深度学习系列（五）循环神经网络 2020.6.22

前言

本节学习循环神经网络

• 引⼊状态变量来存储过去的信息
• ⽤其与当前的输⼊共同决定当前的输出

1、语言模型

假设⼀段⻓度为T的⽂本中的词依次为w1，w2……wt
语言模型计算序列w1，w2……wt的概率P(w1，w2……wt)
需要计算词的概率，以及⼀个词在给定前⼏个词的情况下的条件概率，即语⾔模型参数
其中有个n元语法，即n阶⻢尔可夫链

2、循环神经网络

• 相较于多层感知机，多了个时间步的隐藏变量
• 由当前时间步的输⼊和上⼀时间步的隐藏变量共同决定

一个基于字符级循环神经⽹络的语⾔模型

• ⽂本序列为“想”“要”“有”“直”“升”“机”
• 对每个时间步的输出层输出使⽤softmax运算
• 然后使⽤交叉熵损失函数来计算它与标签的误差

3、实现

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

"""实现⼀个基于字符级循环神经⽹络的语⾔模型"""
# 读取周杰伦专辑歌词数据集
(corpus_indices, char_to_idx, idx_to_char, vocab_size) = d2l.load_data_jay_lyrics()
def to_onehot(X, size):  #将词表⽰成向量输⼊到神经⽹络
    return [nd.one_hot(x, size) for x in X.T]
X = nd.arange(10).reshape((2, 5))
inputs = to_onehot(X, vocab_size)
print(len(inputs), inputs[0].shape)

# 模型参数
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

# 模型
def init_rnn_state(batch_size, num_hiddens, ctx): #初始化隐藏状态
    return (nd.zeros(shape=(batch_size, num_hiddens), ctx=ctx), )
def rnn(inputs, state, params): #在⼀个时间步⾥计算隐藏状态和输出
    # 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,)
# 观察
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)
print(len(outputs), outputs[0].shape, state_new[0].shape)

# 预测函数
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])

# 裁剪梯度
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

# 训练
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))

# 参数设置
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']
# 训练与创作
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)

结语

初步了解了RNN
之后进行深入了解