一、LSTM简介

LSTM（long short-term memory）长短期记忆网络，RNN的改进，克服了RNN中“记忆低下”的问题。通过“门”结构实现信息的添加和移除，通过记忆元将序列处理过程中的相关信息一直传递下去，经典结构如下：

二、LSTM中的核心结构

记忆元（memory cell）-长期记忆：

就像一个cell一样，信息通过这条只有少量线性交互的线传递。传递过程中有3种“门”结构可以告诉它该学习或者保存哪些信息
三个门结构-短期记忆
遗忘门：用来决定当前状态哪些信息被移除

输入门：决定放入哪些信息到细胞状态

输出门：决定哪些信息用于输出

细节注意：

• 新的细胞状态只需要遗忘门和输入门就可以更新，公式为：$C_t=f_t\ast C_{t-1}+i_t\ast \widetilde{C_t}$（注意所有的$\ast$都表示Hadamard 乘积）
• 只有隐状态h_t会传递到输出层，记忆元完全属于内部信息，不可手动修改

三、如何解决RNN中的梯度消失/爆炸问题

解决是指很大程度上缓解，不是让它彻底消失。先解释RNN为什么会有这些问题：
$$\begin{array}{rl}& \frac{\partial L_t}{\partial U}=\sum _{k=0}^t\frac{\partial L_t}{\partial O_t}\frac{\partial O_t}{\partial S_t}(\prod _{j=k+1}^t\frac{\partial S_j}{\partial S_{j-1}})\frac{\partial S_k}{\partial U}\\ & \frac{\partial L_t}{\partial W}=\sum _{k=0}^t\frac{\partial L_t}{\partial O_t}\frac{\partial O_t}{\partial S_t}(\prod _{j=k+1}^t\frac{\partial S_j}{\partial S_{j-1}})\frac{\partial S_k}{\partial W}\end{array}$$（具体过程可以看这里）

上面是训练过程任意时刻更新W、U需要用到的求偏导的结果。实际使用会加上激活函数，通常为tanh、sigmoid等
tanh和其导数图像如下

sigmoid和其导数如下

这些激活函数的导数都比1要小，又因为${\prod }_{j=k+1}^t\frac{\partial S_j}{\partial S_{j-1}}={\prod }_{j=k+1}^{t}tan{h}^{\prime }(W_s)$，所以当$W_s$过小过大就会分别造成梯度消失和爆炸的问题，特别是过小。
LSTM如何缓解
由链式法则和三个门的公式可以得到：
$$\begin{array}{rl}& \frac{\partial C_t}{\partial C_{t-1}}\\ & =\frac{\partial C_t}{\partial f_t}\frac{\partial f_t}{\partial h_{t-1}}\frac{\partial h_{t-1}}{\partial C_{t-1}}+\frac{\partial C_t}{\partial i_t}\frac{\partial i_t}{\partial h_{t-1}}\frac{\partial h_{t-1}}{\partial C_{t-1}}+\frac{\partial C_t}{\partial \widetilde{C_t}}\frac{\partial \widetilde{C_t}}{\partial h_{t-1}}\frac{\partial h_{t-1}}{\partial C_{t-1}}+\frac{\partial C_t}{\partial C_{t-1}}\\ & =C_{t-1}{\sigma }^{\prime }(\cdot )W_f\ast o_{t-1}tan{h}^{\prime }(C_{t-1})+\widetilde{C_t}{\sigma }^{\prime }(\cdot )W_i\ast o_{t-1}tan{h}^{\prime }(C_{t-1})\\ & +i_{t}tan{h}^{\prime }(\cdot )W_c\ast o_{t-1}tan{h}^{\prime }(C_{t-1})+f_t\end{array}$$

• 由相乘变成了相加，不容易叠加
• sigmoid函数使单元间传递结果非常接近0或者1，使模型变成非线性，并且可以在学习过程中内部调整

四、情感分类实战（google colab）

环境和库：

!pip install torch
!pip install torchtext
!python -m spacy download en# K80 gpu for 12 hours
import torch
from torch import nn, optim
from torchtext import data, datasetsprint('GPU:', torch.cuda.is_available())torch.manual_seed(123)

加载数据集：

TEXT = data.Field(tokenize='spacy')
LABEL = data.LabelField(dtype=torch.float)
train_data, test_data = datasets.IMDB.splits(TEXT, LABEL)print(train_data.examples[15].text)
print(train_data.examples[15].label)

网络结构：

class RNN(nn.Module):def __init__(self, vocab_size, embedding_dim, hidden_dim):""""""super(RNN, self).__init__()# [0-10001] => [100]self.embedding = nn.Embedding(vocab_size, embedding_dim)# [100] => [256]self.rnn = nn.LSTM(embedding_dim, hidden_dim, num_layers=2, bidirectional=True, dropout=0.5)# [256*2] => [1]self.fc = nn.Linear(hidden_dim*2, 1)self.dropout = nn.Dropout(0.5)def forward(self, x):"""x: [seq_len, b] vs [b, 3, 28, 28]"""# [seq, b, 1] => [seq, b, 100]embedding = self.dropout(self.embedding(x))# output: [seq, b, hid_dim*2]# hidden/h: [num_layers*2, b, hid_dim]# cell/c: [num_layers*2, b, hid_di]output, (hidden, cell) = self.rnn(embedding)# [num_layers*2, b, hid_dim] => 2 of [b, hid_dim] => [b, hid_dim*2]hidden = torch.cat([hidden[-2], hidden[-1]], dim=1)# [b, hid_dim*2] => [b, 1]hidden = self.dropout(hidden)out = self.fc(hidden)return out

Embedding

rnn = RNN(len(TEXT.vocab), 100, 256)pretrained_embedding = TEXT.vocab.vectors
print('pretrained_embedding:', pretrained_embedding.shape)
rnn.embedding.weight.data.copy_(pretrained_embedding)
print('embedding layer inited.')optimizer = optim.Adam(rnn.parameters(), lr=1e-3)
criteon = nn.BCEWithLogitsLoss().to(device)
rnn.to(device)

训练并测试

import numpy as npdef binary_acc(preds, y):"""get accuracy"""preds = torch.round(torch.sigmoid(preds))correct = torch.eq(preds, y).float()acc = correct.sum() / len(correct)return accdef train(rnn, iterator, optimizer, criteon):avg_acc = []rnn.train()for i, batch in enumerate(iterator):# [seq, b] => [b, 1] => [b]pred = rnn(batch.text).squeeze(1)# loss = criteon(pred, batch.label)acc = binary_acc(pred, batch.label).item()avg_acc.append(acc)optimizer.zero_grad()loss.backward()optimizer.step()if i%10 == 0:print(i, acc)avg_acc = np.array(avg_acc).mean()print('avg acc:', avg_acc)def eval(rnn, iterator, criteon):avg_acc = []rnn.eval()with torch.no_grad():for batch in iterator:# [b, 1] => [b]pred = rnn(batch.text).squeeze(1)#loss = criteon(pred, batch.label)acc = binary_acc(pred, batch.label).item()avg_acc.append(acc)avg_acc = np.array(avg_acc).mean()print('>>test:', avg_acc)for epoch in range(10):eval(rnn, test_iterator, criteon)train(rnn, train_iterator, optimizer, criteon)

最后得到的准确率结果如下：

完整colab链接：lstm
完整代码：

# -*- coding: utf-8 -*-
"""lstmAutomatically generated by Colaboratory.Original file is located athttps://colab.research.google.com/drive/1GX0Rqur8T45MSYhLU9MYWAbycfLH4-Fu
"""!pip install torch
!pip install torchtext
!python -m spacy download en# K80 gpu for 12 hours
import torch
from torch import nn, optim
from torchtext import data, datasetsprint('GPU:', torch.cuda.is_available())torch.manual_seed(123)TEXT = data.Field(tokenize='spacy')
LABEL = data.LabelField(dtype=torch.float)
train_data, test_data = datasets.IMDB.splits(TEXT, LABEL)print('len of train data:', len(train_data))
print('len of test data:', len(test_data))print(train_data.examples[15].text)
print(train_data.examples[15].label)# word2vec, glove
TEXT.build_vocab(train_data, max_size=10000, vectors='glove.6B.100d')
LABEL.build_vocab(train_data)batchsz = 30
device = torch.device('cuda')
train_iterator, test_iterator = data.BucketIterator.splits((train_data, test_data),batch_size = batchsz,device=device
)class RNN(nn.Module):def __init__(self, vocab_size, embedding_dim, hidden_dim):""""""super(RNN, self).__init__()# [0-10001] => [100]self.embedding = nn.Embedding(vocab_size, embedding_dim)# [100] => [256]self.rnn = nn.LSTM(embedding_dim, hidden_dim, num_layers=2, bidirectional=True, dropout=0.5)# [256*2] => [1]self.fc = nn.Linear(hidden_dim*2, 1)self.dropout = nn.Dropout(0.5)def forward(self, x):"""x: [seq_len, b] vs [b, 3, 28, 28]"""# [seq, b, 1] => [seq, b, 100]embedding = self.dropout(self.embedding(x))# output: [seq, b, hid_dim*2]# hidden/h: [num_layers*2, b, hid_dim]# cell/c: [num_layers*2, b, hid_di]output, (hidden, cell) = self.rnn(embedding)# [num_layers*2, b, hid_dim] => 2 of [b, hid_dim] => [b, hid_dim*2]hidden = torch.cat([hidden[-2], hidden[-1]], dim=1)# [b, hid_dim*2] => [b, 1]hidden = self.dropout(hidden)out = self.fc(hidden)return outrnn = RNN(len(TEXT.vocab), 100, 256)pretrained_embedding = TEXT.vocab.vectors
print('pretrained_embedding:', pretrained_embedding.shape)
rnn.embedding.weight.data.copy_(pretrained_embedding)
print('embedding layer inited.')optimizer = optim.Adam(rnn.parameters(), lr=1e-3)
criteon = nn.BCEWithLogitsLoss().to(device)
rnn.to(device)import numpy as npdef binary_acc(preds, y):"""get accuracy"""preds = torch.round(torch.sigmoid(preds))correct = torch.eq(preds, y).float()acc = correct.sum() / len(correct)return accdef train(rnn, iterator, optimizer, criteon):avg_acc = []rnn.train()for i, batch in enumerate(iterator):# [seq, b] => [b, 1] => [b]pred = rnn(batch.text).squeeze(1)# loss = criteon(pred, batch.label)acc = binary_acc(pred, batch.label).item()avg_acc.append(acc)optimizer.zero_grad()loss.backward()optimizer.step()if i%10 == 0:print(i, acc)avg_acc = np.array(avg_acc).mean()print('avg acc:', avg_acc)def eval(rnn, iterator, criteon):avg_acc = []rnn.eval()with torch.no_grad():for batch in iterator:# [b, 1] => [b]pred = rnn(batch.text).squeeze(1)#loss = criteon(pred, batch.label)acc = binary_acc(pred, batch.label).item()avg_acc.append(acc)avg_acc = np.array(avg_acc).mean()print('>>test:', avg_acc)for epoch in range(10):eval(rnn, test_iterator, criteon)train(rnn, train_iterator, optimizer, criteon)