NLP经典书籍鱼书笔记4：对比计数统计和推理

import numpy as np
import time
import matplotlib.pyplot as plt
%matplotlib inline

c = np.array([[1,0,0,0,0,0,0]])
W = np.random.randn(7,3)
h = np.dot(c,W)

h

array([[ 0.12477247, -0.25928347, -0.21568563]])

class MatMul:
    def __init__(self, W):
        self.params = [W]  # 保存学习的参数；权重矩阵
        self.grads = [np.zeros_like(W)]  # 构造一个和W矩阵维度一致，但是全为0的矩阵
        self.x = None
    
    # 前向传播
    def forward(self, x):
        W, = self.params    # 参数
        out = np.dot(x,W)   # 矩阵x和矩阵w相乘
        self.x = x
        return out
    
    # 后向传播
    def backward(self, dout):
        W, = self.params
        dx = np.dot(dout, W.T)  # dout是上游传来的；W.T是把W转置了
        dW = np.dot(self.x.T, dout)
        # grads[0][...] 使用了省略号：可以固定Numpy数组的内存地址，覆盖Numpy数组的元素
        self.grads[0][...] = dW  # 实例变量grads中设置权重的梯度
        return dx

import sys 
sys.path.append("..")
import numpy as np

c = np.array([[1,0,0,0,0,0,0]])
W = np.random.randn(7,3)

layer = MatMul(W)  # 类的实例化
h = layer.forward(c)  # 调用类的forward方法

h

array([[-0.23997344, -0.90521716,  0.74001086]])

import sys
sys.path.append('..')

import numpy as np

#  上下文的one-hot编码表示
c0 = np.array([[1,0,0,0,0,0,0]])
c1 = np.array([[0,0,1,0,0,0,0]])

# 权重的初始值
W_in = np.random.randn(7,3)
W_out = np.random.randn(3,7)

# 生成层
in_layer0 = MatMul(W_in)  # 层的内部实现矩阵乘积
in_layer1 = MatMul(W_in)
out_layer = MatMul(W_out)

# 正向传播过程
h0 = in_layer0.forward(c0)
h1 = in_layer1.forward(c1)
h = 0.5 * (h0 + h1)  # 中间层的均值

s = out_layer.forward(h)  # 计算各个单词的得分
s

array([[-0.03647001,  1.22730525, -1.35937841,  1.0817182 ,  1.64785619,

         1.49898799, -0.18553477]])

# 第二章的precess函数 ；经常使用

def preprocess(text):
    text = text.lower()  # 转成小写
    text = text.replace('.', ' .')  # 增加空格
    words = text.split(' ')  #  切割

    # 单词和单词ID的对应关系
    word_to_id = {}
    id_to_word = {}
    for word in words:
        if word not in word_to_id.keys():   # 原文 if word not in word_to_id:
            new_id = len(word_to_id)
            word_to_id[word] = new_id
            id_to_word[new_id] = word
    # 单词列表-----> 单词ID列表
    corpus = np.array([word_to_id[w] for w in words])

    return corpus, word_to_id, id_to_word

import sys
sys.path.append('..')

text = 'You say goodbye and I say hello.'
corpus, word_to_id, id_to_word = preprocess(text)

corpus

array([0, 1, 2, 3, 4, 1, 5, 6])

id_to_word

{0: 'you', 1: 'say', 2: 'goodbye', 3: 'and', 4: 'i', 5: 'hello', 6: '.'}

corpus[1:-1]

array([1, 2, 3, 4, 1, 5])

def create_contexts_target(corpus, window_size=1):
    target = corpus[window_size:-window_size]  # 目标词从第2个元素开始（索引号为1）
    
    contexts = []  # 二维数据，contexts[0] 保存的就是第0个上下文
    
    for idx in range(window_size, len(corpus) - window_size):
        #print("idx: ", idx)
        cs = []
        for t in range(-window_size, window_size + 1):  # [-1,2) 即 -1 0 1；
            #print("t: ", t)
            if t == 0:  # 单词本身跳过；只寻找-1和1的上下文
                continue
            cs.append(corpus[idx + t])
            #print("cs: \n", cs)
        contexts.append(cs)
    return np.array(contexts), np.array(target)

contexts, target = create_contexts_target(corpus, window_size=1)

contexts   # 上下文

array([[0, 2],

       [1, 3],

       [2, 4],

       [3, 1],

       [4, 5],

       [1, 6]])

target   # 目标值

array([1, 2, 3, 4, 1, 5])

def convert_one_hot(corpus, vocab_size):
    """
    corpus：单词ID列表；一维或者二维的numpy数组形式
    vocab_size：词汇个数
    """
    N = corpus.shape[0]  # 
    
    if corpus.ndim == 1:
        one_hot = np.zeros((N, vocab_size), dtype=np.int32)
        
        for idx, word_id in enumerate(corpus):
            one_hot[idx, word_id] = 1
            
    elif corpus.ndim == 2:
        C = corpus.shape[1]
        one_hot = np.zeros((N, C, vocab_size), dtype=np.int32)
        
        for idx_0, word_ids in enumerate(corpus):
            for idx_1, word_id in enumerate(word_ids):
                one_hot[idx_0, idx_1, word_id] = 1
                
    return one_hot

#text = 'You say goodbye and I say hello.'
#corpus, word_to_id, id_to_word = preprocess(text)
#contexts, target = create_contexts_target(corpus, window_size=1)

vocab_size = len(word_to_id)
target = convert_one_hot(target, vocab_size)
contexts = convert_one_hot(contexts, vocab_size)

target  # 转成One-Hot编码后的形式

array([[0, 1, 0, 0, 0, 0, 0],

       [0, 0, 1, 0, 0, 0, 0],

       [0, 0, 0, 1, 0, 0, 0],

       [0, 0, 0, 0, 1, 0, 0],

       [0, 1, 0, 0, 0, 0, 0],

       [0, 0, 0, 0, 0, 1, 0]])

contexts  #  转成One-Hot编码后的形式

array([[[1, 0, 0, 0, 0, 0, 0],

        [0, 0, 1, 0, 0, 0, 0]],

       [[0, 1, 0, 0, 0, 0, 0],

        [0, 0, 0, 1, 0, 0, 0]],

       [[0, 0, 1, 0, 0, 0, 0],

        [0, 0, 0, 0, 1, 0, 0]],

       [[0, 0, 0, 1, 0, 0, 0],

        [0, 1, 0, 0, 0, 0, 0]],

       [[0, 0, 0, 0, 1, 0, 0],

        [0, 0, 0, 0, 0, 1, 0]],

       [[0, 1, 0, 0, 0, 0, 0],

        [0, 0, 0, 0, 0, 0, 1]]])

def cross_entropy_error(y, t):
    """
    交叉损失熵损失的实现
    """
    if y.ndim == 1:
        t = t.reshape(1, t.size)
        y = y.reshape(1, y.size)
        
    # 在监督标签为one-hot-vector的情况下，转换为正确解标签的索引
    if t.size == y.size:
        t = t.argmax(axis=1)
             
    batch_size = y.shape[0]

    return -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size

# 定义softmax函数
def softmax(x):
    if x.ndim == 2:
        x = x - x.max(axis=1, keepdims=True)
        x = np.exp(x)
        x /= x.sum(axis=1, keepdims=True)
    elif x.ndim == 1:
        x = x - np.max(x)
        x = np.exp(x) / np.sum(np.exp(x))

    return x


# 基于交叉损失熵的softmax损失层
class SoftmaxWithLoss:
    def __init__(self):
        self.params, self.grads = [], []
        self.y = None  # softmax的输出
        self.t = None  # 监督标签
 
    def forward(self, x, t):  # 前向传播
        self.t = t
        self.y = softmax(x)
 
        # 在监督标签为one-hot向量的情况下，转换为正确解标签的索引
        if self.t.size == self.y.size:
            self.t = self.t.argmax(axis=1)
         
        loss = cross_entropy_error(self.y, self.t)  # 调用交叉损失熵函数
        return loss
 
    def backward(self, dout=1):
        batch_size = self.t.shape[0]
 
        dx = self.y.copy()
        dx[np.arange(batch_size), self.t] -= 1
        dx *= dout
        dx = dx / batch_size
        
        return dx

import sys
sys.path.append('..')

import numpy as np

class SimpleCBOW:
    def __init__(self, vocab_size, hidden_size):
        """
        vocab_size：词汇个数;
        hidden_size：中间层的神经元个数
        """
        V,H = vocab_size, hidden_size
        
        # 权重参数
        W_in = 0.01 * np.random.randn(V,H).astype('f')
        W_out = 0.01 * np.random.randn(H,V).astype('f')
        
        # 生成层：两个输入侧的MatMul 和 一个输出侧 + Softmax_with_loss层
        self.in_layer0 = MatMul(W_in)
        self.in_layer1 = MatMul(W_in)
        self.out_layer = MatMul(W_out)
        self.loss_layer = SoftmaxWithLoss()
        
        # 将所有的权重和梯度保存到列表中
        layers = [self.in_layer0, self.in_layer1, self.out_layer]
        
        self.params, self.grads = [], []
        
        for layer in layers:
            self.params += layer.params
            self.grads += layer.grads
            
        #  将单词的分布式表示设置为成员变量
        self.word_vecs = W_in
    
    
    # 基于上下文的正向传播forward   
    def forward(self, contexts, target):
        h0 = self.in_layer0.forward(contexts[:,0])
        h1 = self.in_layer1.forward(contexts[:,1])

        h = (h0 + h1) / 2

        score = self.out_layer.forward(h)
        loss = self.loss_layer.forward(score, target)
        return loss
        
    #  反向传播   
    def backward(self, dout=1):
        ds = self.loss_layer.backward(dout)
        da = self.out_layer.backward(ds)
        da *= 0.5

        self.in_layer1.backward(da)
        self.in_layer0.backward(da)

        return None

# def forward(self, contexts, target):
#     h0 = self.in_layer0.farward(contexts[:,0])
#     h1 = self.in_layer.farward(contexts[:,1])
    
#     h = (h0 + h1) / 2
    
#     score = self.out_layer.farward(h)
#     loss = self.loss_layer.farward(score, target)
#     return loss

# def backward(self, dout=1):
#     ds = self.loss_layer.backward(dout)
#     da = self.out_layer.backward(ds)
#     da *= 0.5
    
#     self.in_layer1.backward(da)
#     self.in_layer0.backward(da)
    
#     return None

#  参数去重

def remove_duplicate(params, grads):
    '''
    将参数列表中重复的权重整合为1个，
    加上与该权重对应的梯度
    '''
    params, grads = params[:], grads[:]  # 副本

    while True:
        find_flg = False
        L = len(params)

        for i in range(0, L - 1):
            for j in range(i + 1, L):
                # 在共享权重的情况下
                if params[i] is params[j]:
                    grads[i] += grads[j]  # 加上梯度
                    find_flg = True
                    params.pop(j)
                    grads.pop(j)
                # 在作为转置矩阵共享权重的情况下（weight tying）
                elif params[i].ndim == 2 and params[j].ndim == 2 and \
                     params[i].T.shape == params[j].shape and np.all(params[i].T == params[j]):
                    grads[i] += grads[j].T
                    find_flg = True
                    params.pop(j)
                    grads.pop(j)

                if find_flg: 
                    break
            if find_flg: 
                break

        if not find_flg:
            break

    return params, grads


class Trainer:
    def __init__(self, model, optimizer):
            self.model = model
            self.optimizer = optimizer
            self.loss_list = []
            self.eval_interval = None
            self.current_epoch = 0
            

    def fit(self, x, t, max_epoch=10, batch_size=32, max_grad=None, eval_interval=20):
        """
        x: 输入数据
        t: 监督标签
        max_epoch: 进行学习的epoch数
        batch_size: mini-batch的大小
        max_grad: 梯度的最大范数
        eval_interval: 输出结果的间隔——迭代次数
        """
        data_size = len(x)
        max_iters = data_size // batch_size
        self.eval_interval = eval_interval
        model, optimizer = self.model, self.optimizer
        total_loss = 0
        loss_count = 0
        
        start_time = time.time()
        for epoch in range(max_epoch):
            # 打乱
            idx = np.random.permutation(np.arange(data_size))
            x = x[idx]
            t = t[idx]

            for iters in range(max_iters):
                batch_x = x[iters*batch_size:(iters+1)*batch_size]
                batch_t = t[iters*batch_size:(iters+1)*batch_size]

                # 计算梯度，更新参数
                loss = model.forward(batch_x, batch_t)
                model.backward()
                
                # 参数去重
                params, grads = remove_duplicate(model.params, model.grads)  # 将共享的权重整合为1个
                if max_grad is not None:
                    clip_grads(grads, max_grad)
                optimizer.update(params, grads)
                total_loss += loss
                loss_count += 1
                
                # 评价
                if (eval_interval is not None) and (iters % eval_interval) == 0:
                    avg_loss = total_loss / loss_count
                    elapsed_time = time.time() - start_time
                    self.loss_list.append(float(avg_loss))
                    total_loss, loss_count = 0, 0

            self.current_epoch += 1

    def plot(self, ylim=None):
        x = np.arange(len(self.loss_list))
        if ylim is not None:
            plt.ylim(*ylim)
        plt.plot(x, self.loss_list, label='train')
        plt.xlabel('iterations (x' + str(self.eval_interval) + ')')
        plt.ylabel('loss')
        plt.show()

class SGD:
    def __init__(self, lr=0.05):
        self.lr = lr  # 学习率设置
    
    def update(self, params, grads):
        for i in range(len(params)):
            params[i] -= self.lr * grads[i]  # 参数更新

window_size = 1
hidden_size = 5
batch_size = 3
max_epoch = 1000

#  实际数据
text = 'You say goodbye and I say hello.'
corpus, word_to_id, id_to_word = preprocess(text)  # 数据预处理
contexts, target = create_contexts_target(corpus, window_size=1)  

vocab_size = len(word_to_id)
target = convert_one_hot(target, vocab_size)
contexts = convert_one_hot(contexts, vocab_size)

model = SimpleCBOW(vocab_size, hidden_size)
optimizer = SGD()
trainer = Trainer(model, optimizer)
trainer.fit(contexts, target, max_epoch, batch_size)
trainer.plot()

word_vecs = model.word_vecs  # 变量权重

for word_id, word in id_to_word.items():
    print(word, word_vecs[word_id])

you [ 0.56529504 -0.89804494  2.2253568  -0.06463418 -1.1290963 ]

say [-1.1766486   0.99819845 -1.1207973   0.6008937   1.1576382 ]

goodbye [ 1.5599341   0.2788804  -0.38262236 -0.35986307 -1.1309035 ]

and [-0.8373688  -0.9373508  -1.2509673   1.8487976   0.51270753]

i [ 1.593292   0.2917557 -0.3518384 -0.3507546 -1.129358 ]

hello [ 0.5445614  -0.89658004  2.2065814  -0.07632335 -1.112859  ]

. [-0.3468702   1.9544731   0.13033707 -1.2471999   0.658087  ]