Transformer¶
Abstract
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks that include an encoder and a decoder. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles, by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
1 Model Architecture¶
Transformer follows the encoder-decoder architecture using stacked self-attention and point-wise, fully connected layers for both the encoder and decoder.
class EncoderDecoder(nn.Module):
"""
A standard Encoder-Decoder architecture. Base for this and many
other models.
"""
def __init__(self, encoder, decoder, src_embed, tgt_embed, generator):
super(EncoderDecoder, self).__init__()
self.encoder = encoder
self.decoder = decoder
self.src_embed = src_embed
self.tgt_embed = tgt_embed
self.generator = generator
def forward(self, src, tgt, src_mask, tgt_mask):
"Take in and process masked src and target sequences."
return self.decode(self.encode(src, src_mask), src_mask, tgt, tgt_mask)
def encode(self, src, src_mask):
return self.encoder(self.src_embed(src), src_mask)
def decode(self, memory, src_mask, tgt, tgt_mask):
return self.decoder(self.tgt_embed(tgt), memory, src_mask, tgt_mask)
class Generator(nn.Module):
"Define standard linear + softmax generation step."
def __init__(self, d_model, vocab):
super(Generator, self).__init__()
self.proj = nn.Linear(d_model, vocab)
def forward(self, x):
return log_softmax(self.proj(x), dim=-1)
1.1 Encoder and Decoder¶
Encoder: The encoder is composed of a stack of \(N=6\) identical layers. Each layer has two sub-layers. The first is a multi-head self-attention mechanism, and the second is a simple, position-wise fully connected feed-forward network.
def clones(module, N):
"Produce N identical layers."
return nn.ModuleList([copy.deepcopy(module) for _ in range(N)])
class Encoder(nn.Module):
"Core encoder is a stack of N layers"
def __init__(self, layer, N):
super(Encoder, self).__init__()
self.layers = clones(layer, N)
self.norm = LayerNorm(layer.size)
def forward(self, x, mask):
"Pass the input (and mask) through each layer in turn."
for layer in self.layers:
x = layer(x, mask)
return self.norm(x)
We employ a residual connection around each of the two sub-layers, followed by layer normalization. That is, the output of each sub-layer is \(\text{LayerNorm}(x+\text{Sublayer}(x))\), where \(\text{Sublayer}(x)\) is the function implemented by the sub-layer itself.
class LayerNorm(nn.Module):
"Construct a layernorm module (See citation for details)."
def __init__(self, features, eps=1e-6):
super(LayerNorm, self).__init__()
self.a_2 = nn.Parameter(torch.ones(features))
self.b_2 = nn.Parameter(torch.zeros(features))
self.eps = eps
def forward(self, x):
mean = x.mean(-1, keepdim=True)
std = x.std(-1, keepdim=True)
return self.a_2 * (x - mean) / (std + self.eps) + self.b_2
class SublayerConnection(nn.Module):
"""
A residual connection followed by a layer norm.
Note for code simplicity the norm is first as opposed to last.
"""
def __init__(self, size, dropout):
super(SublayerConnection, self).__init__()
self.norm = LayerNorm(size)
self.dropout = nn.Dropout(dropout)
def forward(self, x, sublayer):
"Apply residual connection to any sublayer with the same size."
return x + self.dropout(sublayer(self.norm(x)))
Note
Here, in the code implementation, we use pre-LN instead of normal-LN, that is, our implementation is
We use Pre-LN because it stabilizes gradient flow, improves convergence, and makes it possible to train very deep Transformer models reliably.
class EncoderLayer(nn.Module):
"Encoder is made up of self-attn and feed forward (defined below)"
def __init__(self, size, self_attn, feed_forward, dropout):
super(EncoderLayer, self).__init__()
self.self_attn = self_attn
self.feed_forward = feed_forward
self.sublayer = clones(SublayerConnection(size, dropout), 2)
self.size = size
def forward(self, x, mask):
"Follow Figure 1 (left) for connections."
x = self.sublayer[0](x, lambda x: self.self_attn(x, x, x, mask))
return self.sublayer[1](x, self.feed_forward)
Decoder: The decoder is also composed of a stack of \(N=6\) identical layers.
class Decoder(nn.Module):
"Generic N layer decoder with masking."
def __init__(self, layer, N):
super(Decoder, self).__init__()
self.layers = clones(layer, N)
self.norm = LayerNorm(layer.size)
def forward(self, x, memory, src_mask, tgt_mask):
for layer in self.layers:
x = layer(x, memory, src_mask, tgt_mask)
return self.norm(x)
In addition to the two sub-layers in each encoder layer, the decoder inserts a third sub-layer, which performs multi-head attention over the output of the encoder stack. Similar to the encoder, we employ residual connections around each of the sub-layers, followed by layer normalization.
class DecoderLayer(nn.Module):
"Decoder is made of self-attn, src-attn, and feed forward (defined below)"
def __init__(self, size, self_attn, src_attn, feed_forward, dropout):
super(DecoderLayer, self).__init__()
self.size = size
self.self_attn = self_attn
self.src_attn = src_attn
self.feed_forward = feed_forward
self.sublayer = clones(SublayerConnection(size, dropout), 3)
def forward(self, x, memory, src_mask, tgt_mask):
"Follow Figure 1 (right) for connections."
m = memory
x = self.sublayer[0](x, lambda x: self.self_attn(x, x, x, tgt_mask))
x = self.sublayer[1](x, lambda x: self.src_attn(x, m, m, src_mask))
return self.sublayer[2](x, self.feed_forward)
We also modify the self-attention sub-layer in the decoder stack to prevent positions from attending to subsequent positions. This masking, combined with fact that the output embeddings are offset by one position, ensures that the predictions for position \(i\) can depend only on the known outputs as positions less than \(i\).
1.2 Attention¶
An attention function can be described as mapping a query and a set of key-value pairs to an output, where the query, keys, values, and output are all vectors. The output is computed as a weighted sum of values, where the weight assigned to each value is computed by a compatibility function of the query with the corresponding key.
1.2.1 Scaled Dot-Product Attention¶
The input consists of queries and keys of dimension \(d_k\), and values of dimension \(d_v\). We compute the dot products of the query with all keys, divide each by \(\sqrt{d_k}\), and apply a softmax function to obtain the weights on the values.
In practice, we compute the attention function on a set of queries simultaneously, packed together into a matrix \(Q\). The keys and values are also packed together into matrices \(K\) and \(V\). We compute the matrix of output as:
While for small values of \(d_k\), additive attention and dot-product(multiplicative) attention perform similarly, additive attention outperforms dot product attention without scaling for large values of \(d_k\). We suspect that for large values of \(d_k\), the dot products grow large in magnitude, pushing the softmax function into regions where it has extermely small gradients. To counteract this effect, we scale the dot products by \(1/\sqrt{d_k}\).
def attention(query, key, value, mask=None, dropout=None):
"Compute 'Scaled Dot Product Attention'"
d_k = query.size(-1)
scores = torch.matmul(query, key.transpose(-2, -1)) / math.sqrt(d_k)
if mask is not None:
scores = scores.masked_fill(mask == 0, -1e9)
p_attn = scores.softmax(dim=-1)
if dropout is not None:
p_attn = dropout(p_attn)
return torch.matmul(p_attn, value), p_attn
1.2.2 Multi-Head Attention¶
Instead of performing a single attention function with \(d_{model}\)-dimensional keys, values and queries, we found it benefical to linearly project the queries, keys and values \(h\) times with different, learned linear projections to \(d_k\), \(d_k\) and \(d_v\) dimensions, respectively.
On each of these projected versions of queries, keys and values we then perform the attention function in parallel, yielding \(d_v\)-dimensional output values. These are concatenated and once again projected, resulting in the final values.
Multi-head attention allows the model to jointly attend to information from different representation subspaces at different positions. With a single attention head, averaging inhibits this.
where \(\text{head}_i=\text{Attention}(QW_i^Q,KW_i^K,VW_i^V)\)
where the projections are parameter matrices \(W_i^Q \in \mathbb{R}^{d_model \times d_k}\), \(W_i^K \in \mathbb{R}^{d_model \times d_k}\), \(W_i^V \in \mathbb{R}^{d_model \times d_v}\) and \(W^O \in \mathbb{R}^{hd_v \times d_{model}}\)
class MultiHeadedAttention(nn.Module):
def __init__(self, h, d_model, dropout=0.1):
"Take in model size and number of heads."
super(MultiHeadedAttention, self).__init__()
assert d_model % h == 0
# We assume d_v always equals d_k
self.d_k = d_model // h
self.h = h
self.linears = clones(nn.Linear(d_model, d_model), 4)
self.attn = None
self.dropout = nn.Dropout(p=dropout)
def forward(self, query, key, value, mask=None):
"Implements Figure 2"
if mask is not None:
# Same mask applied to all h heads.
mask = mask.unsqueeze(1)
nbatches = query.size(0)
# 1) Do all the linear projections in batch from d_model => h x d_k
query, key, value = [
lin(x).view(nbatches, -1, self.h, self.d_k).transpose(1, 2)
for lin, x in zip(self.linears, (query, key, value))
]
# 2) Apply attention on all the projected vectors in batch.
x, self.attn = attention(
query, key, value, mask=mask, dropout=self.dropout
)
# 3) "Concat" using a view and apply a final linear.
x = (
x.transpose(1, 2)
.contiguous()
.view(nbatches, -1, self.h * self.d_k)
)
del query
del key
del value
return self.linears[-1](x)
1.2.3 Applications of Attention in Transformer¶
The Transformer uses multi-head attention in three different ways:
- In "encoder-decoder attention" layers, the queries come from the previous decoder layer, and the memory keys and values come from the output of the encoder. This allows every position in the decoder to attend over all positions in the input sequence.
- The encoder contains self-attention layers. In a self-attention layer all of the keys, values and queries come from the same place, in this case, the output of the previous layer in the encoder. Each position in the encoder can attend to all positions in the previous layer of the encoder.
- Similarly, self-attention layers in the decoder allow each position in the decoder to attend to all positions in the decoder up to and including that position. We need to prevent leftward information flow in the decoder to preserve the auto-regerssive property. We implement this inside of scaled dot-product attention by masking out(setting to \(-\infty\)) all values in the input of the softmax which correspond to illegal connections.
1.3 Position-wise Feed-Forward Networks¶
In addition to attention sub-layers, each of the layers in our encoder and decoder contains a fully connected feed-forward network, which is applied to each position separately and identically. This consists of two linear transformations with a ReLU activation in between.
While the linear transformations are the same across different positions, they use different parameters from layer to layer.
class PositionwiseFeedForward(nn.Module):
"Implements FFN equation."
def __init__(self, d_model, d_ff, dropout=0.1):
super(PositionwiseFeedForward, self).__init__()
self.w_1 = nn.Linear(d_model, d_ff)
self.w_2 = nn.Linear(d_ff, d_model)
self.dropout = nn.Dropout(dropout)
def forward(self, x):
return self.w_2(self.dropout(self.w_1(x).relu()))
1.4 Embeddings and Softmax¶
We use learned embeddings to convert the input tokens and output tokens to vectors of dimension \(d_model\). We also use the usual learned linear transformation and softmax function to convert the decoder output to predicted next-token probabilities. In our model, we share the same weight matrix between the two embedding layers and pre-softmax linear transformation. In the embedding layers, we multiply those weights by \(\sqrt{d_model}\)
class Embeddings(nn.Module):
def __init__(self, d_model, vocab):
super(Embeddings, self).__init__()
self.lut = nn.Embedding(vocab, d_model)
self.d_model = d_model
def forward(self, x):
return self.lut(x) * math.sqrt(self.d_model)
1.5 Positional Encoding¶
In order for the model to make use of the order of the sequence, we must inject some information about the relative or absolute position of the tokens in the sequence. To this end, we add "positional encodings" to the input embeddings at the bottoms of the encoder and decoder stacks.
In this work, we use sine and cosine functions of different frequencies:
where \(pos\) is the position and \(i\) is the dimension. That is, each dimension of the positional encoding corresponds to a sinusoid.
class PositionalEncoding(nn.Module):
"Implement the PE function."
def __init__(self, d_model, dropout, max_len=5000):
super(PositionalEncoding, self).__init__()
self.dropout = nn.Dropout(p=dropout)
# Compute the positional encodings once in log space.
pe = torch.zeros(max_len, d_model)
position = torch.arange(0, max_len).unsqueeze(1)
div_term = torch.exp(
torch.arange(0, d_model, 2) * -(math.log(10000.0) / d_model)
)
pe[:, 0::2] = torch.sin(position * div_term)
pe[:, 1::2] = torch.cos(position * div_term)
pe = pe.unsqueeze(0)
self.register_buffer("pe", pe)
def forward(self, x):
x = x + self.pe[:, : x.size(1)].requires_grad_(False)
return self.dropout(x)
2 Full Model¶
Here we define a function from hyperparamters to a full model
def make_model(
src_vocab, tgt_vocab, N=6, d_model=512, d_ff=2048, h=8, dropout=0.1
):
"Helper: Construct a model from hyperparameters."
c = copy.deepcopy
attn = MultiHeadedAttention(h, d_model)
ff = PositionwiseFeedForward(d_model, d_ff, dropout)
position = PositionalEncoding(d_model, dropout)
model = EncoderDecoder(
Encoder(EncoderLayer(d_model, c(attn), c(ff), dropout), N),
Decoder(DecoderLayer(d_model, c(attn), c(attn), c(ff), dropout), N),
nn.Sequential(Embeddings(d_model, src_vocab), c(position)),
nn.Sequential(Embeddings(d_model, tgt_vocab), c(position)),
Generator(d_model, tgt_vocab),
)
# This was important from their code.
# Initialize parameters with Glorot / fan_avg.
for p in model.parameters():
if p.dim() > 1:
nn.init.xavier_uniform_(p)
return model
3 Training¶
3.1 Optimizer¶
We use the Adam optimizer with \(\beta_1=0.9\), \(\beta_2=0.98\) and \(\epsilon=10^{-9}\). We varied the learning rate over the course of training, according to the formula:
This corresponds to increasing the learning rate linearly for the first \(warmup\_steps\) training steps, and decreasing it thereafter proportionally to the inverse square root of the step number.
3.2 Regularization¶
Residual Dropout We apply dropout to the output of each sub-layer, before it is added to the sub-layer input and normalized. In addition, we apply dropout to the sums of the embeddings and the positional encodings in both the encoder and decoder stacks.
Label Smoothing During training, we employed label smoothing of value \(\epsilon_{ls}=0.1\). This hurts perplexity, as the model learns to be more unsure, but improves accuracy and BLEU score.