The Transformer is the first transduction model relying entirely on self-attention to compute representations of its input and output without using sequence aligned RNNs or convolution.
the-annotated-transformer_0_0.png
# !pip install http://download.pytorch.org/whl/cu80/torch-0.3.0.post4-cp36-cp36m-linux_x86_64.whl numpy matplotlib spacy torchtext seaborn
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import math, copy, time
from torch.autograd import Variable
import matplotlib.pyplot as plt
import seaborn
seaborn.set_context(context="talk")
%matplotlib inline
# 模型结构
transformer也是encoder-decoder结构；encoder 将输入(x1,...,x2)映射为连续表征Z=(z1, z_2, ... , z_n)。基于Z，decoder 生成结果(y1, y2, ... , y_m）,但是每次只生成一个结果的元素。每个解码过程都是自回归，需要使用前面的输出结果作为decoder的输出。
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 F.log_softmax(self.proj(x), dim=-1)
Transformer的整体结构是由self-attention和点乘、全连接层堆叠而成的编码器和解码器构成：[图片上传中...(subsequentMask.png-4c75d9-1661848712265-0)]
the-annotated-transformer_14_0.png
# 编码器和解码器堆叠：
## 编码器：
编码器由6个相同的层堆叠而成：
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)
单个encoder的两个子层利用残差连接，后面接一个层标准化。
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
encode每个子层结果是LayerNorm(x + Sublayer(x))。Sublayer(x) 表示子层,在加上输入x和标准化之前添加dropout。
子层
每一层都有两个子层，第一层是multi-head self-attentio，第二层采用全连接前馈网络层。
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
Decoder也由6个相同的层堆叠而成。
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)
每个子层比encoder 多了一层--multi-head attention over the output of the encoder stack。其它的与encoder差不多。
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)
self-attention 子层有所修改，预测某个位置输出，就不使用该位置之后的输出信息,之后的信息需要隐藏掉。
def subsequent_mask(size):
"Mask out subsequent positions."
attn_shape = (1, size, size)
subsequent_mask = np.triu(np.ones(attn_shape), k=1).astype('uint8')
return torch.from_numpy(subsequent_mask) == 0
Below the attention mask shows the position each tgt word (row) is allowed to look at (column). Words are blocked for attending to future words during training.
from pylab import xticks,yticks,np
plt.figure(figsize=(5,5))
xticks(np.linspace(0,9,10,endpoint=True))
yticks(np.linspace(1,10,10,endpoint=True))
plt.imshow(subsequent_mask(10)[0])
subsequentMask.png
## Attention
Attention就是将一个query和一组key-value对映射到输出输出，输出为value的加权和，其中每个value的权重通过query与相应key计算的。
这儿的attention 就是 “Scaled Dot-Product Attention”.
the-annotated-transformer_33_0.png
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 = F.softmax(scores, dim = -1)
if dropout is not None:
p_attn = dropout(p_attn)
return torch.matmul(p_attn, value), p_attn
两种最常用的注意力函数是相加注意力和点乘（乘法）注意力。这儿使用的点乘注意力机制。
虽然两者在理论复杂度上相似，但在实践中，点积关注速度更快，空间效率更高，因为它可以使用高度优化的矩阵乘法代码实现。
d_k 小的时候，二者差异不大，但是 d_k 打的时候，点积大幅度增长，将softmax函数推向具有极小梯度的区域,造成梯度消失。为了抵消这种影响，将点积缩小
## Multi-head attention
多头注意力机制允许模型在不同位置关注来自不同表示子空间的信息。
在这儿使用h=8的并行attention机制, d_k=d_v=d_model/h=64
由于每个头部的维数减小，总计算成本与全维单头部注意力的计算成本相似。
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 = \
[l(x).view(nbatches, -1, self.h, self.d_k).transpose(1, 2)
for l, 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)
return self.linears[-1](x)
## 注意力在我们Transformer 中的应用
- 在encoder-decoder attention层中，queries来自decoder层，而keys和values来自encoder的输出。这使得decoder中的每个位置都能关注到输入序列中的所有位置。
- encoder中self-attention层。在self-attention层中，所有key，value和query来自同一个地方，即encoder中前一层的输出。在这种情况下，encoder中的每个位置都可以关注到encoder上一层的所有位置。
- decoder中的self-attention层允许decoder中的每个位置都关注decoder层中当前位置之前的所有位置。
## 前馈神经网络
除了子层之外，编码器和解码器中的每个层都包含一个完全连接的前馈网络，该网络分别应用于相同位置。FFN包括两个线性变换，中间有一个ReLU激活。
虽然线性变换在不同位置上是相同的，但它们在不同层之间使用不同的参数。
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()))
## Embeddings and Softmax
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)
## 位置编码
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 + Variable(self.pe[:, :x.size(1)],
requires_grad=False)
return self.dropout(x)
plt.figure(figsize=(15, 5))
pe = PositionalEncoding(20, 0)
y = pe.forward(Variable(torch.zeros(1, 100, 20)))
plt.plot(np.arange(100), y[0, :, 4:8].data.numpy())
plt.legend(["dim %d"%p for p in [4,5,6,7]])
6ba09324272b45b39f40b246ff841ae3.png
## 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
# Small example model.
tmp_model = make_model(10, 10, 1)
None
EncoderDecoder(
(encoder): Encoder(
(layers): ModuleList(
(0): EncoderLayer(
(self_attn): MultiHeadedAttention(
(linears): ModuleList(
(0): Linear(in_features=512, out_features=512, bias=True)
(1): Linear(in_features=512, out_features=512, bias=True)
(2): Linear(in_features=512, out_features=512, bias=True)
(3): Linear(in_features=512, out_features=512, bias=True)
)
(dropout): Dropout(p=0.1, inplace=False)
)
(feed_forward): PositionwiseFeedForward(
(w_1): Linear(in_features=512, out_features=2048, bias=True)
(w_2): Linear(in_features=2048, out_features=512, bias=True)
(dropout): Dropout(p=0.1, inplace=False)
)
(sublayer): ModuleList(
(0): SublayerConnection(
(norm): LayerNorm()
(dropout): Dropout(p=0.1, inplace=False)
)
(1): SublayerConnection(
(norm): LayerNorm()
(dropout): Dropout(p=0.1, inplace=False)
)
)
)
)
(norm): LayerNorm()
)
(decoder): Decoder(
(layers): ModuleList(
(0): DecoderLayer(
(self_attn): MultiHeadedAttention(
(linears): ModuleList(
(0): Linear(in_features=512, out_features=512, bias=True)
(1): Linear(in_features=512, out_features=512, bias=True)
(2): Linear(in_features=512, out_features=512, bias=True)
(3): Linear(in_features=512, out_features=512, bias=True)
)
(dropout): Dropout(p=0.1, inplace=False)
)
(src_attn): MultiHeadedAttention(
(linears): ModuleList(
(0): Linear(in_features=512, out_features=512, bias=True)
(1): Linear(in_features=512, out_features=512, bias=True)
(2): Linear(in_features=512, out_features=512, bias=True)
(3): Linear(in_features=512, out_features=512, bias=True)
)
(dropout): Dropout(p=0.1, inplace=False)
)
(feed_forward): PositionwiseFeedForward(
(w_1): Linear(in_features=512, out_features=2048, bias=True)
(w_2): Linear(in_features=2048, out_features=512, bias=True)
(dropout): Dropout(p=0.1, inplace=False)
)
(sublayer): ModuleList(
(0): SublayerConnection(
(norm): LayerNorm()
(dropout): Dropout(p=0.1, inplace=False)
)
(1): SublayerConnection(
(norm): LayerNorm()
(dropout): Dropout(p=0.1, inplace=False)
)
(2): SublayerConnection(
(norm): LayerNorm()
(dropout): Dropout(p=0.1, inplace=False)
)
)
)
)
(norm): LayerNorm()
)
(src_embed): Sequential(
(0): Embeddings(
(lut): Embedding(10, 512)
)
(1): PositionalEncoding(
(dropout): Dropout(p=0.1, inplace=False)
)
)
(tgt_embed): Sequential(
(0): Embeddings(
(lut): Embedding(10, 512)
)
(1): PositionalEncoding(
(dropout): Dropout(p=0.1, inplace=False)
)
)
(generator): Generator(
(proj): Linear(in_features=512, out_features=10, bias=True)
)
)
# 原文
The Annotated Transformer