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循环神经网络（RNN）及现代RNN

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1.目标

​ 学习RNN的基本结构，并以此延伸出来的现代循环神经网络：GRU、LSTM、深度循环神经网络、双向循环神经网络、编码器-解码器结构、序列到序列学习（seq2seq）、束搜索。

​ 通过自己大致复现一遍经典循环神经网络结构，熟悉代码的架构和模板。这里基础知识尽可能精简，多写一些模型和不同方法适用的场景。

2.Basic RNN Structure

​ 利用Pytorch框架的高级API简洁实现RNN网络，最后利用困惑度指标来进行评价模型的训练情况。

  • 导入库并下载数据集：
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import torch
from torch import nn
from torch.nn import functional as F
from d2l import torch as d2l

batch_size, num_steps = 32, 35
train_iter, vocab = d2l.load_data_time_machine(batch_size,num_steps)
  • 定义模型及其参数：
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#构造一个256个隐藏单元的单隐藏层的RNN
num_hiddens = 256
rnn_layer = nn.RNN(len(vocab), num_hiddens)

#使用张量初始化隐状态
state = torch.zeros((1,batch_size, num_hiddens))
state.shape
#Output：torch.Size([1, 32, 256])

#利用一个隐状态和输入，我们可以用更新后的隐状态计算输出
X = torch.rand(size=(num_steps, batch_size, len(vocab)))
Y, state_new = rnn_layer(X, state)
Y.shape,state_new.shape
#Output：(torch.Size([35, 32, 256]), torch.Size([1, 32, 256]))

class RNNModel(nn.Module):
    "循环神经网络模型"
    def __init__(self,rnn_layer, vocab_size, **kwargs):
        super(RNNModel, self).__init__(**kwargs)
        self.rnn = rnn_layer
        self.vocab_size = vocab_size
        self.num_hiddens = self.rnn.hidden_size
        if not self.rnn.bidirectional:
            self.num_directions = 1
            self.linear = nn.Linear(self.num_hiddens, self.vocab_size)
        else:
            self.num_directions = 2
            self.linear = nn.Linear(self.num_hiddens * 2, self.vocab_size)
    
    def forward(self, inputs,state):
        X = F.one_hot(inputs.T.long(), self.vocab_size)
        X = X.to(torch.float32)
        Y, state = self.rnn(X, state)
        output = self.linear(Y.reshape((-1, Y.shape[-1])))
        return output, state
    
    def begin_state(self, device, batch_size=1):
        if not isinstance(self.rnn, nn.LSTM):
            return torch.zeros((self.num_directions * self.rnn.num_layers,
                                batch_size,self.num_hiddens),
                               device=device)
        else:
            return(torch.zeros((
                self.num_directions * self.rnn.num_layers,
                batch_size, self.num_hiddens), device=device),
                   torch.zeros((
                       self.num_directions * self.rnn.num_layers,
                       batch_size,self.num_hiddens), device=device))
  • 训练及预测：
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#训练和预测
device = d2l.try_gpu()
net = RNNModel(rnn_layer, vocab_size=len(vocab))
net = net.to(device)
# d2l.predict_ch8('time traveller', 10, net, vocab, device)
num_epochs, lr = 2000, 0.5
d2l.train_ch8(net, train_iter, vocab, lr, num_epochs, device)
  • 输出：
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perplexity 1.0, 503854.1 tokens/sec on cuda:0
time travelleryou can show black is white by argument said filby
travelleryou can show black is white by argument said filby

注意：高级API的循环神经网络返回一个输出和一个更新后的隐状态，我们还要计算整个模型的输出层。

3.Modern RNN Structure

3.1GRU

  • 重置门、更新门、候选隐状态、隐状态

代码实现：

  • 导入依赖库：
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import torch
from torch import nn
from d2l import torch as d2l

batch_size, num_steps = 32, 35
train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)
  • 初始化模型参数并定义模型：
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#初始化模型参数
def get_params(vocab_size, num_hiddens, device):
    num_inputs = num_outputs = vocab_size
    
    def normal(shape):
        return torch.randn(size=shape,device=device)*0.01
    def three():
        return (normal((num_inputs, num_hiddens)),
                normal((num_hiddens, num_hiddens)),
                torch.zeros(num_hiddens, device=device))
    W_xz, W_hz, b_z = three() # 更新门参数
    W_xr, W_hr, b_r = three() # 重置门参数
    W_xh, W_hh, b_h = three() # 候选隐状态参数
    # 输出层参数
    W_hq = normal((num_hiddens,num_outputs))
    b_q = torch.zeros(num_outputs,device=device)
    # 附加梯度
    params = [W_xz, W_hz, b_z, W_xr, W_hr, b_r, W_xh, W_hh, b_h, W_hq, b_q]
    for param in params:
        param.requires_grad_(True)
    return params

#定义隐状态初始化函数
def init_gru_state(batch_size,num_hiddens,device):
    return (torch.zeros((batch_size,num_hiddens), device=device),)

#定义门控单元模型
def gru(inputs, state, params):
    W_xz, W_hz, b_z, W_xr, W_hr, b_r, W_xh, W_hh, b_h, W_hq, b_q = params
    H, = state
    outputs = []
    for X in inputs: #@为矩阵乘法
        Z = torch.sigmoid((X @ W_xz) + (H @ W_hz) + b_z)
        R = torch.sigmoid((X @ W_xr) + (H @ W_hr) + b_r)
        H_tilda = torch.tanh((X @ W_xh) + ((R * H)@ W_hh) + b_h)
        H = Z * H + (1 - Z) * H_tilda
        Y = H @ W_hq + b_q
        outputs.append(Y)
    return torch.cat(outputs,dim=0),(H,)
  • 训练预测：
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#训练和预测
vocab_size, num_hiddens, device = len(vocab), 256, d2l.try_gpu()
num_epochs, lr = 500, 1
model = d2l.RNNModelScratch(len(vocab), num_hiddens, device, get_params,
                            init_gru_state, gru)
d2l.train_ch8(model, train_iter, vocab, lr, num_epochs, device)
  • 输出：
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perplexity 1.1, 27726.3 tokens/sec on cuda:0
time traveller withou sereface bach a cain and seemed to be and 
traveller with a slight accession ofcheerfulness really thi

3.2LSTM

​ 主要关注三个门：

  1. 忘记门：将值朝0减少
  2. 输入门：决定不是忽略掉输入数据
  3. 输出门：决定是不是使用隐状态
  4. 候选记忆单元
  5. 记忆元：控制输入、遗忘、跳过。输入门控制采用多少来自的新数据，而遗忘门控制保留多少过去的记忆元的内容。
  6. 隐状态​：，这就是输出门发挥作用的地方。在长短期记忆网络中，它仅仅是记忆元的的门控版本。这就确保了的值始终在区间内

代码实现：

  • 依赖库和初始化模型参数：
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import torch
from torch import nn
from d2l import torch as d2l

batch_size, num_steps = 32, 35
train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)

def get_lstm_params(vocab_size, num_hiddens, device):
    num_inputs = num_outputs = vocab_size

    def normal(shape):
        return torch.randn(size=shape, device=device)*0.01

    def three():
        return (normal((num_inputs, num_hiddens)),
                normal((num_hiddens, num_hiddens)),
                torch.zeros(num_hiddens, device=device))

    W_xi, W_hi, b_i = three()  # 输入门参数
    W_xf, W_hf, b_f = three()  # 遗忘门参数
    W_xo, W_ho, b_o = three()  # 输出门参数
    W_xc, W_hc, b_c = three()  # 候选记忆元参数
    # 输出层参数
    W_hq = normal((num_hiddens, num_outputs))
    b_q = torch.zeros(num_outputs, device=device)
    # 附加梯度
    params = [W_xi, W_hi, b_i, W_xf, W_hf, b_f, W_xo, W_ho, b_o, W_xc, W_hc,
              b_c, W_hq, b_q]
    for param in params:
        param.requires_grad_(True)
    return params

def init_lstm_state(batch_size,num_hiddens,device):
    return (torch.zeros((batch_size,num_hiddens),device=device),
            torch.zeros((batch_size,num_hiddens),device=device))
    
def lstm(inputs, state, params):
    [W_xi, W_hi, b_i, W_xf, W_hf, b_f, W_xo, W_ho, b_o, W_xc, W_hc, b_c,
     W_hq, b_q] = params
    (H, C) = state
    outputs = []
    for X in inputs:
        I = torch.sigmoid((X @ W_xi) + (H @ W_hi) + b_i)
        F = torch.sigmoid((X @ W_xf) + (H @ W_hf) + b_f)
        O = torch.sigmoid((X @ W_xo) + (H @ W_ho) + b_o)
        C_tilda = torch.tanh((X @ W_xc) + (H @ W_hc) + b_c)
        C = F * C + I * C_tilda
        H = O * torch.tanh(C)
        Y = (H @ W_hq) + b_q
        outputs.append(Y)
    return torch.cat(outputs,dim=0),(H, C)
  • 训练：
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vocab_size, num_hiddens, device = len(vocab), 256, d2l.try_gpu()
num_epochs, lr = 500, 1
model = d2l.RNNModelScratch(vocab_size,num_hiddens,device,get_lstm_params,
                            init_lstm_state,lstm)
d2l.train_ch8(model, train_iter, vocab, lr, num_epochs, device)
  • 输出：
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perplexity 1.1, 22766.8 tokens/sec on cuda:0
time traveller for so it will be convenient to speak of himwas e
travelleryou can show black is white by argument said filby

  • 利用封装高级API简洁实现：
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num_inputs = vocab_size
lstm_layer = nn.LSTM(num_inputs, num_hiddens)
model = d2l.RNNModel(lstm_layer, len(vocab))
model = model.to(device)
d2l.train_ch8(model, train_iter, vocab, lr, num_epochs, device)
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perplexity 1.1, 289795.5 tokens/sec on cuda:0
time travelleryou can show black is white by argument said filby
travelleryou can show black is white by argument said filby

3.3Encoder-Decoder

​ 主要简单复现编码器和解码器的代码架构。

​ 机器翻译是序列转换模型的一个核心问题，其输入和输出都是长度可变的序 列。为了处理这种类型的输入和输出，我们可以设计一个包含两个主要组件的架构：第一个组件是一个编码器 （encoder）：它接受一个长度可变的序列作为输入，并将其转换为具有固定形状的编码状态。第二个组件是解码 器（decoder）：它将固定形状的编码状态映射到长度可变的序列。这被称为编码器-解码器（encoder‐decoder） 架构

​

  • 编码器：我们只指定长度可变的序列作为编码器的输入X
  • 解码器：新增一个init_state函数，用于将编码器的输出enc_outputs转换为编码后状态。为了逐个生成长度可变的词元序列，解码器在每个时间步都会将输入和编码后的状态映射成当前时间步的输出词元
  • 合并结果（编码器-解码器）：代码的架构包含了一个编码器和一个解码器，并且可以添加额外的参数。在前向传播中，编码器的输出用于生成编码的状态，这个状态又会被解码器作为其输入的一部分。
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from torch import nn

class Encoder(nn.Module):
    "编码器接口"
    def __init__(self, **kwargs):
        super(Encoder, self).__init__(**kwargs)
    
    def forward(self, X, *args):
        raise NotImplementedError

class Decoder(nn.Module):
    "解码器接口"
    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
    
#合并编码器和解码器
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)

小结：

  • “编码器－解码器”架构可以将长度可变的序列作为输入和输出，因此适用于机器翻译等序列转换问题。
  • 编码器将长度可变的序列作为输入，并将其转换为具有固定形状的编码状态。
  • 解码器将具有固定形状的编码状态映射为长度可变的序列。

3.4seq2seq

  • 导入库
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import collections
import math
import torch
from torch import nn
from d2l import torch as d2l
  • 编码器架构：
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class Seq2SeqEncoder(d2l.Encoder):
    """用于序列到序列学习的循环神经网络编码器"""
    def __init__(self, vocab_size, embed_size, num_hiddens, num_layers,
                 dropout=0, **kwargs):
        super(Seq2SeqEncoder, self).__init__(**kwargs)
        # 嵌入层
        self.embedding = nn.Embedding(vocab_size, embed_size)
        self.rnn = nn.GRU(embed_size, num_hiddens, num_layers,
                          dropout=dropout)

    def forward(self, X, *args):
        # 输出'X'的形状：(batch_size,num_steps,embed_size)
        X = self.embedding(X)
        # 在循环神经网络模型中，第一个轴对应于时间步
        X = X.permute(1, 0, 2)
        # 如果未提及状态，则默认为0
        output, state = self.rnn(X)
        # output的形状:(num_steps,batch_size,num_hiddens)
        # state的形状:(num_layers,batch_size,num_hiddens)
        return output, state

实例化上述编码器,最后一层output隐状态输出的一个张量，形状为（时间步数，批量大小，隐藏单元数）state是最后一个时间步的多层隐状态，形状为（隐藏层数量，批量大小，隐藏单元数）

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encoder = Seq2SeqEncoder(vocab_size=10, embed_size=8, num_hiddens=16,num_layers=2)

encoder.eval()
X = torch.zeros((4,7), dtype = torch.long)
output, state = encoder(X)
print(output.shape)
print(state.shape)
#output:
#torch.Size([7, 4, 16])
#torch.Size([2, 4, 16])
  • 解码器架构：
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class Seq2SeqDecoder(d2l.Decoder):
    """用于序列到序列学习的循环神经网络解码器"""
    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.GRU(embed_size + num_hiddens, 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):
        # 输出'X'的形状：(batch_size,num_steps,embed_size)
        X = self.embedding(X).permute(1, 0, 2)
        # 广播context，使其具有与X相同的num_steps
        context = state[-1].repeat(X.shape[0], 1, 1)
        X_and_context = torch.cat((X, context), 2)
        output, state = self.rnn(X_and_context, state)
        output = self.dense(output).permute(1, 0, 2)
        # output的形状:(batch_size,num_steps,vocab_size)
        # state的形状:(num_layers,batch_size,num_hiddens)
        return output, state

实例化上述解码器，输出形状为（批量大小，时间步数，词表大小）

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decoder = Seq2SeqDecoder(vocab_size=10, embed_size=8, num_hiddens=16,
                         num_layers=2)
decoder.eval()
state = decoder.init_state(encoder(X))
output, state = decoder(X, state)
output.shape, state.shape

#Output:
#(torch.Size([4, 7, 10]), torch.Size([2, 4, 16]))
  • 损失函数：
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# 屏蔽不相关项
def sequence_mask(X, valid_len, value=0):
    """在序列中屏蔽不相关的项"""
    maxlen = X.size(1)
    mask = torch.arange((maxlen), dtype=torch.float32,
                        device=X.device)[None, :] < valid_len[:, None]
    X[~mask] = value
    return X
# 例子：
# X = torch.ones(2, 3, 4)
# sequence_mask(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):
    """带遮蔽的softmax交叉熵损失函数"""
    # pred的形状：(batch_size,num_steps,vocab_size)
    # label的形状：(batch_size,num_steps)
    # valid_len的形状：(batch_size,)
    def forward(self, pred, label, valid_len):
        weights = torch.ones_like(label)
        weights = sequence_mask(weights, valid_len)
        self.reduction='none'
        unweighted_loss = super(MaskedSoftmaxCELoss, self).forward(
            pred.permute(0, 2, 1), label)
        weighted_loss = (unweighted_loss * weights).mean(dim=1)
        return weighted_loss
    
#利用三个相同的序列进行代码健全性检查，能不能跑，然后分别指定相应的valid_len为4，2，0
loss = MaskedSoftmaxCELoss()
loss(torch.ones(3, 4, 10), torch.ones((3, 4), dtype=torch.long),
     torch.tensor([4, 2, 0]))

#Output
#tensor([2.3026, 1.1513, 0.0000])

结果就是，第一个序列的损失应为第二个序列的两倍，而第三个序列的损失应为零。

  • 训练：
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def train_seq2seq(net, data_iter, lr, num_epochs, tgt_vocab, device):
    """训练序列到序列模型"""
    def xavier_init_weights(m):
        if type(m) == nn.Linear:
            nn.init.xavier_uniform_(m.weight)
        if type(m) == nn.GRU:
            for param in m._flat_weights_names:
                if "weight" in param:
                    nn.init.xavier_uniform_(m._parameters[param])

    net.apply(xavier_init_weights)
    net.to(device)
    optimizer = torch.optim.Adam(net.parameters(), lr=lr)
    loss = MaskedSoftmaxCELoss()
    net.train()
    animator = d2l.Animator(xlabel='epoch', ylabel='loss',
                     xlim=[10, num_epochs])
    for epoch in range(num_epochs):
        timer = d2l.Timer()
        metric = d2l.Accumulator(2)  # 训练损失总和，词元数量
        for batch in data_iter:
            optimizer.zero_grad()
            X, X_valid_len, Y, Y_valid_len = [x.to(device) for x in batch]
            bos = torch.tensor([tgt_vocab['<bos>']] * Y.shape[0],
                          device=device).reshape(-1, 1)
            dec_input = torch.cat([bos, Y[:, :-1]], 1)  # 强制教学
            Y_hat, _ = net(X, dec_input, X_valid_len)
            l = loss(Y_hat, Y, Y_valid_len)
            l.sum().backward()	# 损失函数的标量进行“反向传播”
            d2l.grad_clipping(net, 1)
            num_tokens = Y_valid_len.sum()
            optimizer.step()
            with torch.no_grad():
                metric.add(l.sum(), num_tokens)
        if (epoch + 1) % 10 == 0:
            animator.add(epoch + 1, (metric[0] / metric[1],))
    print(f'loss {metric[0] / metric[1]:.3f}, {metric[1] / timer.stop():.1f} '
        f'tokens/sec on {str(device)}')

设置超参数开始训练

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embed_size, num_hiddens, num_layers, dropout = 32, 32, 2, 0.1
batch_size, num_steps = 64, 10
lr, num_epochs, device = 0.005, 300, d2l.try_gpu()

train_iter, src_vocab, tgt_vocab = d2l.load_data_nmt(batch_size, num_steps)
encoder = Seq2SeqEncoder(len(src_vocab), embed_size, num_hiddens, num_layers,
                        dropout)
decoder = Seq2SeqDecoder(len(tgt_vocab), embed_size, num_hiddens, num_layers,
                        dropout)
net = d2l.EncoderDecoder(encoder, decoder)
train_seq2seq(net, train_iter, lr, num_epochs, tgt_vocab, device)

  • 定义预测函数以及预测序列评估BLEU：
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def predict_seq2seq(net, src_sentence, src_vocab, tgt_vocab, num_steps,
                    device, save_attention_weights=False):
    """序列到序列模型的预测"""
    # 在预测时将net设置为评估模式
    net.eval()
    src_tokens = src_vocab[src_sentence.lower().split(' ')] + [
        src_vocab['<eos>']]
    enc_valid_len = torch.tensor([len(src_tokens)], device=device)
    src_tokens = d2l.truncate_pad(src_tokens, num_steps, src_vocab['<pad>'])
    # 添加批量轴
    enc_X = torch.unsqueeze(
        torch.tensor(src_tokens, dtype=torch.long, device=device), dim=0)
    enc_outputs = net.encoder(enc_X, enc_valid_len)
    dec_state = net.decoder.init_state(enc_outputs, enc_valid_len)
    # 添加批量轴
    dec_X = torch.unsqueeze(torch.tensor(
        [tgt_vocab['<bos>']], dtype=torch.long, device=device), dim=0)
    output_seq, attention_weight_seq = [], []
    for _ in range(num_steps):
        Y, dec_state = net.decoder(dec_X, dec_state)
        # 我们使用具有预测最高可能性的词元，作为解码器在下一时间步的输入
        dec_X = Y.argmax(dim=2)
        pred = dec_X.squeeze(dim=0).type(torch.int32).item()
        # 保存注意力权重（稍后讨论）
        if save_attention_weights:
            attention_weight_seq.append(net.decoder.attention_weights)
        # 一旦序列结束词元被预测，输出序列的生成就完成了
        if pred == tgt_vocab['<eos>']:
            break
        output_seq.append(pred)
    return ' '.join(tgt_vocab.to_tokens(output_seq)), attention_weight_seq

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def bleu(pred_seq, label_seq, k):  #@save
    """计算BLEU"""
    pred_tokens, label_tokens = pred_seq.split(' '), label_seq.split(' ')
    len_pred, len_label = len(pred_tokens), len(label_tokens)
    score = math.exp(min(0, 1 - len_label / len_pred))
    for n in range(1, k + 1):
        num_matches, label_subs = 0, collections.defaultdict(int)
        for i in range(len_label - n + 1):
            label_subs[' '.join(label_tokens[i: i + n])] += 1
        for i in range(len_pred - n + 1):
            if label_subs[' '.join(pred_tokens[i: i + n])] > 0:
                num_matches += 1
                label_subs[' '.join(pred_tokens[i: i + n])] -= 1
        score *= math.pow(num_matches / (len_pred - n + 1), math.pow(0.5, n))
    return score

最后利用上述训练好的RNN“编码器-解码器”模型，进行预测并计算BLEU：

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engs = ['go .', "i lost .", 'he\'s calm .', 'i\'m home .']
fras = ['va !', 'j\'ai perdu .', 'il est calme .', 'je suis chez moi .']
for eng, fra in zip(engs, fras):
    translation, attention_weight_seq = predict_seq2seq(
        net, eng, src_vocab, tgt_vocab, num_steps, device)
    print(f'{eng} => {translation}, bleu {bleu(translation, fra, k=2):.3f}')

输出：

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go . => va chercher tom ., bleu 0.000
i lost . => j'ai perdu ?, bleu 0.687
he's calm . => il est riche demande maintenant ., bleu 0.473
i'm home . => je suis chez moi <unk> ., bleu 0.803

关于seq2seq的思考：

  1. 根据“编码器-解码器”架构的设计，我们可以使用两个循环神经网络来设计一个序列到序列学习的模型。
  • 在实现编码器和解码器时，我们可以使用多层循环神经网络。
  • 我们可以使用遮蔽来过滤不相关的计算，例如在计算损失时。
  • 在“编码器－解码器”训练中，强制教学方法将原始输出序列（而非预测结果）输入解码器。
  • BLEU是一种常用的评估方法，它通过测量预测序列和标签序列之间的元语法的匹配度来评估预测。
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