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8.5.rnn scratch

梯度裁剪

类似于球形投影，使梯度的 L2 范数不超过阈值。

训练

注意训练时候每个批量的隐状态是分别存储的，不会相互影响。

  • 多久一次 backward？
    • 要将一个批量内所有样本的所有时间步（在程序开始时设定，比如样本 size = 32，单次输入时间步 num_steps 为 35）forward 以后（每次 forward 仅进行一个时间步的预测），才进行 backward。因此权重参数矩阵会累乘，容易导致梯度爆炸，故进行梯度裁剪。d2l 代码中，梯度裁剪在 backward 后，updater 之前执行。
    • 注意对每个批量而言，每次输入仅有一个 token，并非多个时间步 token 同时输入。

手绘

2:15:13

手动代码

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)

# 获取初始参数
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
    # 隐藏层参数
    W_xh = normal((num_inputs, num_hiddens))
    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))
    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

# 前向传播 forward
# 一次 forward 就将各个批量的所有时间步都生成完了
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 = []
    # 循环每个时间步
    for X in inputs:
        # X的形状：(批量大小，词表大小)
        # 注意这里隐状态包含所有批量各自的隐状态
        # H 形状: (批量大小，隐藏单元个数)
        H = torch.tanh(torch.mm(X, W_xh) + torch.mm(H, W_hh) + b_h)

        # 本步输出不会影响下一步输出，只有隐状态才会
        # Y 形状: (批量大小，词表大小)，因为前面已经指定 num_outputs = vocab_size
        Y = torch.mm(H, W_hq) + b_q
        outputs.append(Y)
    # 返回一个元组，即所有时间步的输出 y 和最后一个隐状态
    return torch.cat(outputs, dim=0), (H,)
    # torch.cat 输出为 (ns * n, n_vocab)

def init_rnn_state(batch_size, num_hiddens, device):
    return (torch.zeros((batch_size, num_hiddens), device=device), )

# 模型封装
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())

# 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:]:  # 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])

# 梯度裁剪
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
    norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))
    if norm > theta:
        for param in params:
            param.grad[:] *= theta / norm

# 训练一个 epoch
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_()
            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)
        # y.shape: (ns * n)
        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()

# 训练多个 epoch
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())