聊聊神经网络模型流程与卷积神经网络的实现

神经网络模型流程

神经网络模型的搭建流程，整理下自己的思路，这个过程不会细分出来，而是主流程。

在这里我主要是把整个流程分为两个主流程，即预训练与推理。预训练过程主要是生成超参数文件与搭设神经网络结构；而推理过程就是在应用超参数与神经网络。

卷积神经网络的实现

在 聊聊卷积神经网络CNN中，将卷积神经的理论概述了一下，现在要大概的实践了。整个代码不基于pytorch/tensorflow这类大框架，而是基于numpy库原生来实现算法。pytorch/tensorflow中的算子/函数只是由别人已实现了，我们调用而已；而基于numpy要自己实现一遍，虽然并不很严谨，但用于学习足以。源代码是来自《深度学习入门：基于Python的理论与实现》，可以在 https://www.ituring.com.cn/book/1921 上获取下载

搭建CNN

网络构成如下:

如图所示，网络的构成是"Conv-ReLU-Pooling-Affine-ReLU-Affine-Softmax". 对于卷积层与池化层的计算，由于其是四维数据(数据量,通道,高,长)，不太好计算，使用im2col函数将其展开成二维 2 × 2的数据，最后输出时，利用numpy库的reshape函数转换输出的大小，方便计算。其示意图如下:

这样也满足了矩阵内积计算的要求，即 行列数要对应

CNN程序代码实现如下:

# coding: utf-8
import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import pickle
import numpy as np
from collections import OrderedDict
from DeepLearn_Base.common.layers import *
from DeepLearn_Base.common.gradient import numerical_gradient

class SimpleConvNet:
    """简单的ConvNet

    conv - relu - pool - affine - relu - affine - softmax
    
    Parameters
    ----------
    input_dim: 输入数据的维度，通道、高、长
    conv_param: 卷积核参数; filter_num:卷积核数量; filter_size:卷积核大小; stride:步幅; pad:填充
    input_size : 输入大小（MNIST的情况下为784）
    hidden_size_list : 隐藏层的神经元数量的列表（e.g. [100, 100, 100]）
    output_size : 输出大小（MNIST的情况下为10）
    activation : 'relu' or 'sigmoid'
    weight_init_std : 指定权重的标准差（e.g. 0.01）
        指定'relu'或'he'的情况下设定“He的初始值”
        指定'sigmoid'或'xavier'的情况下设定“Xavier的初始值”
    """
    def __init__(self, input_dim=(1, 28, 28), 
                 conv_param={'filter_num':30, 'filter_size':5, 'pad':0, 'stride':1},
                 hidden_size=100, output_size=10, weight_init_std=0.01):
        filter_num = conv_param['filter_num']
        filter_size = conv_param['filter_size']
        filter_pad = conv_param['pad']
        filter_stride = conv_param['stride']
        input_size = input_dim[1]
        conv_output_size = (input_size - filter_size + 2*filter_pad) / filter_stride + 1
        pool_output_size = int(filter_num * (conv_output_size/2) * (conv_output_size/2))

        # 初始化权重
        self.params = {}
        self.params['W1'] = weight_init_std * \
                            np.random.randn(filter_num, input_dim[0], filter_size, filter_size)
        self.params['b1'] = np.zeros(filter_num)
        self.params['W2'] = weight_init_std * \
                            np.random.randn(pool_output_size, hidden_size)
        self.params['b2'] = np.zeros(hidden_size)
        self.params['W3'] = weight_init_std * \
                            np.random.randn(hidden_size, output_size)
        self.params['b3'] = np.zeros(output_size)

        # 生成层
        self.layers = OrderedDict()
        self.layers['Conv1'] = Convolution(self.params['W1'], self.params['b1'],
                                           conv_param['stride'], conv_param['pad'])
        self.layers['Relu1'] = Relu()
        self.layers['Pool1'] = Pooling(pool_h=2, pool_w=2, stride=2)
        self.layers['Affine1'] = Affine(self.params['W2'], self.params['b2'])
        self.layers['Relu2'] = Relu()
        self.layers['Affine2'] = Affine(self.params['W3'], self.params['b3'])

        self.last_layer = SoftmaxWithLoss()

    # 需要处理数据，将输入数据的多维与卷积核的多维分别展平后做矩阵运算
    # 在神经网络的中间层(conv,relu,pooling,affine等)的forward函数中用到了img2col与reshape结合展平数据，用向量内积运算
    def predict(self, x):
        for layer in self.layers.values():
            x = layer.forward(x)

        return x

    def loss(self, x, t):
        """求损失函数
        参数x是输入数据、t是教师标签
        """
        y = self.predict(x)
        return self.last_layer.forward(y, t)

    # 计算精确度
    def accuracy(self, x, t, batch_size=100):
        if t.ndim != 1 : t = np.argmax(t, axis=1)
        
        acc = 0.0
        
        for i in range(int(x.shape[0] / batch_size)):
            tx = x[i*batch_size:(i+1)*batch_size]
            tt = t[i*batch_size:(i+1)*batch_size]
            y = self.predict(tx)
            y = np.argmax(y, axis=1)
            acc += np.sum(y == tt) 
        
        return acc / x.shape[0]

    def numerical_gradient(self, x, t):
        """求梯度（数值微分）

        Parameters
        ----------
        x : 输入数据
        t : 教师标签

        Returns
        -------
        具有各层的梯度的字典变量
            grads['W1']、grads['W2']、...是各层的权重
            grads['b1']、grads['b2']、...是各层的偏置
        """
        loss_w = lambda w: self.loss(x, t)

        grads = {}
        for idx in (1, 2, 3):
            grads['W' + str(idx)] = numerical_gradient(loss_w, self.params['W' + str(idx)])
            grads['b' + str(idx)] = numerical_gradient(loss_w, self.params['b' + str(idx)])

        return grads

    def gradient(self, x, t):
        """求梯度（误差反向传播法）

        Parameters
        ----------
        x : 输入数据
        t : 教师标签

        Returns
        -------
        具有各层的梯度的字典变量
            grads['W1']、grads['W2']、...是各层的权重
            grads['b1']、grads['b2']、...是各层的偏置
        """
        # forward
        self.loss(x, t)

        # backward
        dout = 1
        dout = self.last_layer.backward(dout)

        layers = list(self.layers.values())
        layers.reverse()
        for layer in layers:
            dout = layer.backward(dout)

        # 设定
        grads = {}
        grads['W1'], grads['b1'] = self.layers['Conv1'].dW, self.layers['Conv1'].db
        grads['W2'], grads['b2'] = self.layers['Affine1'].dW, self.layers['Affine1'].db
        grads['W3'], grads['b3'] = self.layers['Affine2'].dW, self.layers['Affine2'].db

        return grads
        
    def save_params(self, file_name="params.pkl"):
        params = {}
        for key, val in self.params.items():
            params[key] = val
        with open(file_name, 'wb') as f:
            pickle.dump(params, f)

    def load_params(self, file_name="params.pkl"):
        with open(file_name, 'rb') as f:
            params = pickle.load(f)
        for key, val in params.items():
            self.params[key] = val

        for i, key in enumerate(['Conv1', 'Affine1', 'Affine2']):
            self.layers[key].W = self.params['W' + str(i+1)]
            self.layers[key].b = self.params['b' + str(i+1)]

激活函数与卷积函数的实现代码没有详细的写出来，可以自己去下载查看

在这整个的过程中，我个人觉得最难的就是神经网络层的搭建与数据的计算。前者决定了神经网络的结构，而后者决定了是否最终结果。通过将数据展平，才能方便，正确的进行向量内积计算。

预训练

trainer.py文件是进行神经网络训练的类，会统计执行完一个epoch后的精确度，过程要选择梯度更新算法，学习率，批大小，epoch次数等参数。

# coding: utf-8
import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
from DeepLearn_Base.common.optimizer import *

class Trainer:
    """进行神经网络的训练的类
    epochs: 以所有数据走完前向、后向传播为一次;该数值表示为总次数
    mini_batch_size: 100; 每批次迭代多少数据
    evaluate_sample_num_per_epoch: 1000;
    """
    def __init__(self, network, x_train, t_train, x_test, t_test,
                 epochs=20, mini_batch_size=100,
                 optimizer='SGD', optimizer_param={'lr':0.01}, 
                 evaluate_sample_num_per_epoch=None, verbose=True):
        self.network = network
        self.verbose = verbose
        self.x_train = x_train
        self.t_train = t_train
        self.x_test = x_test
        self.t_test = t_test
        self.epochs = epochs
        self.batch_size = mini_batch_size
        self.evaluate_sample_num_per_epoch = evaluate_sample_num_per_epoch

        # optimzer: 梯度更新优化器; 更新多种梯度更新算法实现梯度更新.
        optimizer_class_dict = {'sgd':SGD, 'momentum':Momentum, 'nesterov':Nesterov,
                                'adagrad':AdaGrad, 'rmsprpo':RMSprop, 'adam':Adam}
        self.optimizer = optimizer_class_dict[optimizer.lower()](**optimizer_param)
        
        self.train_size = x_train.shape[0]
        self.iter_per_epoch = max(self.train_size / mini_batch_size, 1)
        self.max_iter = int(epochs * self.iter_per_epoch)
        self.current_iter = 0
        self.current_epoch = 0
        
        self.train_loss_list = []
        self.train_acc_list = []
        self.test_acc_list = []

    def train_step(self):
        # 随机挑选批次的数据进行梯度更新
        batch_mask = np.random.choice(self.train_size, self.batch_size)
        x_batch = self.x_train[batch_mask]
        t_batch = self.t_train[batch_mask]
        # 开始更新梯度
        grads = self.network.gradient(x_batch, t_batch)
        self.optimizer.update(self.network.params, grads)
        
        # 计算损失
        loss = self.network.loss(x_batch, t_batch)
        self.train_loss_list.append(loss)
        if self.verbose: print("train loss:" + str(loss))
        
        # 计算是否完成了一个epoch的执行
        if self.current_iter % self.iter_per_epoch == 0:
            self.current_epoch += 1
            
            x_train_sample, t_train_sample = self.x_train, self.t_train
            x_test_sample, t_test_sample = self.x_test, self.t_test
            if not self.evaluate_sample_num_per_epoch is None:
                t = self.evaluate_sample_num_per_epoch
                x_train_sample, t_train_sample = self.x_train[:t], self.t_train[:t]
                x_test_sample, t_test_sample = self.x_test[:t], self.t_test[:t]
                
            train_acc = self.network.accuracy(x_train_sample, t_train_sample)
            test_acc = self.network.accuracy(x_test_sample, t_test_sample)
            self.train_acc_list.append(train_acc)
            self.test_acc_list.append(test_acc)

            if self.verbose: print("=== epoch:" + str(self.current_epoch) + ", train acc:" + str(train_acc) + ", test acc:" + str(test_acc) + " ===")
        self.current_iter += 1

    def train(self):
        for i in range(self.max_iter):
            self.train_step()

        test_acc = self.network.accuracy(self.x_test, self.t_test)

        if self.verbose:
            print("=============== Final Test Accuracy ===============")
            print("test acc:" + str(test_acc))

在神经网络训练中，epoch参数是指将整个训练集通过模型一次，并更新模型参数的过程。每一次epoch，模型都会将训练集中的所有样本通过一次，并根据这些样本的标签和模型预测的结果计算损失值，然后根据损失值对模型的参数进行更新。这个过程会重复进行，直到达到预设的epoch数。

正式开始预训练，要准备好训练数据集，初始化CNN，梯度优化参数，超参数存储路径等。如下所示:

# coding: utf-8
import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
import matplotlib.pyplot as plt
from DeepLearn_Base.dataset.mnist import load_mnist
from simple_convnet import SimpleConvNet
from DeepLearn_Base.common.trainer import Trainer

# 读入数据
# 输入数据的表现形式，可以是多维的，可以是展平(reshape)为一维的
(x_train, t_train), (x_test, t_test) = load_mnist(flatten=False)

# 处理花费时间较长的情况下减少数据，截取部分数据
# 训练数据截取 5000 条
# 测试数据截取 1000 条
x_train, t_train = x_train[:5000], t_train[:5000]
x_test, t_test = x_test[:1000], t_test[:1000]

# 初始化epoch
max_epochs = 20

# 初始化CNN
# input_dim, 输入数据: channel, height, width
# conv_param, 卷积核参数: filter_num:卷积核数量; filter_size:卷积核大小; stride:步幅; pad:填充; 30个5 × 5，通道为1的卷积核
network = SimpleConvNet(input_dim=(1,28,28), 
                        conv_param = {'filter_num': 30, 'filter_size': 5, 'pad': 0, 'stride': 1},
                        hidden_size=100, output_size=10, weight_init_std=0.01)

# 初始化预训练
# optimizer: 梯度优化算法; lr表示学习率
trainer = Trainer(network, x_train, t_train, x_test, t_test,
                  epochs=max_epochs, mini_batch_size=100,
                  optimizer='Adam', optimizer_param={'lr': 0.001},
                  evaluate_sample_num_per_epoch=1000)
trainer.train()

# 保存参数
network.save_params("E:\\workcode\\code\\DeepLearn_Base\\ch07\\cnn_params.pkl")
print("Saved Network Parameters!")

# 绘制图形
markers = {'train': 'o', 'test': 's'}
x = np.arange(max_epochs)
plt.plot(x, trainer.train_acc_list, marker='o', label='train', markevery=2)
plt.plot(x, trainer.test_acc_list, marker='s', label='test', markevery=2)
plt.xlabel("epochs")
plt.ylabel("accuracy")
plt.ylim(0, 1.0)
plt.legend(loc='lower right')
plt.show()

预训练好后，查看是否生成超参数文件。

推理

准备好测试数据集，应用已预训练好的神经网络模型与超参数。

# coding: utf-8
import sys, os
# 为了导入父目录的文件而进行的设定
sys.path.append(os.pardir)  
import numpy as np
from DeepLearn_Base.dataset.mnist import load_mnist
from DeepLearn_Base.common.functions import sigmoid, softmax
from simple_convnet import SimpleConvNet

def get_data():
    (x_train, t_train), (x_test, t_test) = load_mnist(flatten=False)
    return x_test, t_test

# 下载mnist数据集
# 分别下载测试图像包、测试标签包、训练图像包、训练标签包
x, t = get_data()

conv = SimpleConvNet()
# 获取预训练好的权重与偏置参数
conv.load_params("E:\\workcode\\code\\DeepLearn_Base\\ch07\\cnn_params.pkl")

# 初始化
batch_size = 100
accuracy_cnt = 0

for i in range(int(x.shape[0] / batch_size)):
    # 批次取数据
    x_batch = x[i * batch_size : (i+1) * batch_size]
    tt = t[i * batch_size : (i+1) * batch_size]
    # 执行推理
    y_batch = conv.predict(x_batch)
    p = np.argmax(y_batch, axis=1)
    # 统计预测正确的数据
    accuracy_cnt += np.sum(p == tt)
    print(f'第 {i} 批次，输入数据量{(i+1) * batch_size}个，准确预测数为 {accuracy_cnt}')

print("Accuracy:" + str(float(accuracy_cnt) / x.shape[0]))

最后的输出如下: