循环神经网络的构造
从零开始实现循环神经网络
我们先尝试从零开始实现一个基于字符级循环神经网络的语言模型，这里我们使用周杰伦的歌词作为语料，首先我们读入数据：
import torch import torch.nn as nn import time import math import sys sys.path.append("/home/input") import d2l_jay4504 as d2l (corpus_indices, char_to_idx, idx_to_char, vocab_size) = d2l.load_data_jay_lyrics() device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
one-hot向量
我们需要将字符表示成向量，这里采用one-hot向量。假设词典大小是，每次字符对应一个从到的唯一的索引，则该字符的向量是一个长度为的向量，若字符的索引是，则该向量的第个位置为，其他位置为。下面分别展示了索引为0和2的one-hot向量，向量长度等于词典大小。
def one_hot(x, n_class, dtype=torch.float32): result = torch.zeros(x.shape[0], n_class, dtype=dtype, device=x.device) # shape: (n, n_class) result.scatter_(1, x.long().view(-1, 1), 1) # result[i, x[i, 0]] = 1 return result x = torch.tensor([0, 2]) x_one_hot = one_hot(x, vocab_size) print(x_one_hot) print(x_one_hot.shape) print(x_one_hot.sum(axis=1))
输出：tensor([[1., 0., 0., ..., 0., 0., 0.], [0., 0., 1., ..., 0., 0., 0.]]) torch.Size([2, 1027]) tensor([1., 1.])
def to_onehot(X, n_class): return [one_hot(X[:, i], n_class) for i in range(X.shape[1])] X = torch.arange(10).view(2, 5) inputs = to_onehot(X, vocab_size)
初始化模型参数
num_inputs, num_hiddens, num_outputs = vocab_size, 256, vocab_size # num_inputs: d # num_hiddens: h, 隐藏单元的个数是超参数 # num_outputs: q def get_params(): def _one(shape): param = torch.zeros(shape, device=device, dtype=torch.float32) nn.init.normal_(param, 0, 0.01) return torch.nn.Parameter(param) # 隐藏层参数 W_xh = _one((num_inputs, num_hiddens)) W_hh = _one((num_hiddens, num_hiddens)) b_h = torch.nn.Parameter(torch.zeros(num_hiddens, device=device)) # 输出层参数 W_hq = _one((num_hiddens, num_outputs)) b_q = torch.nn.Parameter(torch.zeros(num_outputs, device=device)) return (W_xh, W_hh, b_h, W_hq, b_q)
定义模型
函数rnn用循环的方式依次完成循环神经网络每个时间步的计算。
def rnn(inputs, state, params): # inputs和outputs皆为num_steps个形状为(batch_size, vocab_size)的矩阵 W_xh, W_hh, b_h, W_hq, b_q = params H, = state outputs = [] for X in inputs: H = torch.tanh(torch.matmul(X, W_xh) + torch.matmul(H, W_hh) + b_h) Y = torch.matmul(H, W_hq) + b_q outputs.append(Y) return outputs, (H,)
函数init_rnn_state初始化隐藏变量，这里的返回值是一个元组。
def init_rnn_state(batch_size, num_hiddens, device): return (torch.zeros((batch_size, num_hiddens), device=device), )
做个简单的测试来观察输出结果的个数（时间步数），以及第一个时间步的输出层输出的形状和隐藏状态的形状。
print(X.shape) print(num_hiddens) print(vocab_size) state = init_rnn_state(X.shape[0], num_hiddens, device) inputs = to_onehot(X.to(device), vocab_size) params = get_params() outputs, state_new = rnn(inputs, state, params) print(len(inputs), inputs[0].shape) print(len(outputs), outputs[0].shape) print(len(state), state[0].shape) print(len(state_new), state_new[0].shape)
输出：torch.Size([2, 5]) 256 1027 5 torch.Size([2, 1027]) 5 torch.Size([2, 1027]) 1 torch.Size([2, 256]) 1 torch.Size([2, 256])
裁剪梯度
def grad_clipping(params, theta, device): norm = torch.tensor([0.0], device=device) for param in params: norm += (param.grad.data ** 2).sum() norm = norm.sqrt().item() if norm > theta: for param in params: param.grad.data *= (theta / norm)
定义预测函数
以下函数基于前缀prefix（含有数个字符的字符串）来预测接下来的num_chars个字符。这个函数稍显复杂，其中我们将循环神经单元rnn设置成了函数参数，这样在后面小节介绍其他循环神经网络时能重复使用这个函数。
def predict_rnn(prefix, num_chars, rnn, params, init_rnn_state, num_hiddens, vocab_size, device, idx_to_char, char_to_idx): state = init_rnn_state(1, num_hiddens, device) output = [char_to_idx[prefix[0]]] # output记录prefix加上预测的num_chars个字符 for t in range(num_chars + len(prefix) - 1): # 将上一时间步的输出作为当前时间步的输入 X = to_onehot(torch.tensor([[output[-1]]], device=device), vocab_size) # 计算输出和更新隐藏状态 (Y, state) = rnn(X, state, params) # 下一个时间步的输入是prefix里的字符或者当前的最佳预测字符 if t < len(prefix) - 1: output.append(char_to_idx[prefix[t + 1]]) else: output.append(Y[0].argmax(dim=1).item()) return ''.join([idx_to_char[i] for i in output])
我们先测试一下predict_rnn函数。我们将根据前缀“分开”创作长度为10个字符（不考虑前缀长度）的一段歌词。因为模型参数为随机值，所以预测结果也是随机的。
predict_rnn('分开', 10, rnn, params, init_rnn_state, num_hiddens, vocab_size, device, idx_to_char, char_to_idx)
输出：'分开濡时食提危踢拆田唱母'
困惑度
我们通常使用困惑度（perplexity）来评价语言模型的好坏。回忆一下“softmax回归”一节中交叉熵损失函数的定义。困惑度是对交叉熵损失函数做指数运算后得到的值。特别地，
- 最佳情况下，模型总是把标签类别的概率预测为1，此时困惑度为1；
- 最坏情况下，模型总是把标签类别的概率预测为0，此时困惑度为正无穷；
- 基线情况下，模型总是预测所有类别的概率都相同，此时困惑度为类别个数。
显然，任何一个有效模型的困惑度必须小于类别个数。在本例中，困惑度必须小于词典大小vocab_size。
定义模型训练函数
跟之前章节的模型训练函数相比，这里的模型训练函数有以下几点不同：
- 使用困惑度评价模型。
- 在迭代模型参数前裁剪梯度。
- 对时序数据采用不同采样方法将导致隐藏状态初始化的不同。
def train_and_predict_rnn(rnn, get_params, init_rnn_state, num_hiddens, vocab_size, device, corpus_indices, idx_to_char, char_to_idx, is_random_iter, num_epochs, num_steps, lr, clipping_theta, batch_size, pred_period, pred_len, prefixes): if is_random_iter: data_iter_fn = d2l.data_iter_random else: data_iter_fn = d2l.data_iter_consecutive params = get_params() loss = nn.CrossEntropyLoss() for epoch in range(num_epochs): if not is_random_iter: # 如使用相邻采样，在epoch开始时初始化隐藏状态 state = init_rnn_state(batch_size, num_hiddens, device) l_sum, n, start = 0.0, 0, time.time() data_iter = data_iter_fn(corpus_indices, batch_size, num_steps, device) for X, Y in data_iter: if is_random_iter: # 如使用随机采样，在每个小批量更新前初始化隐藏状态 state = init_rnn_state(batch_size, num_hiddens, device) else: # 否则需要使用detach函数从计算图分离隐藏状态 for s in state: s.detach_() # inputs是num_steps个形状为(batch_size, vocab_size)的矩阵 inputs = to_onehot(X, vocab_size) # outputs有num_steps个形状为(batch_size, vocab_size)的矩阵 (outputs, state) = rnn(inputs, state, params) # 拼接之后形状为(num_steps * batch_size, vocab_size) outputs = torch.cat(outputs, dim=0) # Y的形状是(batch_size, num_steps)，转置后再变成形状为 # (num_steps * batch_size,)的向量，这样跟输出的行一一对应 y = torch.flatten(Y.T) # 使用交叉熵损失计算平均分类误差 l = loss(outputs, y.long()) # 梯度清0 if params[0].grad is not None: for param in params: param.grad.data.zero_() l.backward() grad_clipping(params, clipping_theta, device) # 裁剪梯度 d2l.sgd(params, lr, 1) # 因为误差已经取过均值，梯度不用再做平均 l_sum += l.item() * y.shape[0] n += y.shape[0] if (epoch + 1) % pred_period == 0: print('epoch %d, perplexity %f, time %.2f sec' % ( epoch + 1, math.exp(l_sum / n), time.time() - start)) for prefix in prefixes: print(' -', predict_rnn(prefix, pred_len, rnn, params, init_rnn_state, num_hiddens, vocab_size, device, idx_to_char, char_to_idx))
训练模型并创作歌词
现在我们可以训练模型了。首先，设置模型超参数。我们将根据前缀“分开”和“不分开”分别创作长度为50个字符（不考虑前缀长度）的一段歌词。我们每过50个迭代周期便根据当前训练的模型创作一段歌词。
num_epochs, num_steps, batch_size, lr, clipping_theta = 250, 35, 32, 1e2, 1e-2 pred_period, pred_len, prefixes = 50, 50, ['分开', '不分开'] train_and_predict_rnn(rnn, get_params, init_rnn_state, num_hiddens, vocab_size, device, corpus_indices, idx_to_char, char_to_idx, True, num_epochs, num_steps, lr, clipping_theta, batch_size, pred_period, pred_len, prefixes)
循环神经网络的简介实现
定义模型
我们使用Pytorch中的nn.RNN来构造循环神经网络。在本节中，我们主要关注nn.RNN的以下几个构造函数参数：
input_size- The number of expected features in the input xhidden_size– The number of features in the hidden state hnonlinearity– The non-linearity to use. Can be either 'tanh' or 'relu'. Default: 'tanh'batch_first– If True, then the input and output tensors are provided as (batch_size, num_steps, input_size). Default: False
这里的batch_first决定了输入的形状，我们使用默认的参数False，对应的输入形状是 (num_steps, batch_size, input_size)。
forward函数的参数为：
inputof shape (num_steps, batch_size, input_size): tensor containing the features of the input sequence.h_0of shape (num_layers * num_directions, batch_size, hidden_size): tensor containing the initial hidden state for each element in the batch. Defaults to zero if not provided. If the RNN is bidirectional, num_directions should be 2, else it should be 1.
forward函数的返回值是：
outputof shape (num_steps, batch_size, num_directions * hidden_size): tensor containing the output features (h_t) from the last layer of the RNN, for each t.h_nof shape (num_layers * num_directions, batch_size, hidden_size): tensor containing the hidden state for t = num_steps.
现在我们构造一个nn.RNN实例，并用一个简单的例子来看一下输出的形状。
rnn_layer = nn.RNN(input_size=vocab_size, hidden_size=num_hiddens) num_steps, batch_size = 35, 2 X = torch.rand(num_steps, batch_size, vocab_size) state = None Y, state_new = rnn_layer(X, state) class RNNModel(nn.Module): def __init__(self, rnn_layer, vocab_size): super(RNNModel, self).__init__() self.rnn = rnn_layer self.hidden_size = rnn_layer.hidden_size * (2 if rnn_layer.bidirectional else 1) self.vocab_size = vocab_size self.dense = nn.Linear(self.hidden_size, vocab_size) def forward(self, inputs, state): # inputs.shape: (batch_size, num_steps) X = to_onehot(inputs, vocab_size) X = torch.stack(X) # X.shape: (num_steps, batch_size, vocab_size) hiddens, state = self.rnn(X, state) hiddens = hiddens.view(-1, hiddens.shape[-1]) # hiddens.shape: (num_steps * batch_size, hidden_size) output = self.dense(hiddens) return output, state
类似的，我们需要实现一个预测函数，与前面的区别在于前向计算和初始化隐藏状态。
def predict_rnn_pytorch(prefix, num_chars, model, vocab_size, device, idx_to_char, char_to_idx): state = None output = [char_to_idx[prefix[0]]] # output记录prefix加上预测的num_chars个字符 for t in range(num_chars + len(prefix) - 1): X = torch.tensor([output[-1]], device=device).view(1, 1) (Y, state) = model(X, state) # 前向计算不需要传入模型参数 if t < len(prefix) - 1: output.append(char_to_idx[prefix[t + 1]]) else: output.append(Y.argmax(dim=1).item()) return ''.join([idx_to_char[i] for i in output]) model = RNNModel(rnn_layer, vocab_size).to(device) predict_rnn_pytorch('分开', 10, model, vocab_size, device, idx_to_char, char_to_idx)
输出：'分开胸呵以轮轮轮轮轮轮轮'
接下来实现训练函数，这里只使用了相邻采样。
def train_and_predict_rnn_pytorch(model, num_hiddens, vocab_size, device, corpus_indices, idx_to_char, char_to_idx, num_epochs, num_steps, lr, clipping_theta, batch_size, pred_period, pred_len, prefixes): loss = nn.CrossEntropyLoss() optimizer = torch.optim.Adam(model.parameters(), lr=lr) model.to(device) for epoch in range(num_epochs): l_sum, n, start = 0.0, 0, time.time() data_iter = d2l.data_iter_consecutive(corpus_indices, batch_size, num_steps, device) # 相邻采样 state = None for X, Y in data_iter: if state is not None: # 使用detach函数从计算图分离隐藏状态 if isinstance (state, tuple): # LSTM, state:(h, c) state[0].detach_() state[1].detach_() else: state.detach_() (output, state) = model(X, state) # output.shape: (num_steps * batch_size, vocab_size) y = torch.flatten(Y.T) l = loss(output, y.long()) optimizer.zero_grad() l.backward() grad_clipping(model.parameters(), clipping_theta, device) optimizer.step() l_sum += l.item() * y.shape[0] n += y.shape[0] if (epoch + 1) % pred_period == 0: print('epoch %d, perplexity %f, time %.2f sec' % ( epoch + 1, math.exp(l_sum / n), time.time() - start)) for prefix in prefixes: print(' -', predict_rnn_pytorch( prefix, pred_len, model, vocab_size, device, idx_to_char, char_to_idx)) num_epochs, batch_size, lr, clipping_theta = 250, 32, 1e-3, 1e-2 pred_period, pred_len, prefixes = 50, 50, ['分开', '不分开'] train_and_predict_rnn_pytorch(model, num_hiddens, vocab_size, device, corpus_indices, idx_to_char, char_to_idx, num_epochs, num_steps, lr, clipping_theta, batch_size, pred_period, pred_len, prefixes)
参考文献
[1]《动手深度学习》李沐
[2]伯禹教育课程
