（1）网络结构：基于潜变量自回归模型，每个时间步输出基于当前xt和前一时刻ht-1。（RNN的特征在于，对于每个RNN神经元，其参数始终共享，即对于文本序列，任何一个输入都经过相同的处理，得到一个输出）

 （2）困惑度：度量语言模型的质量

 （3）梯度裁剪

（4）零基础实现

# %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
train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)
# one-hot编码
print(F.one_hot(torch.tensor([0, 2]), len(vocab)))

# 小批量数据形状是批量大小和时间步数
X = torch.arange(10).reshape((2, 5))
print(F.one_hot(X.T, 28).shape)


# 初始化循环神经网络模型的模型参数
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

    W_xh = normal((num_inputs, num_hiddens))
    W_hh = normal((num_hiddens, num_hiddens))
    b_h = torch.zeros(num_hiddens, device=device)
    W_hq = normal((num_hiddens, num_outputs))
    b_q = torch.zeros(num_outputs, device=device)
    params = [W_xh, W_hh, b_h, W_hq, b_q]
    for param in params:
        param.requires_grad_(True)

    return params


# 初始隐藏状态
def init_rnn_state(batch_size, num_hiddens, device):
    return (torch.zeros((batch_size, num_hiddens), device=device),)


# rnn函数定义了如何在一个时间步内计算隐藏状态和输出
def rnn(inputs, state, params):
    # `inputs`的形状：(`时间步数量`，`批量大小`，`词表大小`)
    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)
    return torch.cat(outputs, dim=0), (H,)


class RNNModelScratch:
    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)


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)
print(Y.shape, len(new_state), new_state[0].shape)


# 预测
def predict_ch8(prefix, num_preds, net, vocab, device):
    """在`prefix`后面生成新字符。"""
    state = net.begin_state(batch_size=1, device=device)
    outputs = [vocab[prefix[0]]]
    get_input = lambda: torch.tensor([outputs[-1]], device=device).reshape((1, 1))
    for y in prefix[1:]:
        _, state = net(get_input(), state)
        outputs.append(vocab[y])
    for _ in range(num_preds):
        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])


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


# 梯度裁剪
def grad_clipping(net, theta):
    if isinstance(net, nn.Module):
        params = [p for p in net.parameters() if p.requires_grad]
    else:
        params = net.params
    norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))
    if norm > theta:
        for param in params:
            param.grad[:] *= theta / norm


def train_epoch_ch8(net, train_iter, loss, updater, device, use_random_iter):
    """训练模型一个迭代周期（定义见第8章）。"""
    state,timer = None,d2l.Timer()

    # @save
    def train_epoch_ch8(net, train_iter, loss, updater, device, use_random_iter):
        """训练模型一个迭代周期（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_()
                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)
            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()

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())

（5）简洁实现

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)

num_hiddens = 256
rnn_layer = nn.RNN(len(vocab), num_hiddens)
state = torch.zeros((1,batch_size,num_hiddens))
print(state.shape)

X = torch.rand(size=(num_steps, batch_size, len(vocab)))
Y, state_new = rnn_layer(X, state)
print(Y.shape, state_new.shape)

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` 以张量作为隐藏状态
            return  torch.zeros((self.num_directions * self.rnn.num_layers,
                                 batch_size, self.num_hiddens),
                                device=device)
        else:
            # `nn.LSTM` 以张量作为隐藏状态
            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)
print(d2l.predict_ch8('time traveller', 10, net, vocab, device))

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