Salute！NNLM的PyTorch实现

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本文主要首先介绍一篇年代久远但意义重大的论文A Neural Probabilistic Language Model(2003)，然后给出PyTorch实现

A Neural Probabilistic Language Model

本文算是训练语言模型的经典之作，Bengio将神经网络引入语言模型的训练中，并得到了词向量这个副产物。词向量对后面深度学习在自然语言处理方面有很大的贡献，也是获取词的语义特征的有效方法

其主要架构为三层神经网络，如下图所示

现在的任务是输入 $w_{t-n+1},…,w_{t-1}$ 这前n-1个单词，然后预测出下一个单词 $w_t$

数学符号说明：

$C (i)$ ：单词 $w$ 对应的词向量，其中 $i$ 为词 $w$ 在整个词汇表中的索引
$C$ ：词向量，大小为 $∣V∣×m|V|\times m$ 的矩阵
$∣ V ∣$ ：词汇表的大小，即预料库中去重后的单词个数
$m$ ：词向量的维度，一般是50到200
$H$ ：隐藏层的weight
$d$ ：隐藏层的bias
$U$ ：输出层的weight
$b$ ：输出层的bias
$W$ ：输入层到输出层的weight
$h$ ：隐藏层神经元个数

计算流程：

首先将输入的n-1个单词索引转为词向量，然后将这n-1个词向量进行concat，形成一个(n-1)*w的向量，用X表示
将X送入隐藏层进行计算， $hidden_{out} = tanh(d+X*H)$
输出层共有 $∣ V ∣$ 个节点，每个节点 $y_i$ 表示预测下一个单词 $i$ 的概率， $y$ 的计算公式为 $y=b+X*W+hidden_{out}*U$

代码实现（PyTorch）

# code by Tae Hwan Jung @graykode, modify by wmathor
import torch
import torch.nn as nn
import torch.optim as optim
import torch.utils.data as Data

dtype = torch.FloatTensor

sentences = [ "i like dog", "i love coffee", "i hate milk"]

word_list = " ".join(sentences).split() # ['i', 'like', 'dog', 'dog', 'i', 'love', 'coffee', 'i', 'hate', 'milk']
word_list = list(set(word_list)) # ['i', 'like', 'dog', 'love', 'coffee', 'hate', 'milk']
word_dict = {w: i for i, w in enumerate(word_list)} # {'i':0, 'like':1, 'dog':2, 'love':3, 'coffee':4, 'hate':5, 'milk':6}
number_dict = {i: w for i, w in enumerate(word_list)} # {0:'i', 1:'like', 2:'dog', 3:'love', 4:'coffee', 5:'hate', 6:'milk'}
n_class = len(word_dict) # number of Vocabulary, just like |V|, in this task n_class=7

# NNLM(Neural Network Language Model) Parameter
n_step = len(sentences[0].split())-1 # n-1 in paper, look back n_step words and predict next word. In this task n_step=2
n_hidden = 2 # h in paper
m = 2 # m in paper, word embedding dim

由于PyTorch中输入数据是以mini-batch小批量进行的，下面的函数首先将原始数据（词）全部转为索引，然后通过TensorDataset()和DataLoader()编写一个实用的mini-batch迭代器

def make_batch(sentences):
	input_batch = []
    target_batch = []

    for sen in sentences:
        word = sen.split()
        input = [word_dict[n] for n in word[:-1]] # [0, 1], [0, 3], [0, 5]
        target = word_dict[word[-1]] # 2, 4, 6

        input_batch.append(input) # [[0, 1], [0, 3], [0, 5]]
        target_batch.append(target) # [2, 4, 6]

    return input_batch, target_batch

input_batch, target_batch = make_batch(sentences)
input_batch = torch.LongTensor(input_batch)
target_batch = torch.LongTensor(target_batch)

dataset = Data.TensorDataset(input_batch, target_batch)
loader = Data.DataLoader(dataset=dataset, batch_size=16, shuffle=True)

class NNLM(nn.Module):
  def __init__(self):
    super(NNLM, self).__init__()
    self.C = nn.Embedding(n_class, m)
    self.H = nn.Parameter(torch.randn(n_step * m, n_hidden).type(dtype))
    self.W = nn.Parameter(torch.randn(n_step * m, n_class).type(dtype))
    self.d = nn.Parameter(torch.randn(n_hidden).type(dtype))
    self.U = nn.Parameter(torch.randn(n_hidden, n_class).type(dtype))
    self.b = nn.Parameter(torch.randn(n_class).type(dtype))

  def forward(self, X):
    '''
    X: [batch_size, n_step]
    '''
    X = self.C(X) # [batch_size, n_step] => [batch_size, n_step, m]
    X = X.view(-1, n_step * m) # [batch_size, n_step * m]
    hidden_out = torch.tanh(self.d + torch.mm(X, self.H)) # [batch_size, n_hidden]
    output = self.b + torch.mm(X, self.W) + torch.mm(hidden_out, self.U) # [batch_size, n_class]
    return output

model = NNLM()
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=1e-3)

nn.Parameter()的作用是将该参数添加进模型中，使其能够通过model.parameters()找到、管理、并且更新。更具体的来说就是：

nn.Parameter()与nn.Module一起使用时会有一些特殊的属性，其会被自动加到 Module 的parameters()迭代器中
使用很简单：torch.nn.Parameter(data, requires_grad=True)，其中data为tensor

简单解释一下执行X=self.C(X)这一步之后X发生了什么变化，假设初始X=[[0, 1], [0, 3]]

通过Embedding()之后，会将每一个词的索引，替换为对应的词向量，例如love这个词的索引是3，通过查询Word Embedding表得到行索引为3的向量为[0.2, 0.1]，于是就会将原来X中3的值替换为该向量，所有值都替换完之后，X=[[[0.3, 0.8], [0.2, 0.4]], [[0.3, 0.8], [0.2, 0.1]]]

# Training
for epoch in range(5000):
  for batch_x, batch_y in loader:
    optimizer.zero_grad()
    output = model(batch_x)

    # output : [batch_size, n_class], batch_y : [batch_size] (LongTensor, not one-hot)
    loss = criterion(output, batch_y)
    if (epoch + 1)%1000 == 0:
        print('Epoch:', '%04d' % (epoch + 1), 'cost =', '{:.6f}'.format(loss))

    loss.backward()
    optimizer.step()

# Predict
predict = model(input_batch).data.max(1, keepdim=True)[1]

# Test
print([sen.split()[:n_step] for sen in sentences], '->', [number_dict[n.item()] for n in predict.squeeze()])

完整代码：

# code by Tae Hwan Jung @graykode, modify by wmathor
import torch
import torch.nn as nn
import torch.optim as optim
import torch.utils.data as Data

dtype = torch.FloatTensor

sentences = [ "i like dog", "i love coffee", "i hate milk"]

word_list = " ".join(sentences).split() # ['i', 'like', 'dog', 'dog', 'i', 'love', 'coffee', 'i', 'hate', 'milk']
word_list = list(set(word_list)) # ['i', 'like', 'dog', 'love', 'coffee', 'hate', 'milk']
word_dict = {w: i for i, w in enumerate(word_list)} # {'i':0, 'like':1, 'dog':2, 'love':3, 'coffee':4, 'hate':5, 'milk':6}
number_dict = {i: w for i, w in enumerate(word_list)} # {0:'i', 1:'like', 2:'dog', 3:'love', 4:'coffee', 5:'hate', 6:'milk'}
n_class = len(word_dict) # number of Vocabulary, just like |V|, in this task n_class=7

# NNLM(Neural Network Language Model) Parameter
n_step = len(sentences[0].split())-1 # n-1 in paper, look back n_step words and predict next word. In this task n_step=2
n_hidden = 2 # h in paper
m = 2 # m in paper, word embedding dim

def make_batch(sentences):
  input_batch = []
  target_batch = []

  for sen in sentences:
    word = sen.split()
    input = [word_dict[n] for n in word[:-1]] # [0, 1], [0, 3], [0, 5]
    target = word_dict[word[-1]] # 2, 4, 6

    input_batch.append(input) # [[0, 1], [0, 3], [0, 5]]
    target_batch.append(target) # [2, 4, 6]

  return input_batch, target_batch

input_batch, target_batch = make_batch(sentences)
input_batch = torch.LongTensor(input_batch)
target_batch = torch.LongTensor(target_batch)

dataset = Data.TensorDataset(input_batch, target_batch)
loader = Data.DataLoader(dataset=dataset, batch_size=16, shuffle=True)

class NNLM(nn.Module):
  def __init__(self):
    super(NNLM, self).__init__()
    self.C = nn.Embedding(n_class, m)
    self.H = nn.Parameter(torch.randn(n_step * m, n_hidden).type(dtype))
    self.W = nn.Parameter(torch.randn(n_step * m, n_class).type(dtype))
    self.d = nn.Parameter(torch.randn(n_hidden).type(dtype))
    self.U = nn.Parameter(torch.randn(n_hidden, n_class).type(dtype))
    self.b = nn.Parameter(torch.randn(n_class).type(dtype))

  def forward(self, X):
    '''
    X: [batch_size, n_step]
    '''
    X = self.C(X) # [batch_size, n_step] => [batch_size, n_step, m]
    X = X.view(-1, n_step * m) # [batch_size, n_step * m]
    hidden_out = torch.tanh(self.d + torch.mm(X, self.H)) # [batch_size, n_hidden]
    output = self.b + torch.mm(X, self.W) + torch.mm(hidden_out, self.U) # [batch_size, n_class]
    return output

model = NNLM()
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=1e-3)

# Training
for epoch in range(5000):
  for batch_x, batch_y in loader:
    optimizer.zero_grad()
    output = model(batch_x)

    # output : [batch_size, n_class], batch_y : [batch_size] (LongTensor, not one-hot)
    loss = criterion(output, batch_y)
    if (epoch + 1)%1000 == 0:
        print('Epoch:', '%04d' % (epoch + 1), 'cost =', '{:.6f}'.format(loss))

    loss.backward()
    optimizer.step()

# Predict
predict = model(input_batch).data.max(1, keepdim=True)[1]

# Test
print([sen.split()[:n_step] for sen in sentences], '->', [number_dict[n.item()] for n in predict.squeeze()])

这个代码一开始是在GitHub的一个项目中给出的，下面参考文献给出了链接，代码本身写的没有问题，但是其中有一行注释有问题，就是X=X.view(-1, n_step*m)后面的注释，我很确信我写的是正确的。下面两篇参考文献都是一样的错误，需要注意一下

参考文献

A Neural Probabilitic Language Model 论文阅读及实战

NLP-tutorial