6.4 循环神经网络的从零开始实现

import d2lzh as d2l
import math
from mxnet import autograd, nd
from mxnet.gluon import loss as gloss
import time

(corpus_indices, char_to_idx, idx_to_char,
 vocab_size) = d2l.load_data_jay_lyrics()

6.4.1 one-hot向量

Mxnet:

nd.one_hot(nd.array([0, 2]), vocab_size)

def to_onehot(X, size):  # 本函数已保存在d2lzh包中方便以后使用
    return [nd.one_hot(x, size) for x in X.T]

X = nd.arange(10).reshape((2, 5))
inputs = to_onehot(X, vocab_size)
len(inputs), inputs[0].shape

Pytorch:

def one_hot(x, n_class, dtype=torch.float32): 
    # X shape: (batch), output shape: (batch, n_class)
    x = x.long()
    res = torch.zeros(x.shape[0], n_class, dtype=dtype, device=x.device)
    res.scatter_(1, x.view(-1, 1), 1)
    return res
    
x = torch.tensor([0, 2])
one_hot(x, vocab_size)

# 本函数已保存在d2lzh_pytorch包中方便以后使用
def to_onehot(X, n_class):  
    # X shape: (batch, seq_len), output: seq_len elements of (batch, 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)
print(len(inputs), inputs[0].shape)

6.4.2 初始化模型参数

Mxnet:

num_inputs, num_hiddens, num_outputs = vocab_size, 256, vocab_size
ctx = d2l.try_gpu()
print('will use', ctx)

def get_params():
    def _one(shape):
        return nd.random.normal(scale=0.01, shape=shape, ctx=ctx)

    # 隐藏层参数
    W_xh = _one((num_inputs, num_hiddens))
    W_hh = _one((num_hiddens, num_hiddens))
    b_h = nd.zeros(num_hiddens, ctx=ctx)
    # 输出层参数
    W_hq = _one((num_hiddens, num_outputs))
    b_q = nd.zeros(num_outputs, ctx=ctx)
    # 附上梯度
    params = [W_xh, W_hh, b_h, W_hq, b_q]
    for param in params:
        param.attach_grad()
    return params

Pytorch:

num_inputs, num_hiddens, num_outputs = vocab_size, 256, vocab_size
print('will use', device)

def get_params():
    def _one(shape):
        ts = torch.tensor(np.random.normal(0, 0.01, size=shape), device=device, dtype=torch.float32)
        return torch.nn.Parameter(ts, requires_grad=True)

    # 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, requires_grad=True))
    # 输出层参数
    W_hq = _one((num_hiddens, num_outputs))
    b_q = torch.nn.Parameter(torch.zeros(num_outputs, device=device, requires_grad=True))
    return nn.ParameterList([W_xh, W_hh, b_h, W_hq, b_q])

6.4.3 定义模型

Mxnet:

def init_rnn_state(batch_size, num_hiddens, ctx):
    return (nd.zeros(shape=(batch_size, num_hiddens), ctx=ctx), )

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 = nd.tanh(nd.dot(X, W_xh) + nd.dot(H, W_hh) + b_h)
        Y = nd.dot(H, W_hq) + b_q
        outputs.append(Y)
    return outputs, (H,)

state = init_rnn_state(X.shape[0], num_hiddens, ctx)
inputs = to_onehot(X.as_in_context(ctx), vocab_size)
params = get_params()
outputs, state_new = rnn(inputs, state, params)
len(outputs), outputs[0].shape, state_new[0].shape

Pytorch:

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

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,)

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(outputs), outputs[0].shape, state_new[0].shape)

6.4.4 定义预测函数

Mxnet:

# 本函数已保存在d2lzh包中方便以后使用
def predict_rnn(prefix, num_chars, rnn, params, init_rnn_state,
                num_hiddens, vocab_size, ctx, idx_to_char, char_to_idx):
    state = init_rnn_state(1, num_hiddens, ctx)
    output = [char_to_idx[prefix[0]]]
    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(nd.array([output[-1]], ctx=ctx), 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(int(Y[0].argmax(axis=1).asscalar()))
    return ''.join([idx_to_char[i] for i in output])

Pytorch:

# 本函数已保存在d2lzh_pytorch包中方便以后使用
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]]]
    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(int(Y[0].argmax(dim=1).item()))
    return ''.join([idx_to_char[i] for i in output])

6.4.5 裁剪梯度

Mxnet:

# 本函数已保存在d2lzh包中方便以后使用
def grad_clipping(params, theta, ctx):
    norm = nd.array([0], ctx)
    for param in params:
        norm += (param.grad ** 2).sum()
    norm = norm.sqrt().asscalar()
    if norm > theta:
        for param in params:
            param.grad[:] *= theta / norm

Pytorch:

# 本函数已保存在d2lzh_pytorch包中方便以后使用
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)

6.4.7 定义模型训练函数

Mxnet:

# 本函数已保存在d2lzh包中方便以后使用
def train_and_predict_rnn(rnn, get_params, init_rnn_state, num_hiddens,
                          vocab_size, ctx, 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 = gloss.SoftmaxCrossEntropyLoss()

    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, ctx)
        l_sum, n, start = 0.0, 0, time.time()
        data_iter = data_iter_fn(corpus_indices, batch_size, num_steps, ctx)
        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, ctx)
            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()
            with autograd.record():
                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 = nd.concat(*outputs, dim=0)
                # Y的形状是(batch_size, num_steps)，转置后再变成长度为
                # batch * num_steps 的向量，这样跟输出的行一一对应
                y = Y.T.reshape((-1,))
                # 使用交叉熵损失计算平均分类误差
                l = loss(outputs, y).mean()
            l.backward()
            grad_clipping(params, clipping_theta, ctx)  # 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.asscalar() * y.size
            n += y.size

        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, ctx, idx_to_char, char_to_idx))

Pytorch:

# 本函数已保存在d2lzh_pytorch包中方便以后使用
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 = 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)，转置后再变成长度为
            # batch * num_steps 的向量，这样跟输出的行一一对应
            y = torch.transpose(Y, 0, 1).contiguous().view(-1)
            # 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))

6.4.8 训练模型并创作歌词

Mxnet:

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']
# 下面采用随机采样训练模型并创作歌词
train_and_predict_rnn(rnn, get_params, init_rnn_state, num_hiddens,
                      vocab_size, ctx, corpus_indices, idx_to_char,
                      char_to_idx, True, num_epochs, num_steps, lr,
                      clipping_theta, batch_size, pred_period, pred_len,
                      prefixes)
                      
 # 采用相邻采样训练模型并创作歌词
 train_and_predict_rnn(rnn, get_params, init_rnn_state, num_hiddens,
                      vocab_size, ctx, corpus_indices, idx_to_char,
                      char_to_idx, False, num_epochs, num_steps, lr,
                      clipping_theta, batch_size, pred_period, pred_len,
                      prefixes)

Pytorch:

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)

train_and_predict_rnn(rnn, get_params, init_rnn_state, num_hiddens,
                      vocab_size, device, corpus_indices, idx_to_char,
                      char_to_idx, False, num_epochs, num_steps, lr,
                      clipping_theta, batch_size, pred_period, pred_len,
                      prefixes)