沐神版《动手学深度学习》学习笔记，记录学习过程，详细的内容请大家购买书籍查阅。

b站视频链接
开源教程链接

循环神经网络

潜变量自回归模型：

循环神经网络结构：
简单来说循环神经网络RNN就是在MLP中加了一项，使它可以与前一个时间的$h_{t-1}$发生关系。时序信息存储在$W_{hh}$。

使用循环神经网络的语言模型：

困惑度（Perplexity）定义：
平均交叉熵取指数，困惑度是k的话，代表着下一个词有k种可能，1是最好的情况。

梯度剪裁：
RNN要计算T次，在反向传播过程中会做O(T)的矩阵乘法，导致数值不稳定。梯度剪裁是一个投影操作，如果梯度长度太大，就拉回来。|| ||做了一次L2 norm。

RNN相关应用：生成、分类、问答机翻、Tag生成。

总结

动手学

循环神经网络手动实现

%matplotlib inline
import math
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 # 批量大小，长度
train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)

F.one_hot(torch.tensor([1, 2]), len(vocab)) # 独热编码

tensor([[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
         0, 0, 0, 0],
        [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
         0, 0, 0, 0]])

X = torch.arange(10).reshape((2, 5)) # 小批量数据形状是二维张量:（批量大小，时间步数）
F.one_hot(X.T, 28).shape

torch.Size([5, 2, 28])

def get_params(vocab_size, num_hiddens, device):
    '''初始化循环神经网络的模型参数'''

    num_inputs = num_outputs = vocab_size # RNN输入、输出的维度都是vocab_size

    def normal(shape): # tensor生成辅助函数
        return torch.randn(size=shape, device=device) * 0.01

    # 隐藏层参数
    W_xh = normal((num_inputs, num_hiddens)) # 输入变量映射到隐藏层
    W_hh = normal((num_hiddens, num_hiddens))
    b_h = torch.zeros(num_hiddens, device=device)

    # 输出层参数
    W_hq = normal((num_hiddens, num_outputs)) # 隐藏层到输出变量的映射
    b_q = torch.zeros(num_outputs, device=device)

    # 附加梯度
    params = [W_xh, W_hh, b_h, W_hq, b_q]
    for param in params:
        param.requires_grad_(True)
        
    return params

def init_rnn_state(batch_size, num_hiddens, device):
    '''初始化隐藏变量'''
    return (torch.zeros((batch_size, num_hiddens), device=device), ) # 临时刻时没有隐藏状态

def rnn(inputs, state, params):
    '''rnn计算，类似forward函数'''

    # inputs的形状：(时间步数量，批量大小，词表大小) 与MLP区别在于多一个时间步数量
    W_xh, W_hh, b_h, W_hq, b_q = params
    H, = state
    outputs = []
    # X的形状：(批量大小，词表大小)
    for X in inputs:
        H = torch.tanh(torch.mm(X, W_xh) + torch.mm(H, W_hh) + b_h)
        Y = torch.mm(H, W_hq) + b_q
        outputs.append(Y) # Y：（批量大小*时间长度）*词表大小
        
    return torch.cat(outputs, dim=0), (H,)

class RNNModelScratch: #@save
    """从零开始实现的循环神经网络模型"""

    def __init__(self, vocab_size, num_hiddens, device, get_params, init_state, forward_fn):
        
        self.vocab_size, self.num_hiddens = vocab_size, num_hiddens
        self.params = get_params(vocab_size, num_hiddens, device)
        self.init_state, self.forward_fn = init_state, forward_fn

    def __call__(self, X, state):
        X = F.one_hot(X.T, self.vocab_size).type(torch.float32)
        return self.forward_fn(X, state, self.params)

    def begin_state(self, batch_size, device):
        return self.init_state(batch_size, self.num_hiddens, device)

# 检查输出是否具有正确的形状
num_hiddens = 512
net = RNNModelScratch(len(vocab), num_hiddens, d2l.try_gpu(), get_params, init_rnn_state, rnn)
state = net.begin_state(X.shape[0], d2l.try_gpu())
Y, new_state = net(X.to(d2l.try_gpu()), state)
Y.shape, len(new_state), new_state[0].shape # 28个词，10-批量*时间步，批量*num_hiddens

(torch.Size([10, 28]), 1, torch.Size([2, 512]))

# 预测
def predict_ch8(prefix, num_preds, net, vocab, device):  #@save
    """在prefix后面生成新字符"""

    state = net.begin_state(batch_size=1, device=device)
    outputs = [vocab[prefix[0]]] # outputs最开始长度为1
    get_input = lambda: torch.tensor([outputs[-1]], device=device).reshape((1, 1))
    for y in prefix[1:]:  # 预热期
        _, state = net(get_input(), state)
        outputs.append(vocab[y])
    for _ in range(num_preds):  # 预测num_preds步
        y, state = net(get_input(), state)
        outputs.append(int(y.argmax(dim=1).reshape(1)))

    return ''.join([vocab.idx_to_token[i] for i in outputs])

predict_ch8('time traveller ', 10, net, vocab, d2l.try_gpu())

'time traveller yurlgamfuz'

梯度剪裁
时间步为35，等价于一个35层的MLP，容易发生梯度爆炸。
$$g\leftarrow min(1,\frac{\theta }{\Vert g\Vert })g$$

def grad_clipping(net, theta):  #@save
    """裁剪梯度"""
    
    if isinstance(net, nn.Module):
        params = [p for p in net.parameters() if p.requires_grad]
    else:
        params = net.params # 所有层的参数
    norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))
    if norm > theta:
        for param in params:
            param.grad[:] *= theta / norm # 预防梯度变大

#@save
def train_epoch_ch8(net, train_iter, loss, updater, device, use_random_iter):
    """训练网络一个迭代周期（定义见第8章）"""

    state, timer = None, d2l.Timer()
    metric = d2l.Accumulator(2)  # 训练损失之和,词元数量
    for X, Y in train_iter:
        if state is None or use_random_iter:
            # 在第一次迭代或使用随机抽样时初始化state
            state = net.begin_state(batch_size=X.shape[0], device=device)
        else:
            if isinstance(net, nn.Module) and not isinstance(state, tuple):
                # state对于nn.GRU是个张量
                state.detach_() # 初始化时只关心现在开始后的计算图，之前的计算图丢掉
            else:
                # state对于nn.LSTM或对于我们从零开始实现的模型是个张量
                for s in state:
                    s.detach_()

        y = Y.T.reshape(-1) # 拉长，因为任务本质上就是一个多分类
        X, y = X.to(device), y.to(device)
        y_hat, state = net(X, state)
        l = loss(y_hat, y.long()).mean()

        if isinstance(updater, torch.optim.Optimizer):
            updater.zero_grad()
            l.backward()
            grad_clipping(net, 1)
            updater.step()
        else:
            l.backward()
            grad_clipping(net, 1)
            # 因为已经调用了mean函数
            updater(batch_size=1)
        metric.add(l * y.numel(), y.numel())

    return math.exp(metric[0] / metric[1]), metric[1] / timer.stop()

#@save
def train_ch8(net, train_iter, vocab, lr, num_epochs, device,
              use_random_iter=False):
    """训练模型（定义见第8章）"""

    loss = nn.CrossEntropyLoss()
    animator = d2l.Animator(xlabel='epoch', ylabel='perplexity',
                            legend=['train'], xlim=[10, num_epochs])
    # 初始化
    if isinstance(net, nn.Module):
        updater = torch.optim.SGD(net.parameters(), lr)
    else:
        updater = lambda batch_size: d2l.sgd(net.params, lr, batch_size)
    predict = lambda prefix: predict_ch8(prefix, 50, net, vocab, device)
    
    # 训练和预测
    for epoch in range(num_epochs):
        ppl, speed = train_epoch_ch8(
            net, train_iter, loss, updater, device, use_random_iter)
        if (epoch + 1) % 10 == 0:
            print(predict('time traveller'))
            animator.add(epoch + 1, [ppl])
    print(f'困惑度 {ppl:.1f}, {speed:.1f} 词元/秒 {str(device)}')
    print(predict('time traveller'))
    print(predict('traveller'))

num_epochs, lr = 500, 1
train_ch8(net, train_iter, vocab, lr, num_epochs, d2l.try_gpu())
# 以字符为vocab来训练，字符靠谱，但放在一块不靠谱了，基本将整本书记住了

net = RNNModelScratch(len(vocab), num_hiddens, d2l.try_gpu(), get_params,
                      init_rnn_state, rnn)
train_ch8(net, train_iter, vocab, lr, num_epochs, d2l.try_gpu(),
          use_random_iter=True)

循环神经网络简易实现

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
num_hiddens = 256
rnn_layer = nn.RNN(len(vocab), num_hiddens)

# 使用张量来初始化隐状态，它的形状是（隐藏层数，批量大小，隐藏单元数）
state = torch.zeros((1, batch_size, num_hiddens))
state.shape

# 通过一个隐状态和一个输入，我们就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

(torch.Size([35, 32, 256]), torch.Size([1, 32, 256]))

#@save
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
        # 如果RNN是双向的（之后将介绍），num_directions应该是2，否则应该是1
        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)
        # 全连接层首先将Y的形状改为(时间步数*批量大小,隐藏单元数)
        # 它的输出形状是(时间步数*批量大小,词表大小)。
        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):
            # nn.GRU以张量作为隐状态
            return  torch.zeros((self.num_directions * self.rnn.num_layers,
                                 batch_size, self.num_hiddens),
                                device=device)
        else:
            # nn.LSTM以元组作为隐状态
            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))

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)

'time travellercccccccccc'

num_epochs, lr = 500, 1
d2l.train_ch8(net, train_iter, vocab, lr, num_epochs, device)