eval()
d2l.check_shape(encoder_blk(X, valid_lens), X.shape)
X = np.ones((2, 100, 24))
valid_lens = np.array([3, 2])
encoder_blk = TransformerEncoderBlock(24, 48, 8, 0.5)
encoder_blk.initialize()
d2l.check_shape(encoder_blk(X, valid_lens), X.shape)
X = jnp.ones((2, 100, 24))
valid_lens = jnp.array([3, 2])
encoder_blk = TransformerEncoderBlock(24, 48, 8, 0.5)
(output, _), _ = encoder_blk.init_with_output(d2l.get_key(), X, valid_lens,
training=False)
d2l.check_shape(output, X.shape)
X = tf.ones((2, 100, 24))
valid_lens = tf.constant([3, 2])
norm_shape = [i for i in range(len(X.shape))][1:]
encoder_blk = TransformerEncoderBlock(24, 24, 24, 24, norm_shape, 48, 8, 0.5)
d2l.check_shape(encoder_blk(X, valid_lens, training=False), X.shape)
In the following Transformer encoder implementation, we stack
num_blks instances of the above TransformerEncoderBlock classes.
Since we use the fixed positional encoding whose values are always
between \(-1\) and \(1\), we multiply values of the learnable
input embeddings by the square root of the embedding dimension to
rescale before summing up the input embedding and the positional
encoding.
class TransformerEncoder(d2l.Encoder): #@save
"""The Transformer encoder."""
def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens,
num_heads, num_blks, dropout, use_bias=False):
super().__init__()
self.num_hiddens = num_hiddens
self.embedding = nn.Embedding(vocab_size, num_hiddens)
self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)
self.blks = nn.Sequential()
for i in range(num_blks):
self.blks.add_module("block"+str(i), TransformerEncoderBlock(
num_hiddens, ffn_num_hiddens, num_heads, dropout, use_bias))
def forward(self, X, valid_lens):
# Since positional encoding values are between -1 and 1, the embedding
# values are multiplied by the square root of the embedding dimension
# to rescale before they are summed up
X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))
self.attention_weights = [None] * len(self.blks)
for i, blk in enumerate(self.blks):
X = blk(X, valid_lens)
self.attention_weights[
i] = blk.attention.attention.attention_weights
return X
class TransformerEncoder(d2l.Encoder): #@save
"""The Transformer encoder."""
def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens,
num_heads, num_blks, dropout, use_bias=False):
super().__init__()
self.num_hiddens = num_hiddens
self.embedding = nn.Embedding(vocab_size, num_hiddens)
self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)
self.blks = nn.Sequential()
for _ in range(num_blks):
self.blks.add(TransformerEncoderBlock(
num_hiddens, ffn_num_hiddens, num_heads, dropout, use_bias))
self.initialize()
def forward(self, X, valid_lens):
# Since positional encoding values are between -1 and 1, the embedding
# values are multiplied by the square root of the embedding dimension
# to rescale before they are summed up
X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))
self.attention_weights = [None] * len(self.blks)
for i, blk in enumerate(self.blks):
X = blk(X, valid_lens)
self.attention_weights[
i] = blk.attention.attention.attention_weights
return X
class TransformerEncoder(d2l.Encoder): #@save
"""The Transformer encoder."""
vocab_size: int
num_hiddens:int
ffn_num_hiddens: int
num_heads: int
num_blks: int
dropout: float
use_bias: bool = False
def setup(self):
self.embedding = nn.Embed(self.vocab_size, self.num_hiddens)
self.pos_encoding = d2l.PositionalEncoding(self.num_hiddens, self.dropout)
self.blks = [TransformerEncoderBlock(self.num_hiddens,
self.ffn_num_hiddens,
self.num_heads,
self.dropout, self.use_bias)
for _ in range(self.num_blks)]
def __call__(self, X, valid_lens, training=False):
# Since positional encoding values are between -1 and 1, the embedding
# values are multiplied by the square root of the embedding dimension
# to rescale before they are summed up
X = self.embedding(X) * math.sqrt(self.num_hiddens)
X = self.pos_encoding(X, training=training)
attention_weights = [None] * len(self.blks)
for i, blk in enumerate(self.blks):
X, attention_w = blk(X, valid_lens, training=training)
attention_weights[i] = attention_w
# Flax sow API is used to capture intermediate variables
self.sow('intermediates', 'enc_attention_weights', attention_weights)
return X
class TransformerEncoder(d2l.Encoder): #@save
"""The Transformer encoder."""
def __init__(self, vocab_size, key_size, query_size, value_size,
num_hiddens, norm_shape, ffn_num_hiddens, num_heads,
num_blks, dropout, bias=False):
super().__init__()
self.num_hiddens = num_hiddens
self.embedding = tf.keras.layers.Embedding(vocab_size, num_hiddens)
self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)
self.blks = [TransformerEncoderBlock(
key_size, query_size, value_size, num_hiddens, norm_shape,
ffn_num_hiddens, num_heads, dropout, bias) for _ in range(
num_blks)]
def call(self, X, valid_lens, **kwargs):
# Since positional encoding values are between -1 and 1, the embedding
# values are multiplied by the square root of the embedding dimension
# to rescale before they are summed up
X = self.pos_encoding(self.embedding(X) * tf.math.sqrt(
tf.cast(self.num_hiddens, dtype=tf.float32)), **kwargs)
self.attention_weights = [None] * len(self.blks)
for i, blk in enumerate(self.blks):
X = blk(X, valid_lens, **kwargs)
self.attention_weights[
i] = blk.attention.attention.attention_weights
return X
Below we specify hyperparameters to create a two-layer Transformer
encoder. The shape of the Transformer encoder output is (batch size,
number of time steps, num_hiddens).
encoder = TransformerEncoder(200, 24, 48, 8, 2, 0.5)
d2l.check_shape(encoder(torch.ones((2, 100), dtype=torch.long), valid_lens),
(2, 100, 24))
encoder = TransformerEncoder(200, 24, 48, 8, 2, 0.5)
d2l.check_shape(encoder(np.ones((2, 100)), valid_lens), (2, 100, 24))
encoder = TransformerEncoder(200, 24, 48, 8, 2, 0.5)
d2l.check_shape(encoder.init_with_output(d2l.get_key(),
jnp.ones((2, 100), dtype=jnp.int32),
valid_lens)[0],
(2, 100, 24))
encoder = TransformerEncoder(200, 24, 24, 24, 24, [1, 2], 48, 8, 2, 0.5)
d2l.check_shape(encoder(tf.ones((2, 100)), valid_lens, training=False),
(2, 100, 24))
11.7.5. Decoder¶
As shown in Fig. 11.7.1, the Transformer decoder is
composed of multiple identical layers. Each layer is implemented in the
following TransformerDecoderBlock class, which contains three
sublayers: decoder self-attention, encoder–decoder attention, and
positionwise feed-forward networks. These sublayers employ a residual
connection around them followed by layer normalization.
As we described earlier in this section, in the masked multi-head
decoder self-attention (the first sublayer), queries, keys, and values
all come from the outputs of the previous decoder layer. When training
sequence-to-sequence models, tokens at all the positions (time steps) of
the output sequence are known. However, during prediction the output
sequence is generated token by token; thus, at any decoder time step
only the generated tokens can be used in the decoder self-attention. To
preserve autoregression in the decoder, its masked self-attention
specifies dec_valid_lens so that any query only attends to all
positions in the decoder up to the query position.
class TransformerDecoderBlock(nn.Module):
# The i-th block in the Transformer decoder
def __init__(self, num_hiddens, ffn_num_hiddens, num_heads, dropout, i):
super().__init__()
self.i = i
self.attention1 = d2l.MultiHeadAttention(num_hiddens, num_heads,
dropout)
self.addnorm1 = AddNorm(num_hiddens, dropout)
self.attention2 = d2l.MultiHeadAttention(num_hiddens, num_heads,
dropout)
self.addnorm2 = AddNorm(num_hiddens, dropout)
self.ffn = PositionWiseFFN(ffn_num_hiddens, num_hiddens)
self.addnorm3 = AddNorm(num_hiddens, dropout)
def forward(self, X, state):
enc_outputs, enc_valid_lens = state[0], state[1]
# During training, all the tokens of any output sequence are processed
# at the same time, so state[2][self.i] is None as initialized. When
# decoding any output sequence token by token during prediction,
# state[2][self.i] contains representations of the decoded output at
# the i-th block up to the current time step
if state[2][self.i] is None:
key_values = X
else:
key_values = torch.cat((state[2][self.i], X), dim=1)
state[2][self.i] = key_values
if self.training:
batch_size, num_steps, _ = X.shape
# Shape of dec_valid_lens: (batch_size, num_steps), where every
# row is [1, 2, ..., num_steps]
dec_valid_lens = torch.arange(
1, num_steps + 1, device=X.device).repeat(batch_size, 1)
else:
dec_valid_lens = None
# Self-attention
X2 = self.attention1(X, key_values, key_values, dec_valid_lens)
Y = self.addnorm1(X, X2)
# Encoder-decoder attention. Shape of enc_outputs:
# (batch_size, num_steps, num_hiddens)
Y2 = self.attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)
Z = self.addnorm2(Y, Y2)
return self.addnorm3(Z, self.ffn(Z)), state
class TransformerDecoderBlock(nn.Block):
# The i-th block in the Transformer decoder
def __init__(self, num_hiddens, ffn_num_hiddens, num_heads, dropout, i):
super().__init__()
self.i = i
self.attention1 = d2l.MultiHeadAttention(num_hiddens, num_heads,
dropout)
self.addnorm1 = AddNorm(dropout)
self.attention2 = d2l.MultiHeadAttention(num_hiddens, num_heads,
dropout)
self.addnorm2 = AddNorm(dropout)
self.ffn = PositionWiseFFN(ffn_num_hiddens, num_hiddens)
self.addnorm3 = AddNorm(dropout)
def forward(self, X, state):
enc_outputs, enc_valid_lens = state[0], state[1]
# During training, all the tokens of any output sequence are processed
# at the same time, so state[2][self.i] is None as initialized. When
# decoding any output sequence token by token during prediction,
# state[2][self.i] contains representations of the decoded output at
# the i-th block up to the current time step
if state[2][self.i] is None:
key_values = X
else:
key_values = np.concatenate((state[2][self.i], X), axis=1)
state[2][self.i] = key_values
if autograd.is_training():
batch_size, num_steps, _ = X.shape
# Shape of dec_valid_lens: (batch_size, num_steps), where every
# row is [1, 2, ..., num_steps]
dec_valid_lens = np.tile(np.arange(1, num_steps + 1, ctx=X.ctx),
(batch_size, 1))
else:
dec_valid_lens = None
# Self-attention
X2 = self.attention1(X, key_values, key_values, dec_valid_lens)
Y = self.addnorm1(X, X2)
# Encoder-decoder attention. Shape of enc_outputs:
# (batch_size, num_steps, num_hiddens)
Y2 = self.attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)
Z = self.addnorm2(Y, Y2)
return self.addnorm3(Z, self.ffn(Z)), state
class TransformerDecoderBlock(nn.Module):
# The i-th block in the Transformer decoder
num_hiddens: int
ffn_num_hiddens: int
num_heads: int
dropout: float
i: int
def setup(self):
self.attention1 = d2l.MultiHeadAttention(self.num_hiddens,
self.num_heads,
self.dropout)
self.addnorm1 = AddNorm(self.dropout)
self.attention2 = d2l.MultiHeadAttention(self.num_hiddens,
self.num_heads,
self.dropout)
self.addnorm2 = AddNorm(self.dropout)
self.ffn = PositionWiseFFN(self.ffn_num_hiddens, self.num_hiddens)
self.addnorm3 = AddNorm(self.dropout)
def __call__(self, X, state, training=False):
enc_outputs, enc_valid_lens = state[0], state[1]
# During training, all the tokens of any output sequence are processed
# at the same time, so state[2][self.i] is None as initialized. When
# decoding any output sequence token by token during prediction,
# state[2][self.i] contains representations of the decoded output at
# the i-th block up to the current time step
if state[2][self.i] is None:
key_values = X
else:
key_values = jnp.concatenate((state[2][self.i], X), axis=1)
state[2][self.i] = key_values
if training:
batch_size, num_steps, _ = X.shape
# Shape of dec_valid_lens: (batch_size, num_steps), where every
# row is [1, 2, ..., num_steps]
dec_valid_lens = jnp.tile(jnp.arange(1, num_steps + 1),
(batch_size, 1))
else:
dec_valid_lens = None
# Self-attention
X2, attention_w1 = self.attention1(X, key_values, key_values,
dec_valid_lens, training=training)
Y = self.addnorm1(X, X2, training=training)
# Encoder-decoder attention. Shape of enc_outputs:
# (batch_size, num_steps, num_hiddens)
Y2, attention_w2 = self.attention2(Y, enc_outputs, enc_outputs,
enc_valid_lens, training=training)
Z = self.addnorm2(Y, Y2, training=training)
return self.addnorm3(Z, self.ffn(Z), training=training), state, attention_w1, attention_w2
class TransformerDecoderBlock(tf.keras.layers.Layer):
# The i-th block in the Transformer decoder
def __init__(self, key_size, query_size, value_size, num_hiddens,
norm_shape, ffn_num_hiddens, num_heads, dropout, i):
super().__init__()
self.i = i
self.attention1 = d2l.MultiHeadAttention(
key_size, query_size, value_size, num_hiddens, num_heads, dropout)
self.addnorm1 = AddNorm(norm_shape, dropout)
self.attention2 = d2l.MultiHeadAttention(
key_size, query_size, value_size, num_hiddens, num_heads, dropout)
self.addnorm2 = AddNorm(norm_shape, dropout)
self.ffn = PositionWiseFFN(ffn_num_hiddens, num_hiddens)
self.addnorm3 = AddNorm(norm_shape, dropout)
def call(self, X, state, **kwargs):
enc_outputs, enc_valid_lens = state[0], state[1]
# During training, all the tokens of any output sequence are processed
# at the same time, so state[2][self.i] is None as initialized. When
# decoding any output sequence token by token during prediction,
# state[2][self.i] contains representations of the decoded output at
# the i-th block up to the current time step
if state[2][self.i] is None:
key_values = X
else:
key_values = tf.concat((state[2][self.i], X), axis=1)
state[2][self.i] = key_values
if kwargs["training"]:
batch_size, num_steps, _ = X.shape
# Shape of dec_valid_lens: (batch_size, num_steps), where every
# row is [1, 2, ..., num_steps]
dec_valid_lens = tf.repeat(
tf.reshape(tf.range(1, num_steps + 1),
shape=(-1, num_steps)), repeats=batch_size, axis=0)
else:
dec_valid_lens = None
# Self-attention
X2 = self.attention1(X, key_values, key_values, dec_valid_lens,
**kwargs)
Y = self.addnorm1(X, X2, **kwargs)
# Encoder-decoder attention. Shape of enc_outputs:
# (batch_size, num_steps, num_hiddens)
Y2 = self.attention2(Y, enc_outputs, enc_outputs, enc_valid_lens,
**kwargs)
Z = self.addnorm2(Y, Y2, **kwargs)
return self.addnorm3(Z, self.ffn(Z), **kwargs), state
To facilitate scaled dot product operations in the encoder–decoder
attention and addition operations in the residual connections, the
feature dimension (num_hiddens) of the decoder is the same as that
of the encoder.
decoder_blk = TransformerDecoderBlock(24, 48, 8, 0.5, 0)
X = torch.ones((2, 100, 24))
state = [encoder_blk(X, valid_lens), valid_lens, [None]]
d2l.check_shape(decoder_blk(X, state)[0], X.shape)
decoder_blk = TransformerDecoderBlock(24, 48, 8, 0.5, 0)
decoder_blk.initialize()
X = np.ones((2, 100, 24))
state = [encoder_blk(X, valid_lens), valid_lens, [None]]
d2l.check_shape(decoder_blk(X, state)[0], X.shape)
decoder_blk = TransformerDecoderBlock(24, 48, 8, 0.5, 0)
X = jnp.ones((2, 100, 24))
state = [encoder_blk.init_with_output(d2l.get_key(), X, valid_lens)[0][0],
valid_lens, [None]]
d2l.check_shape(decoder_blk.init_with_output(d2l.get_key(), X, state)[0][0],
X.shape)
decoder_blk = TransformerDecoderBlock(24, 24, 24, 24, [1, 2], 48, 8, 0.5, 0)
X = tf.ones((2, 100, 24))
state = [encoder_blk(X, valid_lens), valid_lens, [None]]
d2l.check_shape(decoder_blk(X, state, training=False)[0], X.shape)
Now we construct the entire Transformer decoder composed of num_blks
instances of TransformerDecoderBlock. In the end, a fully connected
layer computes the prediction for all the vocab_size possible output
tokens. Both of the decoder self-attention weights and the
encoder–decoder attention weights are stored for later visualization.
class TransformerDecoder(d2l.AttentionDecoder):
def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens, num_heads,
num_blks, dropout):
super().__init__()
self.num_hiddens = num_hiddens
self.num_blks = num_blks
self.embedding = nn.Embedding(vocab_size, num_hiddens)
self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)
self.blks = nn.Sequential()
for i in range(num_blks):
self.blks.add_module("block"+str(i), TransformerDecoderBlock(
num_hiddens, ffn_num_hiddens, num_heads, dropout, i))
self.dense = nn.LazyLinear(vocab_size)
def init_state(self, enc_outputs, enc_valid_lens):
return [enc_outputs, enc_valid_lens, [None] * self.num_blks]
def forward(self, X, state):
X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))
self._attention_weights = [[None] * len(self.blks) for _ in range (2)]
for i, blk in enumerate(self.blks):
X, state = blk(X, state)
# Decoder self-attention weights
self._attention_weights[0][
i] = blk.attention1.attention.attention_weights
# Encoder-decoder attention weights
self._attention_weights[1][
i] = blk.attention2.attention.attention_weights
return self.dense(X), state
@property
def attention_weights(self):
return self._attention_weights
class TransformerDecoder(d2l.AttentionDecoder):
def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens, num_heads,
num_blks, dropout):
super().__init__()
self.num_hiddens = num_hiddens
self.num_blks = num_blks
self.embedding = nn.Embedding(vocab_size, num_hiddens)
self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)
self.blks = nn.Sequential()
for i in range(num_blks):
self.blks.add(TransformerDecoderBlock(
num_hiddens, ffn_num_hiddens, num_heads, dropout, i))
self.dense = nn.Dense(vocab_size, flatten=False)
self.initialize()
def init_state(self, enc_outputs, enc_valid_lens):
return [enc_outputs, enc_valid_lens, [None] * self.num_blks]
def forward(self, X, state):
X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))
self._attention_weights = [[None] * len(self.blks) for _ in range (2)]
for i, blk in enumerate(self.blks):
X, state = blk(X, state)
# Decoder self-attention weights
self._attention_weights[0][
i] = blk.attention1.attention.attention_weights
# Encoder-decoder attention weights
self._attention_weights[1][
i] = blk.attention2.attention.attention_weights
return self.dense(X), state
@property
def attention_weights(self):
return self._attention_weights
class TransformerDecoder(nn.Module):
vocab_size: int
num_hiddens: int
ffn_num_hiddens: int
num_heads: int
num_blks: int
dropout: float
def setup(self):
self.embedding = nn.Embed(self.vocab_size, self.num_hiddens)
self.pos_encoding = d2l.PositionalEncoding(self.num_hiddens,
self.dropout)
self.blks = [TransformerDecoderBlock(self.num_hiddens,
self.ffn_num_hiddens,
self.num_heads, self.dropout, i)
for i in range(self.num_blks)]
self.dense = nn.Dense(self.vocab_size)
def init_state(self, enc_outputs, enc_valid_lens):
return [enc_outputs, enc_valid_lens, [None] * self.num_blks]
def __call__(self, X, state, training=False):
X = self.embedding(X) * jnp.sqrt(jnp.float32(self.num_hiddens))
X = self.pos_encoding(X, training=training)
attention_weights = [[None] * len(self.blks) for _ in range(2)]
for i, blk in enumerate(self.blks):
X, state, attention_w1, attention_w2 = blk(X, state,
training=training)
# Decoder self-attention weights
attention_weights[0][i] = attention_w1
# Encoder-decoder attention weights
attention_weights[1][i] = attention_w2
# Flax sow API is used to capture intermediate variables
self.sow('intermediates', 'dec_attention_weights', attention_weights)
return self.dense(X), state
class TransformerDecoder(d2l.AttentionDecoder):
def __init__(self, vocab_size, key_size, query_size, value_size,
num_hiddens, norm_shape, ffn_num_hiddens, num_heads,
num_blks, dropout):
super().__init__()
self.num_hiddens = num_hiddens
self.num_blks = num_blks
self.embedding = tf.keras.layers.Embedding(vocab_size, num_hiddens)
self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)
self.blks = [TransformerDecoderBlock(
key_size, query_size, value_size, num_hiddens, norm_shape,
ffn_num_hiddens, num_heads, dropout, i)
for i in range(num_blks)]
self.dense = tf.keras.layers.Dense(vocab_size)
def init_state(self, enc_outputs, enc_valid_lens):
return [enc_outputs, enc_valid_lens, [None] * self.num_blks]
def call(self, X, state, **kwargs):
X = self.pos_encoding(self.embedding(X) * tf.math.sqrt(
tf.cast(self.num_hiddens, dtype=tf.float32)), **kwargs)
# 2 attention layers in decoder
self._attention_weights = [[None] * len(self.blks) for _ in range(2)]
for i, blk in enumerate(self.blks):
X, state = blk(X, state, **kwargs)
# Decoder self-attention weights
self._attention_weights[0][i] = (
blk.attention1.attention.attention_weights)
# Encoder-decoder attention weights
self._attention_weights[1][i] = (
blk.attention2.attention.attention_weights)
return self.dense(X), state
@property
def attention_weights(self):
return self._attention_weights
11.7.6. Training¶
Let’s instantiate an encoder–decoder model by following the Transformer architecture. Here we specify that both the Transformer encoder and the Transformer decoder have two layers using 4-head attention. As in Section 10.7.6, we train the Transformer model for sequence-to-sequence learning on the English–French machine translation dataset.
data = d2l.MTFraEng(batch_size=128)
num_hiddens, num_blks, dropout = 256, 2, 0.2
ffn_num_hiddens, num_heads = 64, 4
encoder = TransformerEncoder(
len(data.src_vocab), num_hiddens, ffn_num_hiddens, num_heads,
num_blks, dropout)
decoder = TransformerDecoder(
len(data.tgt_vocab), num_hiddens, ffn_num_hiddens, num_heads,
num_blks, dropout)
model = d2l.Seq2Seq(encoder, decoder, tgt_pad=data.tgt_vocab['<pad>'],
lr=0.001)
trainer = d2l.Trainer(max_epochs=30, gradient_clip_val=1, num_gpus=1)
trainer.fit(model, data)
data = d2l.MTFraEng(batch_size=128)
num_hiddens, num_blks, dropout = 256, 2, 0.2
ffn_num_hiddens, num_heads = 64, 4
encoder = TransformerEncoder(
len(data.src_vocab), num_hiddens, ffn_num_hiddens, num_heads,
num_blks, dropout)
decoder = TransformerDecoder(
len(data.tgt_vocab), num_hiddens, ffn_num_hiddens, num_heads,
num_blks, dropout)
model = d2l.Seq2Seq(encoder, decoder, tgt_pad=data.tgt_vocab['<pad>'],
lr=0.001)
trainer = d2l.Trainer(max_epochs=30, gradient_clip_val=1, num_gpus=1)
trainer.fit(model, data)
data = d2l.MTFraEng(batch_size=128)
num_hiddens, num_blks, dropout = 256, 2, 0.2
ffn_num_hiddens, num_heads = 64, 4
encoder = TransformerEncoder(
len(data.src_vocab), num_hiddens, ffn_num_hiddens, num_heads,
num_blks, dropout)
decoder = TransformerDecoder(
len(data.tgt_vocab), num_hiddens, ffn_num_hiddens, num_heads,
num_blks, dropout)
model = d2l.Seq2Seq(encoder, decoder, tgt_pad=data.tgt_vocab['<pad>'],
lr=0.001, training=True)
trainer = d2l.Trainer(max_epochs=30, gradient_clip_val=1, num_gpus=1)
trainer.fit(model, data)
data = d2l.MTFraEng(batch_size=128)
num_hiddens, num_blks, dropout = 256, 2, 0.2
ffn_num_hiddens, num_heads = 64, 4
key_size, query_size, value_size = 256, 256, 256
norm_shape = [2]
with d2l.try_gpu():
encoder = TransformerEncoder(
len(data.src_vocab), key_size, query_size, value_size, num_hiddens,
norm_shape, ffn_num_hiddens, num_heads, num_blks, dropout)
decoder = TransformerDecoder(
len(data.tgt_vocab), key_size, query_size, value_size, num_hiddens,
norm_shape, ffn_num_hiddens, num_heads, num_blks, dropout)
model = d2l.Seq2Seq(encoder, decoder, tgt_pad=data.tgt_vocab['<pad>'],
lr=0.001)
trainer = d2l.Trainer(max_epochs=30, gradient_clip_val=1)
trainer.fit(model, data)
After training, we use the Transformer model to translate a few English sentences into French and compute their BLEU scores.
engs = ['go .', 'i lost .', 'he\'s calm .', 'i\'m home .']
fras = ['va !', 'j\'ai perdu .', 'il est calme .', 'je suis chez moi .']
preds, _ = model.predict_step(
data.build(engs, fras), d2l.try_gpu(), data.num_steps)
for en, fr, p in zip(engs, fras, preds):
translation = []
for token in data.tgt_vocab.to_tokens(p):
if token == '<eos>':
break
translation.append(token)
print(f'{en} => {translation}, bleu,'
f'{d2l.bleu(" ".join(translation), fr, k=2):.3f}')
go . => ['va', '!'], bleu,1.000
i lost . => ['je', 'perdu', '.'], bleu,0.687
he's calm . => ['il', 'est', 'mouillé', '.'], bleu,0.658
i'm home . => ['je', 'suis', 'chez', 'moi', '.'], bleu,1.000
engs = ['go .', 'i lost .', 'he\'s calm .', 'i\'m home .']
fras = ['va !', 'j\'ai perdu .', 'il est calme .', 'je suis chez moi .']
preds, _ = model.predict_step(
data.build(engs, fras), d2l.try_gpu(), data.num_steps)
for en, fr, p in zip(engs, fras, preds):
translation = []
for token in data.tgt_vocab.to_tokens(p):
if token == '<eos>':
break
translation.append(token)
print(f'{en} => {translation}, bleu,'
f'{d2l.bleu(" ".join(translation), fr, k=2):.3f}')
go . => ['va', '!'], bleu,1.000
i lost . => ["j'ai", 'perdu', '.'], bleu,1.000
he's calm . => ['il', 'est', 'calme', 'calme', '!'], bleu,0.651
i'm home . => ['je', 'suis', 'chez', 'moi', 'je', 'suis', 'chez', 'moi', 'je'], bleu,0.522
engs = ['go .', 'i lost .', 'he\'s calm .', 'i\'m home .']
fras = ['va !', 'j\'ai perdu .', 'il est calme .', 'je suis chez moi .']
preds, _ = model.predict_step(
trainer.state.params, data.build(engs, fras), data.num_steps)
for en, fr, p in zip(engs, fras, preds):
translation = []
for token in data.tgt_vocab.to_tokens(p):
if token == '<eos>':
break
translation.append(token)
print(f'{en} => {translation}, bleu,'
f'{d2l.bleu(" ".join(translation), fr, k=2):.3f}')
go . => ['va', '<unk>', '.'], bleu,0.000
i lost . => ["j'ai", 'perdu', '.'], bleu,1.000
he's calm . => ['il', 'est', 'est', 'est', 'mouillé', '.'], bleu,0.473
i'm home . => ['je', 'suis', '<unk>', '.'], bleu,0.512
engs = ['go .', 'i lost .', 'he\'s calm .', 'i\'m home .']
fras = ['va !', 'j\'ai perdu .', 'il est calme .', 'je suis chez moi .']
preds, _ = model.predict_step(
data.build(engs, fras), d2l.try_gpu(), data.num_steps)
for en, fr, p in zip(engs, fras, preds):
translation = []
for token in data.tgt_vocab.to_tokens(p):
if token == '<eos>':
break
translation.append(token)
print(f'{en} => {translation}, bleu,'
f'{d2l.bleu(" ".join(translation), fr, k=2):.3f}')
go . => ['va', '!'], bleu,1.000
i lost . => ["j'ai", 'perdu', '.'], bleu,1.000
he's calm . => ['il', 'est', 'mouillé', '.'], bleu,0.658
i'm home . => ['je', 'suis', 'chez', 'moi', 'chez', 'moi', 'chez', 'moi', 'chez'], bleu,0.522
Let’s visualize the Transformer attention weights when translating the
final English sentence into French. The shape of the encoder
self-attention weights is (number of encoder layers, number of attention
heads, num_steps or number of queries, num_steps or number of
key-value pairs).
_, dec_attention_weights = model.predict_step(
data.build([engs[-1]], [fras[-1]]), d2l.try_gpu(), data.num_steps, True)
enc_attention_weights = torch.cat(model.encoder.attention_weights, 0)
shape = (num_blks, num_heads, -1, data.num_steps)
enc_attention_weights = enc_attention_weights.reshape(shape)
d2l.check_shape(enc_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
_, dec_attention_weights = model.predict_step(
data.build([engs[-1]], [fras[-1]]), d2l.try_gpu(), data.num_steps, True)
enc_attention_weights = np.concatenate(model.encoder.attention_weights, 0)
shape = (num_blks, num_heads, -1, data.num_steps)
enc_attention_weights = enc_attention_weights.reshape(shape)
d2l.check_shape(enc_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
_, (dec_attention_weights, enc_attention_weights) = model.predict_step(
trainer.state.params, data.build([engs[-1]], [fras[-1]]),
data.num_steps, True)
enc_attention_weights = jnp.concatenate(enc_attention_weights, 0)
shape = (num_blks, num_heads, -1, data.num_steps)
enc_attention_weights = enc_attention_weights.reshape(shape)
d2l.check_shape(enc_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
_, dec_attention_weights = model.predict_step(
data.build([engs[-1]], [fras[-1]]), d2l.try_gpu(), data.num_steps, True)
enc_attention_weights = tf.concat(model.encoder.attention_weights, 0)
shape = (num_blks, num_heads, -1, data.num_steps)
enc_attention_weights = tf.reshape(enc_attention_weights, shape)
d2l.check_shape(enc_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
In the encoder self-attention, both queries and keys come from the same input sequence. Since padding tokens do not carry meaning, with specified valid length of the input sequence no query attends to positions of padding tokens. In the following, two layers of multi-head attention weights are presented row by row. Each head independently attends based on a separate representation subspace of queries, keys, and values.
d2l.show_heatmaps(
enc_attention_weights.cpu(), xlabel='Key positions',
ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],
figsize=(7, 3.5))
d2l.show_heatmaps(
enc_attention_weights, xlabel='Key positions', ylabel='Query positions',
titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))
d2l.show_heatmaps(
enc_attention_weights, xlabel='Key positions', ylabel='Query positions',
titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))
d2l.show_heatmaps(
enc_attention_weights, xlabel='Key positions', ylabel='Query positions',
titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))
To visualize the decoder self-attention weights and the encoder–decoder attention weights, we need more data manipulations. For example, we fill the masked attention weights with zero. Note that the decoder self-attention weights and the encoder–decoder attention weights both have the same queries: the beginning-of-sequence token followed by the output tokens and possibly end-of-sequence tokens.
dec_attention_weights_2d = [head[0].tolist()
for step in dec_attention_weights
for attn in step for blk in attn for head in blk]
dec_attention_weights_filled = torch.tensor(
pd.DataFrame(dec_attention_weights_2d).fillna(0.0).values)
shape = (-1, 2, num_blks, num_heads, data.num_steps)
dec_attention_weights = dec_attention_weights_filled.reshape(shape)
dec_self_attention_weights, dec_inter_attention_weights = \
dec_attention_weights.permute(1, 2, 3, 0, 4)
d2l.check_shape(dec_self_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
d2l.check_shape(dec_inter_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
dec_attention_weights_2d = [np.array(head[0]).tolist()
for step in dec_attention_weights
for attn in step for blk in attn for head in blk]
dec_attention_weights_filled = np.array(
pd.DataFrame(dec_attention_weights_2d).fillna(0.0).values)
dec_attention_weights = dec_attention_weights_filled.reshape((-1, 2, num_blks, num_heads, data.
num_steps))
dec_self_attention_weights, dec_inter_attention_weights = \
dec_attention_weights.transpose(1, 2, 3, 0, 4)
d2l.check_shape(dec_self_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
d2l.check_shape(dec_inter_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
dec_attention_weights_2d = [head[0].tolist() for step in dec_attention_weights
for attn in step
for blk in attn for head in blk]
dec_attention_weights_filled = jnp.array(
pd.DataFrame(dec_attention_weights_2d).fillna(0.0).values)
dec_attention_weights = dec_attention_weights_filled.reshape(
(-1, 2, num_blks, num_heads, data.num_steps))
dec_self_attention_weights, dec_inter_attention_weights = \
dec_attention_weights.transpose(1, 2, 3, 0, 4)
d2l.check_shape(dec_self_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
d2l.check_shape(dec_inter_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
dec_attention_weights_2d = [head[0] for step in dec_attention_weights
for attn in step
for blk in attn for head in blk]
dec_attention_weights_filled = tf.convert_to_tensor(
np.asarray(pd.DataFrame(dec_attention_weights_2d).fillna(
0.0).values).astype(np.float32))
dec_attention_weights = tf.reshape(dec_attention_weights_filled, shape=(
-1, 2, num_blks, num_heads, data.num_steps))
dec_self_attention_weights, dec_inter_attention_weights = tf.transpose(
dec_attention_weights, perm=(1, 2, 3, 0, 4))
d2l.check_shape(dec_self_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
d2l.check_shape(dec_inter_attention_weights,
(num_blks, num_heads, data.num_steps, data.num_steps))
Because of the autoregressive property of the decoder self-attention, no query attends to key–value pairs after the query position.
d2l.show_heatmaps(
dec_self_attention_weights[:, :, :, :],
xlabel='Key positions', ylabel='Query positions',
titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))
d2l.show_heatmaps(
dec_self_attention_weights[:, :, :, :],
xlabel='Key positions', ylabel='Query positions',
titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))
d2l.show_heatmaps(
dec_self_attention_weights[:, :, :, :],
xlabel='Key positions', ylabel='Query positions',
titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))
d2l.show_heatmaps(
dec_self_attention_weights[:, :, :, :],
xlabel='Key positions', ylabel='Query positions',
titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))
Similar to the case in the encoder self-attention, via the specified valid length of the input sequence, no query from the output sequence attends to those padding tokens from the input sequence.
d2l.show_heatmaps(
dec_inter_attention_weights, xlabel='Key positions',
ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],
figsize=(7, 3.5))
d2l.show_heatmaps(
dec_inter_attention_weights, xlabel='Key positions',
ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],
figsize=(7, 3.5))
d2l.show_heatmaps(
dec_inter_attention_weights, xlabel='Key positions',
ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],
figsize=(7, 3.5))
d2l.show_heatmaps(
dec_inter_attention_weights, xlabel='Key positions',
ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],
figsize=(7, 3.5))
Although the Transformer architecture was originally proposed for sequence-to-sequence learning, as we will discover later in the book, either the Transformer encoder or the Transformer decoder is often individually used for different deep learning tasks.
11.7.7. Summary¶
The Transformer is an instance of the encoder–decoder architecture, though either the encoder or the decoder can be used individually in practice. In the Transformer architecture, multi-head self-attention is used for representing the input sequence and the output sequence, though the decoder has to preserve the autoregressive property via a masked version. Both the residual connections and the layer normalization in the Transformer are important for training a very deep model. The positionwise feed-forward network in the Transformer model transforms the representation at all the sequence positions using the same MLP.
11.7.8. Exercises¶
Train a deeper Transformer in the experiments. How does it affect the training speed and the translation performance?
Is it a good idea to replace scaled dot product attention with additive attention in the Transformer? Why?
For language modeling, should we use the Transformer encoder, decoder, or both? How would you design this method?
What challenges can Transformers face if input sequences are very long? Why?
How would you improve the computational and memory efficiency of Transformers? Hint: you may refer to the survey paper by Tay et al. (2020).