动手学深度学习-机器翻译及相关技术；注意力机制与Seq2seq模型；Transformer
今天学习了机器翻译及相关技术、注意力机制与Seq2seq模型、Transformer这三节的内容，特来打卡。
一、机器翻译及相关技术
机器翻译（MT）：将一段文本从一种语言自动翻译为另一种语言，用神经网络解决这个问题通常称为神经机器翻译（NMT）。
主要特征：输出是单词序列而不是单个单词。 输出序列的长度可能与源序列的长度不同。
import os
os.listdir('/home/kesci/input/')
['fraeng6506', 'd2l9528']
import sys
sys.path.append('/home/kesci/input/d2l9528/')
import collections
import d2l
import zipfile
from d2l.data.base import Vocab
import time
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils import data
from torch import optim
数据预处理
将数据集清洗、转化为神经网络的输入minbatch
步骤有：去乱码、去大小写、单词与标点之间加空格
下面给出一个例子
with open('/home/kesci/input/fraeng6506/fra.txt', 'r') as f:
raw_text = f.read()
print(raw_text[0:1000])
Go. Va ! CC-BY 2.0 (France) Attribution: tatoeba.org #2877272 (CM) & #1158250 (Wittydev)
Hi. Salut ! CC-BY 2.0 (France) Attribution: tatoeba.org #538123 (CM) & #509819 (Aiji)
Hi. Salut. CC-BY 2.0 (France) Attribution: tatoeba.org #538123 (CM) & #4320462 (gillux)
Run! Cours ! CC-BY 2.0 (France) Attribution: tatoeba.org #906328 (papabear) & #906331 (sacredceltic)
Run! Courez ! CC-BY 2.0 (France) Attribution: tatoeba.org #906328 (papabear) & #906332 (sacredceltic)
Who? Qui ? CC-BY 2.0 (France) Attribution: tatoeba.org #2083030 (CK) & #4366796 (gillux)
Wow! Ça alors ! CC-BY 2.0 (France) Attribution: tatoeba.org #52027 (Zifre) & #374631 (zmoo)
Fire! Au feu ! CC-BY 2.0 (France) Attribution: tatoeba.org #1829639 (Spamster) & #4627939 (sacredceltic)
Help! À l'aide ! CC-BY 2.0 (France) Attribution: tatoeba.org #435084 (lukaszpp) & #128430 (sysko)
Jump. Saute. CC-BY 2.0 (France) Attribution: tatoeba.org #631038 (Shishir) & #2416938 (Phoenix)
Stop! Ça suffit ! CC-BY 2.0 (France) Attribution: tato
def preprocess_raw(text):
text = text.replace('\u202f', ' ').replace('\xa0', ' ')
out = ''
for i, char in enumerate(text.lower()):
if char in (',', '!', '.') and i > 0 and text[i-1] != ' ':
out += ' '
out += char
return out
text = preprocess_raw(raw_text)
print(text[0:1000])
go . va ! cc-by 2 .0 (france) attribution: tatoeba .org #2877272 (cm) & #1158250 (wittydev)
hi . salut ! cc-by 2 .0 (france) attribution: tatoeba .org #538123 (cm) & #509819 (aiji)
hi . salut . cc-by 2 .0 (france) attribution: tatoeba .org #538123 (cm) & #4320462 (gillux)
run ! cours ! cc-by 2 .0 (france) attribution: tatoeba .org #906328 (papabear) & #906331 (sacredceltic)
run ! courez ! cc-by 2 .0 (france) attribution: tatoeba .org #906328 (papabear) & #906332 (sacredceltic)
who? qui ? cc-by 2 .0 (france) attribution: tatoeba .org #2083030 (ck) & #4366796 (gillux)
wow ! ça alors ! cc-by 2 .0 (france) attribution: tatoeba .org #52027 (zifre) & #374631 (zmoo)
fire ! au feu ! cc-by 2 .0 (france) attribution: tatoeba .org #1829639 (spamster) & #4627939 (sacredceltic)
help ! à l'aide ! cc-by 2 .0 (france) attribution: tatoeba .org #435084 (lukaszpp) & #128430 (sysko)
jump . saute . cc-by 2 .0 (france) attribution: tatoeba .org #631038 (shishir) & #2416938 (phoenix)
stop ! ça suffit ! cc-b
字符在计算机里是以编码的形式存在，我们通常所用的空格是 \x20 ，是在标准ASCII可见字符 0x20~0x7e 范围内。
而 \xa0 属于 latin1 （ISO/IEC_8859-1）中的扩展字符集字符，代表不间断空白符nbsp(non-breaking space)，超出gbk编码范围，是需要去除的特殊字符。再数据预处理的过程中，我们首先需要对数据进行清洗。
分词
字符串—单词组成的列表
num_examples = 50000
source, target = [], []
for i, line in enumerate(text.split('\n')):
if i > num_examples:
break
parts = line.split('\t')
if len(parts) >= 2:
source.append(parts[0].split(' '))
target.append(parts[1].split(' '))
source[0:3], target[0:3]
([['go', '.'], ['hi', '.'], ['hi', '.']],
[['va', '!'], ['salut', '!'], ['salut', '.']])
d2l.set_figsize()
d2l.plt.hist([[len(l) for l in source], [len(l) for l in target]],label=['source', 'target'])
d2l.plt.legend(loc='upper right');
建立词典
单词组成的列表—单词id组成的列表
特殊符号：补足
def build_vocab(tokens):
tokens = [token for line in tokens for token in line]
return d2l.data.base.Vocab(tokens, min_freq=3, use_special_tokens=True)
src_vocab = build_vocab(source)
len(src_vocab)
3789
载入数据集
def pad(line, max_len, padding_token):
if len(line) > max_len:
return line[:max_len]
return line + [padding_token] * (max_len - len(line))
pad(src_vocab[source[0]], 10, src_vocab.pad)
[38, 4, 0, 0, 0, 0, 0, 0, 0, 0]
def build_array(lines, vocab, max_len, is_source):
lines = [vocab[line] for line in lines]
if not is_source:
lines = [[vocab.bos] + line + [vocab.eos] for line in lines]
array = torch.tensor([pad(line, max_len, vocab.pad) for line in lines])
valid_len = (array != vocab.pad).sum(1) #第一个维度
return array, valid_len
def load_data_nmt(batch_size, max_len): # This function is saved in d2l.
src_vocab, tgt_vocab = build_vocab(source), build_vocab(target)
src_array, src_valid_len = build_array(source, src_vocab, max_len, True)
tgt_array, tgt_valid_len = build_array(target, tgt_vocab, max_len, False)
train_data = data.TensorDataset(src_array, src_valid_len, tgt_array, tgt_valid_len)
train_iter = data.DataLoader(train_data, batch_size, shuffle=True)
return src_vocab, tgt_vocab, train_iter
src_vocab, tgt_vocab, train_iter = load_data_nmt(batch_size=2, max_len=8)
for X, X_valid_len, Y, Y_valid_len, in train_iter:
print('X =', X.type(torch.int32), '\nValid lengths for X =', X_valid_len,
'\nY =', Y.type(torch.int32), '\nValid lengths for Y =', Y_valid_len)
break
X = tensor([[ 101, 248, 7, 635, 4, 0, 0, 0],
[ 12, 2129, 957, 4, 0, 0, 0, 0]], dtype=torch.int32)
Valid lengths for X = tensor([5, 4])
Y = tensor([[ 1, 244, 8, 41, 12, 729, 4, 2],
[ 1, 15, 3, 2955, 1806, 4, 2, 0]], dtype=torch.int32)
Valid lengths for Y = tensor([8, 7])
机器翻译的难度：输入与输出不是等长的。
Encoder-Decoder
encoder：输入到隐藏状态
decoder：隐藏状态到输出
class Encoder(nn.Module):
def __init__(self, **kwargs):
super(Encoder, self).__init__(**kwargs)
def forward(self, X, *args):
raise NotImplementedError
class Decoder(nn.Module):
def __init__(self, **kwargs):
super(Decoder, self).__init__(**kwargs)
def init_state(self, enc_outputs, *args):
raise NotImplementedError
def forward(self, X, state):
raise NotImplementedError
class EncoderDecoder(nn.Module):
def __init__(self, encoder, decoder, **kwargs):
super(EncoderDecoder, self).__init__(**kwargs)
self.encoder = encoder
self.decoder = decoder
def forward(self, enc_X, dec_X, *args):
enc_outputs = self.encoder(enc_X, *args)
dec_state = self.decoder.init_state(enc_outputs, *args)
return self.decoder(dec_X, dec_state)
可以应用在对话系统、生成式任务中。
Sequence to Sequence模型
从不知道几个单词的输入到不知道几个单词的输出。
模型：
训练
预测
具体结构：
Encoder
class Seq2SeqEncoder(d2l.Encoder):
def __init__(self, vocab_size, embed_size, num_hiddens, num_layers,
dropout=0, **kwargs):
super(Seq2SeqEncoder, self).__init__(**kwargs)
self.num_hiddens=num_hiddens
self.num_layers=num_layers
self.embedding = nn.Embedding(vocab_size, embed_size)
self.rnn = nn.LSTM(embed_size,num_hiddens, num_layers, dropout=dropout)
def begin_state(self, batch_size, device):
return [torch.zeros(size=(self.num_layers, batch_size, self.num_hiddens), device=device),
torch.zeros(size=(self.num_layers, batch_size, self.num_hiddens), device=device)]
def forward(self, X, *args):
X = self.embedding(X) # X shape: (batch_size, seq_len, embed_size)
X = X.transpose(0, 1) # RNN needs first axes to be time
# state = self.begin_state(X.shape[1], device=X.device)
out, state = self.rnn(X)
# The shape of out is (seq_len, batch_size, num_hiddens).
# state contains the hidden state and the memory cell
# of the last time step, the shape is (num_layers, batch_size, num_hiddens)
return out, state
encoder = Seq2SeqEncoder(vocab_size=10, embed_size=8,num_hiddens=16, num_layers=2)
X = torch.zeros((4, 7),dtype=torch.long)
output, state = encoder(X)
output.shape, len(state), state[0].shape, state[1].shape
(torch.Size([7, 4, 16]), 2, torch.Size([2, 4, 16]), torch.Size([2, 4, 16]))
Decoder
class Seq2SeqDecoder(d2l.Decoder):
def __init__(self, vocab_size, embed_size, num_hiddens, num_layers,
dropout=0, **kwargs):
super(Seq2SeqDecoder, self).__init__(**kwargs)
self.embedding = nn.Embedding(vocab_size, embed_size)
self.rnn = nn.LSTM(embed_size,num_hiddens, num_layers, dropout=dropout)
self.dense = nn.Linear(num_hiddens,vocab_size)
def init_state(self, enc_outputs, *args):
return enc_outputs[1]
def forward(self, X, state):
X = self.embedding(X).transpose(0, 1)
out, state = self.rnn(X, state)
# Make the batch to be the first dimension to simplify loss computation.
out = self.dense(out).transpose(0, 1)
return out, state
decoder = Seq2SeqDecoder(vocab_size=10, embed_size=8,num_hiddens=16, num_layers=2)
state = decoder.init_state(encoder(X))
out, state = decoder(X, state)
out.shape, len(state), state[0].shape, state[1].shape
(torch.Size([4, 7, 10]), 2, torch.Size([2, 4, 16]), torch.Size([2, 4, 16]))
损失函数
def SequenceMask(X, X_len,value=0):
maxlen = X.size(1)
mask = torch.arange(maxlen)[None, :].to(X_len.device) < X_len[:, None]
X[~mask]=value
return X
X = torch.tensor([[1,2,3], [4,5,6]])
SequenceMask(X,torch.tensor([1,2]))
tensor([[1, 0, 0],
[4, 5, 0]])
X = torch.ones((2,3, 4))
SequenceMask(X, torch.tensor([1,2]),value=-1)
tensor([[[ 1., 1., 1., 1.],
[-1., -1., -1., -1.],
[-1., -1., -1., -1.]],
[[ 1., 1., 1., 1.],
[ 1., 1., 1., 1.],
[-1., -1., -1., -1.]]])
class MaskedSoftmaxCELoss(nn.CrossEntropyLoss):
# pred shape: (batch_size, seq_len, vocab_size)
# label shape: (batch_size, seq_len)
# valid_length shape: (batch_size, )
def forward(self, pred, label, valid_length):
# the sample weights shape should be (batch_size, seq_len)
weights = torch.ones_like(label)
weights = SequenceMask(weights, valid_length).float()
self.reduction='none'
output=super(MaskedSoftmaxCELoss, self).forward(pred.transpose(1,2), label)
return (output*weights).mean(dim=1)
loss = MaskedSoftmaxCELoss()
loss(torch.ones((3, 4, 10)), torch.ones((3,4),dtype=torch.long), torch.tensor([4,3,0]))
tensor([2.3026, 1.7269, 0.0000])
训练
def train_ch7(model, data_iter, lr, num_epochs, device): # Saved in d2l
model.to(device)
optimizer = optim.Adam(model.parameters(), lr=lr)
loss = MaskedSoftmaxCELoss()
tic = time.time()
for epoch in range(1, num_epochs+1):
l_sum, num_tokens_sum = 0.0, 0.0
for batch in data_iter:
optimizer.zero_grad()
X, X_vlen, Y, Y_vlen = [x.to(device) for x in batch]
Y_input, Y_label, Y_vlen = Y[:,:-1], Y[:,1:], Y_vlen-1
Y_hat, _ = model(X, Y_input, X_vlen, Y_vlen)
l = loss(Y_hat, Y_label, Y_vlen).sum()
l.backward()
with torch.no_grad():
d2l.grad_clipping_nn(model, 5, device)
num_tokens = Y_vlen.sum().item()
optimizer.step()
l_sum += l.sum().item()
num_tokens_sum += num_tokens
if epoch % 50 == 0:
print("epoch {0:4d},loss {1:.3f}, time {2:.1f} sec".format(
epoch, (l_sum/num_tokens_sum), time.time()-tic))
tic = time.time()
embed_size, num_hiddens, num_layers, dropout = 32, 32, 2, 0.0
batch_size, num_examples, max_len = 64, 1e3, 10
lr, num_epochs, ctx = 0.005, 300, d2l.try_gpu()
src_vocab, tgt_vocab, train_iter = d2l.load_data_nmt(
batch_size, max_len,num_examples)
encoder = Seq2SeqEncoder(
len(src_vocab), embed_size, num_hiddens, num_layers, dropout)
decoder = Seq2SeqDecoder(
len(tgt_vocab), embed_size, num_hiddens, num_layers, dropout)
model = d2l.EncoderDecoder(encoder, decoder)
train_ch7(model, train_iter, lr, num_epochs, ctx)
测试
def translate_ch7(model, src_sentence, src_vocab, tgt_vocab, max_len, device):
src_tokens = src_vocab[src_sentence.lower().split(' ')]
src_len = len(src_tokens)
if src_len < max_len:
src_tokens += [src_vocab.pad] * (max_len - src_len)
enc_X = torch.tensor(src_tokens, device=device)
enc_valid_length = torch.tensor([src_len], device=device)
# use expand_dim to add the batch_size dimension.
enc_outputs = model.encoder(enc_X.unsqueeze(dim=0), enc_valid_length)
dec_state = model.decoder.init_state(enc_outputs, enc_valid_length)
dec_X = torch.tensor([tgt_vocab.bos], device=device).unsqueeze(dim=0)
predict_tokens = []
for _ in range(max_len):
Y, dec_state = model.decoder(dec_X, dec_state)
# The token with highest score is used as the next time step input.
dec_X = Y.argmax(dim=2)
py = dec_X.squeeze(dim=0).int().item()
if py == tgt_vocab.eos:
break
predict_tokens.append(py)
return ' '.join(tgt_vocab.to_tokens(predict_tokens))
for sentence in ['Go .', 'Wow !', "I'm OK .", 'I won !']:
print(sentence + ' => ' + translate_ch7(
model, sentence, src_vocab, tgt_vocab, max_len, ctx))
Beam Search
简单greedy search：
维特比算法：选择整体分数最高的句子（搜索空间太大）
集束搜索：
二、注意力机制与Seq2seq模型
在“编码器—解码器（seq2seq）”⼀节⾥，解码器在各个时间步依赖相同的背景变量（context vector）来获取输⼊序列信息。当编码器为循环神经⽹络时，背景变量来⾃它最终时间步的隐藏状态。将源序列输入信息以循环单位状态编码，然后将其传递给解码器以生成目标序列。然而这种结构存在着问题，尤其是RNN机制实际中存在长程梯度消失的问题，对于较长的句子，我们很难寄希望于将输入的序列转化为定长的向量而保存所有的有效信息，所以随着所需翻译句子的长度的增加，这种结构的效果会显著下降。
与此同时，解码的目标词语可能只与原输入的部分词语有关，而并不是与所有的输入有关。例如，当把“Hello world”翻译成“Bonjour le monde”时，“Hello”映射成“Bonjour”，“world”映射成“monde”。在seq2seq模型中，解码器只能隐式地从编码器的最终状态中选择相应的信息。然而，注意力机制可以将这种选择过程显式地建模。
注意力机制框架
Attention 是一种通用的带权池化方法，输入由两部分构成：询问（query）和键值对（key-value pairs）。 X ∈ R l × d X\in \mathbb{R}^{l\times d} X∈Rl×d k i ∈ R d k k_i\in\mathbb{R}^{d_k} ki∈Rdk v i ∈ R d v v_i\in\mathbb{R}^{d_v} vi∈Rdv. Query q ∈ R d q q\in\mathbb{R}^{d_q} q∈Rdq, attention layer得到输出与value的维度一致 o ∈ R d v o \in\mathbb{R}^{d_v} o∈Rdv. 对于一个query来说，attention layer 会与每一个key计算注意力分数并进行权重的归一化，输出的向量 o o o则是value的加权求和，而每个key计算的权重与value一一对应。
为了计算输出，我们首先假设有一个函数 α \alpha α 用于计算query和key的相似性，然后可以计算所有的 attention scores a 1 , … , a n a_1, \ldots, a_n a1,…,an by
a i = α ( q , k i ) . a_i = \alpha(\mathbf q, \mathbf k_i). ai=α(q,ki).
我们使用 softmax函数 获得注意力权重：
b 1 , … , b n = softmax ( a 1 , … , a n ) . b_1, \ldots, b_n = \textrm{softmax}(a_1, \ldots, a_n). b1,…,bn=softmax(a1,…,an).
最终的输出就是value的加权求和：
o = ∑ i = 1 n b i v i . \mathbf o = \sum_{i=1}^n b_i \mathbf v_i. o=i=1∑nbivi.
不同的attetion layer的区别在于score函数的选择，在本节的其余部分，我们将讨论两个常用的注意层 Dot-product Attention 和 Multilayer Perceptron Attention；随后我们将实现一个引入attention的seq2seq模型并在英法翻译语料上进行训练与测试。
import math
import torch
import torch.nn as nn
import os
def file_name_walk(file_dir):
for root, dirs, files in os.walk(file_dir):
# print("root", root) # 当前目录路径
print("dirs", dirs) # 当前路径下所有子目录
print("files", files) # 当前路径下所有非目录子文件
file_name_walk("/home/kesci/input/fraeng6506")
dirs []
files ['_about.txt', 'fra.txt']
Softmax屏蔽
在深入研究实现之前，我们首先介绍softmax操作符的一个屏蔽操作。
def SequenceMask(X, X_len,value=-1e6):
maxlen = X.size(1)
#print(X.size(),torch.arange((maxlen),dtype=torch.float)[None, :],'\n',X_len[:, None] )
mask = torch.arange((maxlen),dtype=torch.float)[None, :] >= X_len[:, None]
#print(mask)
X[mask]=value
return X
def masked_softmax(X, valid_length):
# X: 3-D tensor, valid_length: 1-D or 2-D tensor
softmax = nn.Softmax(dim=-1)
if valid_length is None:
return softmax(X)
else:
shape = X.shape
if valid_length.dim() == 1:
try:
valid_length = torch.FloatTensor(valid_length.numpy().repeat(shape[1], axis=0))#[2,2,3,3]
except:
valid_length = torch.FloatTensor(valid_length.cpu().numpy().repeat(shape[1], axis=0))#[2,2,3,3]
else:
valid_length = valid_length.reshape((-1,))
# fill masked elements with a large negative, whose exp is 0
X = SequenceMask(X.reshape((-1, shape[-1])), valid_length)
return softmax(X).reshape(shape)
masked_softmax(torch.rand((2,2,4),dtype=torch.float), torch.FloatTensor([2,3]))
tensor([[[0.5423, 0.4577, 0.0000, 0.0000],
[0.5290, 0.4710, 0.0000, 0.0000]],
[[0.2969, 0.2966, 0.4065, 0.0000],
[0.3607, 0.2203, 0.4190, 0.0000]]])
超出2维矩阵的乘法
X X X 和 Y Y Y 是维度分别为 ( b , n , m ) (b,n,m) (b,n,m) 和 ( b , m , k ) (b, m, k) (b,m,k)的张量，进行 b b b 次二维矩阵乘法后得到 Z Z Z, 维度为 ( b , n , k ) (b, n, k) (b,n,k)。
Z [ i , : , : ] = d o t ( X [ i , : , : ] , Y [ i , : , : ] ) f o r i = 1 , … , n . Z[i,:,:] = dot(X[i,:,:], Y[i,:,:])\qquad for\ i= 1,…,n\ . Z[i,:,:]=dot(X[i,:,:],Y[i,:,:])for i=1,…,n .
torch.bmm(torch.ones((2,1,3), dtype = torch.float), torch.ones((2,3,2), dtype = torch.float))
tensor([[[3., 3.]],
[[3., 3.]]])
点积注意力
The dot product 假设query和keys有相同的维度, 即 ∀ \forall ∀ i , q , k i ∈ R d i,q,k_i\in\mathbb{R}_d i,q,ki∈Rd. 通过计算query和key转置的乘积来计算attention score,通常还会除去 d \sqrt{d} d 减少计算出来的score对维度的依赖性，如下
α ( q , k ) = < q , k > / d \alpha(q,k)=
假设 Q ∈ R m × d Q\in\mathbb{R}^{m\times d} Q∈Rm×d有 m m m 个query， K ∈ R n × d K\in\mathbb{R}^{n\times d} K∈Rn×d有 n n n 个keys. 我们可以通过矩阵运算的方式计算所有 m n mn mn 个score：
α ( Q , K ) = Q K T / d \alpha(Q,K)=QK^T/\sqrt{d} α(Q,K)=QKT/d
现在让我们实现这个层，它支持一批查询和键值对。此外，它支持作为正则化随机删除一些注意力权重.
# Save to the d2l package.
class DotProductAttention(nn.Module):
def __init__(self, dropout, **kwargs):
super(DotProductAttention, self).__init__(**kwargs)
self.dropout = nn.Dropout(dropout)
# query: (batch_size, #queries, d)
# key: (batch_size, #kv_pairs, d)
# value: (batch_size, #kv_pairs, dim_v)
# valid_length: either (batch_size, ) or (batch_size, xx)
def forward(self, query, key, value, valid_length=None):
d = query.shape[-1]
# set transpose_b=True to swap the last two dimensions of key
scores = torch.bmm(query, key.transpose(1,2)) / math.sqrt(d)
attention_weights = self.dropout(masked_softmax(scores, valid_length))
print("attention_weight\n",attention_weights)
return torch.bmm(attention_weights, value)
测试
现在我们创建了两个批，每个批有一个query和10个key-values对。我们通过valid_length指定，对于第一批，我们只关注前2个键-值对，而对于第二批，我们将检查前6个键-值对。因此，尽管这两个批处理具有相同的查询和键值对，但我们获得的输出是不同的。
atten = DotProductAttention(dropout=0)
keys = torch.ones((2,10,2),dtype=torch.float)
values = torch.arange((40), dtype=torch.float).view(1,10,4).repeat(2,1,1)
atten(torch.ones((2,1,2),dtype=torch.float), keys, values, torch.FloatTensor([2, 6]))
attention_weight
tensor([[[0.5000, 0.5000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
0.0000, 0.0000]],
[[0.1667, 0.1667, 0.1667, 0.1667, 0.1667, 0.1667, 0.0000, 0.0000,
0.0000, 0.0000]]])
tensor([[[ 2.0000, 3.0000, 4.0000, 5.0000]],
[[10.0000, 11.0000, 12.0000, 13.0000]]])
多层感知机注意力
在多层感知器中，我们首先将 query and keys 投影到 R h \mathbb{R}^ℎ Rh .为了更具体，我们将可以学习的参数做如下映射 W k ∈ R h × d k W_k\in\mathbb{R}^{h\times d_k} Wk∈Rh×dk, W q ∈ R h × d q W_q\in\mathbb{R}^{h\times d_q} Wq∈Rh×dq, and v ∈ R h v\in\mathbb{R}^h v∈Rh. 将score函数定义
α ( k , q ) = v T t a n h ( W k k + W q q ) \alpha(k,q)=v^Ttanh(W_kk+W_qq) α(k,q)=vTtanh(Wkk+Wqq).
然后将key 和 value 在特征的维度上合并（concatenate），然后送至 a single hidden layer perceptron 这层中 hidden layer 为 ℎ and 输出的size为 1 .隐层激活函数为tanh，无偏置.
# Save to the d2l package.
class MLPAttention(nn.Module):
def __init__(self, units,ipt_dim,dropout, **kwargs):
super(MLPAttention, self).__init__(**kwargs)
# Use flatten=True to keep query's and key's 3-D shapes.
self.W_k = nn.Linear(ipt_dim, units, bias=False)
self.W_q = nn.Linear(ipt_dim, units, bias=False)
self.v = nn.Linear(units, 1, bias=False)
self.dropout = nn.Dropout(dropout)
def forward(self, query, key, value, valid_length):
query, key = self.W_k(query), self.W_q(key)
#print("size",query.size(),key.size())
# expand query to (batch_size, #querys, 1, units), and key to
# (batch_size, 1, #kv_pairs, units). Then plus them with broadcast.
features = query.unsqueeze(2) + key.unsqueeze(1)
#print("features:",features.size()) #--------------开启
scores = self.v(features).squeeze(-1)
attention_weights = self.dropout(masked_softmax(scores, valid_length))
return torch.bmm(attention_weights, value)
测试
尽管MLPAttention包含一个额外的MLP模型，但如果给定相同的输入和相同的键，我们将获得与DotProductAttention相同的输出
atten = MLPAttention(ipt_dim=2,units = 8, dropout=0)
atten(torch.ones((2,1,2), dtype = torch.float), keys, values, torch.FloatTensor([2, 6]))
tensor([[[ 2.0000, 3.0000, 4.0000, 5.0000]],
[[10.0000, 11.0000, 12.0000, 13.0000]]], grad_fn=)
总结
- 注意力层显式地选择相关的信息。
- 注意层的内存由键-值对组成，因此它的输出接近于键类似于查询的值。
引入注意力机制的Seq2seq模型
本节中将注意机制添加到sequence to sequence 模型中，以显式地使用权重聚合states。下图展示encoding 和decoding的模型结构，在时间步为t的时候。此刻attention layer保存着encodering看到的所有信息——即encoding的每一步输出。在decoding阶段，解码器的 t t t时刻的隐藏状态被当作query，encoder的每个时间步的hidden states作为key和value进行attention聚合. Attetion model的输出当作成上下文信息context vector，并与解码器输入 D t D_t Dt拼接起来一起送到解码器：
F i g 1 具 有 注 意 机 制 的 s e q − t o − s e q 模 型 解 码 的 第 二 步 Fig1具有注意机制的seq-to-seq模型解码的第二步 Fig1具有注意机制的seq−to−seq模型解码的第二步
下图展示了seq2seq机制的所以层的关系，下面展示了encoder和decoder的layer结构
F i g 2 具 有 注 意 机 制 的 s e q − t o − s e q 模 型 中 层 结 构 Fig2具有注意机制的seq-to-seq模型中层结构 Fig2具有注意机制的seq−to−seq模型中层结构
import sys
sys.path.append('/home/kesci/input/d2len9900')
import d2l
解码器
由于带有注意机制的seq2seq的编码器与之前章节中的Seq2SeqEncoder相同，所以在此处我们只关注解码器。我们添加了一个MLP注意层(MLPAttention)，它的隐藏大小与解码器中的LSTM层相同。然后我们通过从编码器传递三个参数来初始化解码器的状态:
-
the encoder outputs of all timesteps：encoder输出的各个状态，被用于attetion layer的memory部分，有相同的key和values
-
the hidden state of the encoder’s final timestep：编码器最后一个时间步的隐藏状态，被用于初始化decoder 的hidden state
-
the encoder valid length: 编码器的有效长度，借此，注意层不会考虑编码器输出中的填充标记（Paddings）
在解码的每个时间步，我们使用解码器的最后一个RNN层的输出作为注意层的query。然后，将注意力模型的输出与输入嵌入向量连接起来，输入到RNN层。虽然RNN层隐藏状态也包含来自解码器的历史信息，但是attention model的输出显式地选择了enc_valid_len以内的编码器输出，这样attention机制就会尽可能排除其他不相关的信息。
class Seq2SeqAttentionDecoder(d2l.Decoder):
def __init__(self, vocab_size, embed_size, num_hiddens, num_layers,
dropout=0, **kwargs):
super(Seq2SeqAttentionDecoder, self).__init__(**kwargs)
self.attention_cell = MLPAttention(num_hiddens,num_hiddens, dropout)
self.embedding = nn.Embedding(vocab_size, embed_size)
self.rnn = nn.LSTM(embed_size+ num_hiddens,num_hiddens, num_layers, dropout=dropout)
self.dense = nn.Linear(num_hiddens,vocab_size)
def init_state(self, enc_outputs, enc_valid_len, *args):
outputs, hidden_state = enc_outputs
# print("first:",outputs.size(),hidden_state[0].size(),hidden_state[1].size())
# Transpose outputs to (batch_size, seq_len, hidden_size)
return (outputs.permute(1,0,-1), hidden_state, enc_valid_len)
#outputs.swapaxes(0, 1)
def forward(self, X, state):
enc_outputs, hidden_state, enc_valid_len = state
#("X.size",X.size())
X = self.embedding(X).transpose(0,1)
# print("Xembeding.size2",X.size())
outputs = []
for l, x in enumerate(X):
# print(f"\n{l}-th token")
# print("x.first.size()",x.size())
# query shape: (batch_size, 1, hidden_size)
# select hidden state of the last rnn layer as query
query = hidden_state[0][-1].unsqueeze(1) # np.expand_dims(hidden_state[0][-1], axis=1)
# context has same shape as query
# print("query enc_outputs, enc_outputs:\n",query.size(), enc_outputs.size(), enc_outputs.size())
context = self.attention_cell(query, enc_outputs, enc_outputs, enc_valid_len)
# Concatenate on the feature dimension
# print("context.size:",context.size())
x = torch.cat((context, x.unsqueeze(1)), dim=-1)
# Reshape x to (1, batch_size, embed_size+hidden_size)
# print("rnn",x.size(), len(hidden_state))
out, hidden_state = self.rnn(x.transpose(0,1), hidden_state)
outputs.append(out)
outputs = self.dense(torch.cat(outputs, dim=0))
return outputs.transpose(0, 1), [enc_outputs, hidden_state,
enc_valid_len]
现在我们可以用注意力模型来测试seq2seq。为了与第9.7节中的模型保持一致，我们对vocab_size、embed_size、num_hiddens和num_layers使用相同的超参数。结果，我们得到了相同的解码器输出形状，但是状态结构改变了。
encoder = d2l.Seq2SeqEncoder(vocab_size=10, embed_size=8,
num_hiddens=16, num_layers=2)
# encoder.initialize()
decoder = Seq2SeqAttentionDecoder(vocab_size=10, embed_size=8,
num_hiddens=16, num_layers=2)
X = torch.zeros((4, 7),dtype=torch.long)
print("batch size=4\nseq_length=7\nhidden dim=16\nnum_layers=2\n")
print('encoder output size:', encoder(X)[0].size())
print('encoder hidden size:', encoder(X)[1][0].size())
print('encoder memory size:', encoder(X)[1][1].size())
state = decoder.init_state(encoder(X), None)
out, state = decoder(X, state)
out.shape, len(state), state[0].shape, len(state[1]), state[1][0].shape
batch size=4
seq_length=7
hidden dim=16
num_layers=2
encoder output size: torch.Size([7, 4, 16])
encoder hidden size: torch.Size([2, 4, 16])
encoder memory size: torch.Size([2, 4, 16])
(torch.Size([4, 7, 10]), 3, torch.Size([4, 7, 16]), 2, torch.Size([2, 4, 16]))
训练
与第9.7.4节相似，通过应用相同的训练超参数和相同的训练损失来尝试一个简单的娱乐模型。从结果中我们可以看出，由于训练数据集中的序列相对较短，额外的注意层并没有带来显著的改进。由于编码器和解码器的注意层的计算开销，该模型比没有注意的seq2seq模型慢得多。
import zipfile
import torch
import requests
from io import BytesIO
from torch.utils import data
import sys
import collections
class Vocab(object): # This class is saved in d2l.
def __init__(self, tokens, min_freq=0, use_special_tokens=False):
# sort by frequency and token
counter = collections.Counter(tokens)
token_freqs = sorted(counter.items(), key=lambda x: x[0])
token_freqs.sort(key=lambda x: x[1], reverse=True)
if use_special_tokens:
# padding, begin of sentence, end of sentence, unknown
self.pad, self.bos, self.eos, self.unk = (0, 1, 2, 3)
tokens = ['', '', '', '']
else:
self.unk = 0
tokens = ['']
tokens += [token for token, freq in token_freqs if freq >= min_freq]
self.idx_to_token = []
self.token_to_idx = dict()
for token in tokens:
self.idx_to_token.append(token)
self.token_to_idx[token] = len(self.idx_to_token) - 1
def __len__(self):
return len(self.idx_to_token)
def __getitem__(self, tokens):
if not isinstance(tokens, (list, tuple)):
return self.token_to_idx.get(tokens, self.unk)
else:
return [self.__getitem__(token) for token in tokens]
def to_tokens(self, indices):
if not isinstance(indices, (list, tuple)):
return self.idx_to_token[indices]
else:
return [self.idx_to_token[index] for index in indices]
def load_data_nmt(batch_size, max_len, num_examples=1000):
"""Download an NMT dataset, return its vocabulary and data iterator."""
# Download and preprocess
def preprocess_raw(text):
text = text.replace('\u202f', ' ').replace('\xa0', ' ')
out = ''
for i, char in enumerate(text.lower()):
if char in (',', '!', '.') and text[i-1] != ' ':
out += ' '
out += char
return out
with open('/home/kesci/input/fraeng6506/fra.txt', 'r') as f:
raw_text = f.read()
text = preprocess_raw(raw_text)
# Tokenize
source, target = [], []
for i, line in enumerate(text.split('\n')):
if i >= num_examples:
break
parts = line.split('\t')
if len(parts) >= 2:
source.append(parts[0].split(' '))
target.append(parts[1].split(' '))
# Build vocab
def build_vocab(tokens):
tokens = [token for line in tokens for token in line]
return Vocab(tokens, min_freq=3, use_special_tokens=True)
src_vocab, tgt_vocab = build_vocab(source), build_vocab(target)
# Convert to index arrays
def pad(line, max_len, padding_token):
if len(line) > max_len:
return line[:max_len]
return line + [padding_token] * (max_len - len(line))
def build_array(lines, vocab, max_len, is_source):
lines = [vocab[line] for line in lines]
if not is_source:
lines = [[vocab.bos] + line + [vocab.eos] for line in lines]
array = torch.tensor([pad(line, max_len, vocab.pad) for line in lines])
valid_len = (array != vocab.pad).sum(1)
return array, valid_len
src_vocab, tgt_vocab = build_vocab(source), build_vocab(target)
src_array, src_valid_len = build_array(source, src_vocab, max_len, True)
tgt_array, tgt_valid_len = build_array(target, tgt_vocab, max_len, False)
train_data = data.TensorDataset(src_array, src_valid_len, tgt_array, tgt_valid_len)
train_iter = data.DataLoader(train_data, batch_size, shuffle=True)
return src_vocab, tgt_vocab, train_iter
embed_size, num_hiddens, num_layers, dropout = 32, 32, 2, 0.0
batch_size, num_steps = 64, 10
lr, num_epochs, ctx = 0.005, 500, d2l.try_gpu()
src_vocab, tgt_vocab, train_iter = load_data_nmt(batch_size, num_steps)
encoder = d2l.Seq2SeqEncoder(
len(src_vocab), embed_size, num_hiddens, num_layers, dropout)
decoder = Seq2SeqAttentionDecoder(
len(tgt_vocab), embed_size, num_hiddens, num_layers, dropout)
model = d2l.EncoderDecoder(encoder, decoder)
训练和预测
d2l.train_s2s_ch9(model, train_iter, lr, num_epochs, ctx)
epoch 50,loss 0.104, time 54.7 sec
epoch 100,loss 0.046, time 54.8 sec
epoch 150,loss 0.031, time 54.7 sec
epoch 200,loss 0.027, time 54.3 sec
epoch 250,loss 0.025, time 54.3 sec
epoch 300,loss 0.024, time 54.4 sec
epoch 350,loss 0.024, time 54.4 sec
epoch 400,loss 0.024, time 54.5 sec
epoch 450,loss 0.023, time 54.4 sec
epoch 500,loss 0.023, time 54.7 sec
for sentence in ['Go .', 'Good Night !', "I'm OK .", 'I won !']:
print(sentence + ' => ' + d2l.predict_s2s_ch9(
model, sentence, src_vocab, tgt_vocab, num_steps, ctx))
Go . => va !
Good Night ! => !
I'm OK . => ça va .
I won ! => j'ai gagné !
三、Transformer
在之前的章节中，我们已经介绍了主流的神经网络架构如卷积神经网络（CNNs）和循环神经网络（RNNs）。让我们进行一些回顾：
- CNNs 易于并行化，却不适合捕捉变长序列内的依赖关系。
- RNNs 适合捕捉长距离变长序列的依赖，但是却难以实现并行化处理序列。
为了整合CNN和RNN的优势，[Vaswani et al., 2017] 创新性地使用注意力机制设计了Transformer模型。该模型利用attention机制实现了并行化捕捉序列依赖，并且同时处理序列的每个位置的tokens，上述优势使得Transformer模型在性能优异的同时大大减少了训练时间。
图10.3.1展示了Transformer模型的架构，与9.7节的seq2seq模型相似，Transformer同样基于编码器-解码器架构，其区别主要在于以下三点：
- Transformer blocks：将seq2seq模型重的循环网络替换为了Transformer Blocks，该模块包含一个多头注意力层（Multi-head Attention Layers）以及两个position-wise feed-forward networks（FFN）。对于解码器来说，另一个多头注意力层被用于接受编码器的隐藏状态。
- Add and norm：多头注意力层和前馈网络的输出被送到两个“add and norm”层进行处理，该层包含残差结构以及层归一化。
- Position encoding：由于自注意力层并没有区分元素的顺序，所以一个位置编码层被用于向序列元素里添加位置信息。
F i g . 10.3.1 T r a n s f o r m e r 架 构 . Fig.10.3.1\ Transformer 架构. Fig.10.3.1 Transformer架构.
在接下来的部分，我们将会带领大家实现Transformer里全新的子结构，并且构建一个神经机器翻译模型用以训练和测试。
import os
import math
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import sys
sys.path.append('/home/kesci/input/d2len9900')
import d2l
以下是复制了上一小节中 masked softmax 实现，这里就不再赘述了。
def SequenceMask(X, X_len,value=-1e6):
maxlen = X.size(1)
X_len = X_len.to(X.device)
#print(X.size(),torch.arange((maxlen),dtype=torch.float)[None, :],'\n',X_len[:, None] )
mask = torch.arange((maxlen), dtype=torch.float, device=X.device)
mask = mask[None, :] < X_len[:, None]
#print(mask)
X[~mask]=value
return X
def masked_softmax(X, valid_length):
# X: 3-D tensor, valid_length: 1-D or 2-D tensor
softmax = nn.Softmax(dim=-1)
if valid_length is None:
return softmax(X)
else:
shape = X.shape
if valid_length.dim() == 1:
try:
valid_length = torch.FloatTensor(valid_length.numpy().repeat(shape[1], axis=0))#[2,2,3,3]
except:
valid_length = torch.FloatTensor(valid_length.cpu().numpy().repeat(shape[1], axis=0))#[2,2,3,3]
else:
valid_length = valid_length.reshape((-1,))
# fill masked elements with a large negative, whose exp is 0
X = SequenceMask(X.reshape((-1, shape[-1])), valid_length)
return softmax(X).reshape(shape)
# Save to the d2l package.
class DotProductAttention(nn.Module):
def __init__(self, dropout, **kwargs):
super(DotProductAttention, self).__init__(**kwargs)
self.dropout = nn.Dropout(dropout)
# query: (batch_size, #queries, d)
# key: (batch_size, #kv_pairs, d)
# value: (batch_size, #kv_pairs, dim_v)
# valid_length: either (batch_size, ) or (batch_size, xx)
def forward(self, query, key, value, valid_length=None):
d = query.shape[-1]
# set transpose_b=True to swap the last two dimensions of key
scores = torch.bmm(query, key.transpose(1,2)) / math.sqrt(d)
attention_weights = self.dropout(masked_softmax(scores, valid_length))
return torch.bmm(attention_weights, value)
多头注意力层
在我们讨论多头注意力层之前，先来迅速理解以下自注意力（self-attention）的结构。自注意力模型是一个正规的注意力模型，序列的每一个元素对应的key，value，query是完全一致的。如图10.3.2 自注意力输出了一个与输入长度相同的表征序列，与循环神经网络相比，自注意力对每个元素输出的计算是并行的，所以我们可以高效的实现这个模块。
F i g . 10.3.2 自 注 意 力 结 构 Fig.10.3.2\ 自注意力结构 Fig.10.3.2 自注意力结构
多头注意力层包含 h h h个并行的自注意力层，每一个这种层被成为一个head。对每个头来说，在进行注意力计算之前，我们会将query、key和value用三个现行层进行映射，这 h h h个注意力头的输出将会被拼接之后输入最后一个线性层进行整合。
F i g . 10.3.3 多 头 注 意 力 Fig.10.3.3\ 多头注意力 Fig.10.3.3 多头注意力
假设query，key和value的维度分别是 d q d_q dq、 d k d_k dk和 d v d_v dv。那么对于每一个头 i = 1 , … , h i=1,\ldots,h i=1,…,h，我们可以训练相应的模型权重 W q ( i ) ∈ R p q × d q W_q^{(i)} \in \mathbb{R}^{p_q\times d_q} Wq(i)∈Rpq×dq、 W k ( i ) ∈ R p k × d k W_k^{(i)} \in \mathbb{R}^{p_k\times d_k} Wk(i)∈Rpk×dk和 W v ( i ) ∈ R p v × d v W_v^{(i)} \in \mathbb{R}^{p_v\times d_v} Wv(i)∈Rpv×dv，以得到每个头的输出：
o ( i ) = a t t e n t i o n ( W q ( i ) q , W k ( i ) k , W v ( i ) v ) o^{(i)} = attention(W_q^{(i)}q, W_k^{(i)}k, W_v^{(i)}v) o(i)=attention(Wq(i)q,Wk(i)k,Wv(i)v)
这里的attention可以是任意的attention function，比如前一节介绍的dot-product attention以及MLP attention。之后我们将所有head对应的输出拼接起来，送入最后一个线性层进行整合，这个层的权重可以表示为 W o ∈ R d 0 × h p v W_o\in \mathbb{R}^{d_0 \times hp_v} Wo∈Rd0×hpv
o = W o [ o ( 1 ) , … , o ( h ) ] o = W_o[o^{(1)}, \ldots, o^{(h)}] o=Wo[o(1),…,o(h)]
接下来我们就可以来实现多头注意力了，假设我们有h个头，隐藏层权重 h i d d e n _ s i z e = p q = p k = p v hidden\_size = p_q = p_k = p_v hidden_size=pq=pk=pv 与query，key，value的维度一致。除此之外，因为多头注意力层保持输入与输出张量的维度不变，所以输出feature的维度也设置为 d 0 = h i d d e n _ s i z e d_0 = hidden\_size d0=hidden_size。
class MultiHeadAttention(nn.Module):
def __init__(self, input_size, hidden_size, num_heads, dropout, **kwargs):
super(MultiHeadAttention, self).__init__(**kwargs)
self.num_heads = num_heads
self.attention = DotProductAttention(dropout)
self.W_q = nn.Linear(input_size, hidden_size, bias=False)
self.W_k = nn.Linear(input_size, hidden_size, bias=False)
self.W_v = nn.Linear(input_size, hidden_size, bias=False)
self.W_o = nn.Linear(hidden_size, hidden_size, bias=False)
def forward(self, query, key, value, valid_length):
# query, key, and value shape: (batch_size, seq_len, dim),
# where seq_len is the length of input sequence
# valid_length shape is either (batch_size, )
# or (batch_size, seq_len).
# Project and transpose query, key, and value from
# (batch_size, seq_len, hidden_size * num_heads) to
# (batch_size * num_heads, seq_len, hidden_size).
query = transpose_qkv(self.W_q(query), self.num_heads)
key = transpose_qkv(self.W_k(key), self.num_heads)
value = transpose_qkv(self.W_v(value), self.num_heads)
if valid_length is not None:
# Copy valid_length by num_heads times
device = valid_length.device
valid_length = valid_length.cpu().numpy() if valid_length.is_cuda else valid_length.numpy()
if valid_length.ndim == 1:
valid_length = torch.FloatTensor(np.tile(valid_length, self.num_heads))
else:
valid_length = torch.FloatTensor(np.tile(valid_length, (self.num_heads,1)))
valid_length = valid_length.to(device)
output = self.attention(query, key, value, valid_length)
output_concat = transpose_output(output, self.num_heads)
return self.W_o(output_concat)
def transpose_qkv(X, num_heads):
# Original X shape: (batch_size, seq_len, hidden_size * num_heads),
# -1 means inferring its value, after first reshape, X shape:
# (batch_size, seq_len, num_heads, hidden_size)
X = X.view(X.shape[0], X.shape[1], num_heads, -1)
# After transpose, X shape: (batch_size, num_heads, seq_len, hidden_size)
X = X.transpose(2, 1).contiguous()
# Merge the first two dimensions. Use reverse=True to infer shape from
# right to left.
# output shape: (batch_size * num_heads, seq_len, hidden_size)
output = X.view(-1, X.shape[2], X.shape[3])
return output
# Saved in the d2l package for later use
def transpose_output(X, num_heads):
# A reversed version of transpose_qkv
X = X.view(-1, num_heads, X.shape[1], X.shape[2])
X = X.transpose(2, 1).contiguous()
return X.view(X.shape[0], X.shape[1], -1)
cell = MultiHeadAttention(5, 9, 3, 0.5)
X = torch.ones((2, 4, 5))
valid_length = torch.FloatTensor([2, 3])
cell(X, X, X, valid_length).shape
torch.Size([2, 4, 9])
基于位置的前馈网络
Transformer 模块另一个非常重要的部分就是基于位置的前馈网络（FFN），它接受一个形状为（batch_size，seq_length, feature_size）的三维张量。Position-wise FFN由两个全连接层组成，他们作用在最后一维上。因为序列的每个位置的状态都会被单独地更新，所以我们称他为position-wise，这等效于一个1x1的卷积。
下面我们来实现PositionWiseFFN：
# Save to the d2l package.
class PositionWiseFFN(nn.Module):
def __init__(self, input_size, ffn_hidden_size, hidden_size_out, **kwargs):
super(PositionWiseFFN, self).__init__(**kwargs)
self.ffn_1 = nn.Linear(input_size, ffn_hidden_size)
self.ffn_2 = nn.Linear(ffn_hidden_size, hidden_size_out)
def forward(self, X):
return self.ffn_2(F.relu(self.ffn_1(X)))
与多头注意力层相似，FFN层同样只会对最后一维的大小进行改变；除此之外，对于两个完全相同的输入，FFN层的输出也将相等。
ffn = PositionWiseFFN(4, 4, 8)
out = ffn(torch.ones((2,3,4)))
print(out, out.shape)
tensor([[[ 0.2040, -0.1118, -0.1163, 0.1494, 0.3978, -0.5561, 0.4662,
-0.6598],
[ 0.2040, -0.1118, -0.1163, 0.1494, 0.3978, -0.5561, 0.4662,
-0.6598],
[ 0.2040, -0.1118, -0.1163, 0.1494, 0.3978, -0.5561, 0.4662,
-0.6598]],
[[ 0.2040, -0.1118, -0.1163, 0.1494, 0.3978, -0.5561, 0.4662,
-0.6598],
[ 0.2040, -0.1118, -0.1163, 0.1494, 0.3978, -0.5561, 0.4662,
-0.6598],
[ 0.2040, -0.1118, -0.1163, 0.1494, 0.3978, -0.5561, 0.4662,
-0.6598]]], grad_fn=) torch.Size([2, 3, 8])
Add and Norm
除了上面两个模块之外，Transformer还有一个重要的相加归一化层，它可以平滑地整合输入和其他层的输出，因此我们在每个多头注意力层和FFN层后面都添加一个含残差连接的Layer Norm层。这里 Layer Norm 与7.5小节的Batch Norm很相似，唯一的区别在于Batch Norm是对于batch size这个维度进行计算均值和方差的，而Layer Norm则是对最后一维进行计算。层归一化可以防止层内的数值变化过大，从而有利于加快训练速度并且提高泛化性能。 (ref)
layernorm = nn.LayerNorm(normalized_shape=2, elementwise_affine=True)
batchnorm = nn.BatchNorm1d(num_features=2, affine=True)
X = torch.FloatTensor([[1,2], [3,4]])
print('layer norm:', layernorm(X))
print('batch norm:', batchnorm(X))
layer norm: tensor([[-1.0000, 1.0000],
[-1.0000, 1.0000]], grad_fn=)
batch norm: tensor([[-1.0000, -1.0000],
[ 1.0000, 1.0000]], grad_fn=)
# Save to the d2l package.
class AddNorm(nn.Module):
def __init__(self, hidden_size, dropout, **kwargs):
super(AddNorm, self).__init__(**kwargs)
self.dropout = nn.Dropout(dropout)
self.norm = nn.LayerNorm(hidden_size)
def forward(self, X, Y):
return self.norm(self.dropout(Y) + X)
由于残差连接，X和Y需要有相同的维度。
add_norm = AddNorm(4, 0.5)
add_norm(torch.ones((2,3,4)), torch.ones((2,3,4))).shape
torch.Size([2, 3, 4])
位置编码
与循环神经网络不同，无论是多头注意力网络还是前馈神经网络都是独立地对每个位置的元素进行更新，这种特性帮助我们实现了高效的并行，却丢失了重要的序列顺序的信息。为了更好的捕捉序列信息，Transformer模型引入了位置编码去保持输入序列元素的位置。
假设输入序列的嵌入表示 X ∈ R l × d X\in \mathbb{R}^{l\times d} X∈Rl×d, 序列长度为 l l l嵌入向量维度为 d d d，则其位置编码为 P ∈ R l × d P \in \mathbb{R}^{l\times d} P∈Rl×d ，输出的向量就是二者相加 X + P X + P X+P。
位置编码是一个二维的矩阵，i对应着序列中的顺序，j对应其embedding vector内部的维度索引。我们可以通过以下等式计算位置编码：
P i , 2 j = s i n ( i / 1000 0 2 j / d ) P_{i,2j} = sin(i/10000^{2j/d}) Pi,2j=sin(i/100002j/d)
P i , 2 j + 1 = c o s ( i / 1000 0 2 j / d ) P_{i,2j+1} = cos(i/10000^{2j/d}) Pi,2j+1=cos(i/100002j/d)
f o r i = 0 , … , l − 1 a n d j = 0 , … , ⌊ ( d − 1 ) / 2 ⌋ for\ i=0,\ldots, l-1\ and\ j=0,\ldots,\lfloor (d-1)/2 \rfloor for i=0,…,l−1 and j=0,…,⌊(d−1)/2⌋
F i g . 10.3.4 位 置 编 码 Fig. 10.3.4\ 位置编码 Fig.10.3.4 位置编码
class PositionalEncoding(nn.Module):
def __init__(self, embedding_size, dropout, max_len=1000):
super(PositionalEncoding, self).__init__()
self.dropout = nn.Dropout(dropout)
self.P = np.zeros((1, max_len, embedding_size))
X = np.arange(0, max_len).reshape(-1, 1) / np.power(
10000, np.arange(0, embedding_size, 2)/embedding_size)
self.P[:, :, 0::2] = np.sin(X)
self.P[:, :, 1::2] = np.cos(X)
self.P = torch.FloatTensor(self.P)
def forward(self, X):
if X.is_cuda and not self.P.is_cuda:
self.P = self.P.cuda()
X = X + self.P[:, :X.shape[1], :]
return self.dropout(X)
测试
下面我们用PositionalEncoding这个类进行一个小测试，取其中的四个维度进行可视化。 我们可以看到，第4维和第5维有相同的频率但偏置不同。第6维和第7维具有更低的频率；因此positional encoding对于不同维度具有可区分性。
import numpy as np
pe = PositionalEncoding(20, 0)
Y = pe(torch.zeros((1, 100, 20))).numpy()
d2l.plot(np.arange(100), Y[0, :, 4:8].T, figsize=(6, 2.5),
legend=["dim %d" % p for p in [4, 5, 6, 7]])
编码器
我们已经有了组成Transformer的各个模块，现在我们可以开始搭建了！编码器包含一个多头注意力层，一个position-wise FFN，和两个 Add and Norm层。对于attention模型以及FFN模型，我们的输出维度都是与embedding维度一致的，这也是由于残差连接天生的特性导致的，因为我们要将前一层的输出与原始输入相加并归一化。
class EncoderBlock(nn.Module):
def __init__(self, embedding_size, ffn_hidden_size, num_heads,
dropout, **kwargs):
super(EncoderBlock, self).__init__(**kwargs)
self.attention = MultiHeadAttention(embedding_size, embedding_size, num_heads, dropout)
self.addnorm_1 = AddNorm(embedding_size, dropout)
self.ffn = PositionWiseFFN(embedding_size, ffn_hidden_size, embedding_size)
self.addnorm_2 = AddNorm(embedding_size, dropout)
def forward(self, X, valid_length):
Y = self.addnorm_1(X, self.attention(X, X, X, valid_length))
return self.addnorm_2(Y, self.ffn(Y))
# batch_size = 2, seq_len = 100, embedding_size = 24
# ffn_hidden_size = 48, num_head = 8, dropout = 0.5
X = torch.ones((2, 100, 24))
encoder_blk = EncoderBlock(24, 48, 8, 0.5)
encoder_blk(X, valid_length).shape
torch.Size([2, 100, 24])
现在我们来实现整个Transformer 编码器模型，整个编码器由n个刚刚定义的Encoder Block堆叠而成，因为残差连接的缘故，中间状态的维度始终与嵌入向量的维度d一致；同时注意到我们把嵌入向量乘以 d \sqrt{d} d 以防止其值过小。
class TransformerEncoder(d2l.Encoder):
def __init__(self, vocab_size, embedding_size, ffn_hidden_size,
num_heads, num_layers, dropout, **kwargs):
super(TransformerEncoder, self).__init__(**kwargs)
self.embedding_size = embedding_size
self.embed = nn.Embedding(vocab_size, embedding_size)
self.pos_encoding = PositionalEncoding(embedding_size, dropout)
self.blks = nn.ModuleList()
for i in range(num_layers):
self.blks.append(
EncoderBlock(embedding_size, ffn_hidden_size,
num_heads, dropout))
def forward(self, X, valid_length, *args):
X = self.pos_encoding(self.embed(X) * math.sqrt(self.embedding_size))
for blk in self.blks:
X = blk(X, valid_length)
return X
# test encoder
encoder = TransformerEncoder(200, 24, 48, 8, 2, 0.5)
encoder(torch.ones((2, 100)).long(), valid_length).shape
torch.Size([2, 100, 24])
解码器
Transformer 模型的解码器与编码器结构类似，然而，除了之前介绍的几个模块之外，编码器部分有另一个子模块。该模块也是多头注意力层，接受编码器的输出作为key和value，decoder的状态作为query。与编码器部分相类似，解码器同样是使用了add and norm机制，用残差和层归一化将各个子层的输出相连。
仔细来讲，在第t个时间步，当前输入 x t x_t xt是query，那么self attention接受了第t步以及前t-1步的所有输入 x 1 , … , x t − 1 x_1,\ldots, x_{t-1} x1,…,xt−1。在训练时，由于第t位置的输入可以观测到全部的序列，这与预测阶段的情形项矛盾，所以我们要通过将第t个时间步所对应的可观测长度设置为t，以消除不需要看到的未来的信息。
class DecoderBlock(nn.Module):
def __init__(self, embedding_size, ffn_hidden_size, num_heads,dropout,i,**kwargs):
super(DecoderBlock, self).__init__(**kwargs)
self.i = i
self.attention_1 = MultiHeadAttention(embedding_size, embedding_size, num_heads, dropout)
self.addnorm_1 = AddNorm(embedding_size, dropout)
self.attention_2 = MultiHeadAttention(embedding_size, embedding_size, num_heads, dropout)
self.addnorm_2 = AddNorm(embedding_size, dropout)
self.ffn = PositionWiseFFN(embedding_size, ffn_hidden_size, embedding_size)
self.addnorm_3 = AddNorm(embedding_size, dropout)
def forward(self, X, state):
enc_outputs, enc_valid_length = state[0], state[1]
# state[2][self.i] stores all the previous t-1 query state of layer-i
# len(state[2]) = num_layers
# If training:
# state[2] is useless.
# If predicting:
# In the t-th timestep:
# state[2][self.i].shape = (batch_size, t-1, hidden_size)
# Demo:
# love dogs ! [EOS]
# | | | |
# Transformer
# Decoder
# | | | |
# I love dogs !
if state[2][self.i] is None:
key_values = X
else:
# shape of key_values = (batch_size, t, hidden_size)
key_values = torch.cat((state[2][self.i], X), dim=1)
state[2][self.i] = key_values
if self.training:
batch_size, seq_len, _ = X.shape
# Shape: (batch_size, seq_len), the values in the j-th column are j+1
valid_length = torch.FloatTensor(np.tile(np.arange(1, seq_len+1), (batch_size, 1)))
valid_length = valid_length.to(X.device)
else:
valid_length = None
X2 = self.attention_1(X, key_values, key_values, valid_length)
Y = self.addnorm_1(X, X2)
Y2 = self.attention_2(Y, enc_outputs, enc_outputs, enc_valid_length)
Z = self.addnorm_2(Y, Y2)
return self.addnorm_3(Z, self.ffn(Z)), state
decoder_blk = DecoderBlock(24, 48, 8, 0.5, 0)
X = torch.ones((2, 100, 24))
state = [encoder_blk(X, valid_length), valid_length, [None]]
decoder_blk(X, state)[0].shape
torch.Size([2, 100, 24])
对于Transformer解码器来说，构造方式与编码器一样，除了最后一层添加一个dense layer以获得输出的置信度分数。下面让我们来实现一下Transformer Decoder，除了常规的超参数例如vocab_size embedding_size 之外，解码器还需要编码器的输出 enc_outputs 和句子有效长度 enc_valid_length。
class TransformerDecoder(d2l.Decoder):
def __init__(self, vocab_size, embedding_size, ffn_hidden_size,
num_heads, num_layers, dropout, **kwargs):
super(TransformerDecoder, self).__init__(**kwargs)
self.embedding_size = embedding_size
self.num_layers = num_layers
self.embed = nn.Embedding(vocab_size, embedding_size)
self.pos_encoding = PositionalEncoding(embedding_size, dropout)
self.blks = nn.ModuleList()
for i in range(num_layers):
self.blks.append(
DecoderBlock(embedding_size, ffn_hidden_size, num_heads,
dropout, i))
self.dense = nn.Linear(embedding_size, vocab_size)
def init_state(self, enc_outputs, enc_valid_length, *args):
return [enc_outputs, enc_valid_length, [None]*self.num_layers]
def forward(self, X, state):
X = self.pos_encoding(self.embed(X) * math.sqrt(self.embedding_size))
for blk in self.blks:
X, state = blk(X, state)
return self.dense(X), state
训练
import zipfile
import torch
import requests
from io import BytesIO
from torch.utils import data
import sys
import collections
class Vocab(object): # This class is saved in d2l.
def __init__(self, tokens, min_freq=0, use_special_tokens=False):
# sort by frequency and token
counter = collections.Counter(tokens)
token_freqs = sorted(counter.items(), key=lambda x: x[0])
token_freqs.sort(key=lambda x: x[1], reverse=True)
if use_special_tokens:
# padding, begin of sentence, end of sentence, unknown
self.pad, self.bos, self.eos, self.unk = (0, 1, 2, 3)
tokens = ['', '', '', '']
else:
self.unk = 0
tokens = ['']
tokens += [token for token, freq in token_freqs if freq >= min_freq]
self.idx_to_token = []
self.token_to_idx = dict()
for token in tokens:
self.idx_to_token.append(token)
self.token_to_idx[token] = len(self.idx_to_token) - 1
def __len__(self):
return len(self.idx_to_token)
def __getitem__(self, tokens):
if not isinstance(tokens, (list, tuple)):
return self.token_to_idx.get(tokens, self.unk)
else:
return [self.__getitem__(token) for token in tokens]
def to_tokens(self, indices):
if not isinstance(indices, (list, tuple)):
return self.idx_to_token[indices]
else:
return [self.idx_to_token[index] for index in indices]
def load_data_nmt(batch_size, max_len, num_examples=1000):
"""Download an NMT dataset, return its vocabulary and data iterator."""
# Download and preprocess
def preprocess_raw(text):
text = text.replace('\u202f', ' ').replace('\xa0', ' ')
out = ''
for i, char in enumerate(text.lower()):
if char in (',', '!', '.') and text[i-1] != ' ':
out += ' '
out += char
return out
with open('/home/kesci/input/fraeng6506/fra.txt', 'r') as f:
raw_text = f.read()
text = preprocess_raw(raw_text)
# Tokenize
source, target = [], []
for i, line in enumerate(text.split('\n')):
if i >= num_examples:
break
parts = line.split('\t')
if len(parts) >= 2:
source.append(parts[0].split(' '))
target.append(parts[1].split(' '))
# Build vocab
def build_vocab(tokens):
tokens = [token for line in tokens for token in line]
return Vocab(tokens, min_freq=3, use_special_tokens=True)
src_vocab, tgt_vocab = build_vocab(source), build_vocab(target)
# Convert to index arrays
def pad(line, max_len, padding_token):
if len(line) > max_len:
return line[:max_len]
return line + [padding_token] * (max_len - len(line))
def build_array(lines, vocab, max_len, is_source):
lines = [vocab[line] for line in lines]
if not is_source:
lines = [[vocab.bos] + line + [vocab.eos] for line in lines]
array = torch.tensor([pad(line, max_len, vocab.pad) for line in lines])
valid_len = (array != vocab.pad).sum(1)
return array, valid_len
src_vocab, tgt_vocab = build_vocab(source), build_vocab(target)
src_array, src_valid_len = build_array(source, src_vocab, max_len, True)
tgt_array, tgt_valid_len = build_array(target, tgt_vocab, max_len, False)
train_data = data.TensorDataset(src_array, src_valid_len, tgt_array, tgt_valid_len)
train_iter = data.DataLoader(train_data, batch_size, shuffle=True)
return src_vocab, tgt_vocab, train_iter
import os
import d2l
# 平台暂时不支持gpu，现在会自动使用cpu训练，gpu可以用了之后会使用gpu来训练
os.environ["CUDA_VISIBLE_DEVICES"] = "1"
embed_size, embedding_size, num_layers, dropout = 32, 32, 2, 0.05
batch_size, num_steps = 64, 10
lr, num_epochs, ctx = 0.005, 250, d2l.try_gpu()
print(ctx)
num_hiddens, num_heads = 64, 4
src_vocab, tgt_vocab, train_iter = load_data_nmt(batch_size, num_steps)
encoder = TransformerEncoder(
len(src_vocab), embedding_size, num_hiddens, num_heads, num_layers,
dropout)
decoder = TransformerDecoder(
len(src_vocab), embedding_size, num_hiddens, num_heads, num_layers,
dropout)
model = d2l.EncoderDecoder(encoder, decoder)
d2l.train_s2s_ch9(model, train_iter, lr, num_epochs, ctx)
cpu
epoch 50,loss 0.048, time 53.3 sec
epoch 100,loss 0.040, time 53.4 sec
epoch 150,loss 0.037, time 53.5 sec
epoch 200,loss 0.036, time 53.6 sec
epoch 250,loss 0.035, time 53.5 sec
model.eval()
for sentence in ['Go .', 'Wow !', "I'm OK .", 'I won !']:
print(sentence + ' => ' + d2l.predict_s2s_ch9(
model, sentence, src_vocab, tgt_vocab, num_steps, ctx))
Go . => !
Wow ! => !
I'm OK . => ça va .
I won ! => j'ai gagné !