加深网络

深度学习相对于一般的神经网络区别就在于使用多层隐藏层。在该例中我们构造一个基于CNN的深度学习网络，其训练完成后对于mnist数据集失败准确率可以超过99%

该网络隐藏层结构：
卷积层—ReLU—卷积层—ReLU—池化层—卷积层—ReLU—卷积层—ReLU—池化层—卷积层—ReLU—卷积层—ReLU—池化层—affine—ReLU—dropout—affine—dropout—softmax

先放上完整代码：

# coding: utf-8
import sys, os
sys.path.append("D:\AI learning source code")  # 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 common.layers import *class DeepConvNet:"""识别率为99%以上的高精度的ConvNet网络结构如下所示conv - relu - conv- relu - pool -conv - relu - conv- relu - pool -conv - relu - conv- relu - pool -affine - relu - dropout - affine - dropout - softmax"""def __init__(self, input_dim=(1, 28, 28),conv_param_1 = {'filter_num':16, 'filter_size':3, 'pad':1, 'stride':1},conv_param_2 = {'filter_num':16, 'filter_size':3, 'pad':1, 'stride':1},conv_param_3 = {'filter_num':32, 'filter_size':3, 'pad':1, 'stride':1},conv_param_4 = {'filter_num':32, 'filter_size':3, 'pad':2, 'stride':1},conv_param_5 = {'filter_num':64, 'filter_size':3, 'pad':1, 'stride':1},conv_param_6 = {'filter_num':64, 'filter_size':3, 'pad':1, 'stride':1},hidden_size=50, output_size=10):# 初始化权重===========# 各层的神经元平均与前一层的几个神经元有连接（TODO:自动计算）pre_node_nums = np.array([1*3*3, 16*3*3, 16*3*3, 32*3*3, 32*3*3, 64*3*3, 64*4*4, hidden_size])wight_init_scales = np.sqrt(2.0 / pre_node_nums)  # 使用ReLU的情况下推荐的初始值self.params = {}pre_channel_num = input_dim[0]for idx, conv_param in enumerate([conv_param_1, conv_param_2, conv_param_3, conv_param_4, conv_param_5, conv_param_6]):self.params['W' + str(idx+1)] = wight_init_scales[idx] * np.random.randn(conv_param['filter_num'], pre_channel_num, conv_param['filter_size'], conv_param['filter_size'])self.params['b' + str(idx+1)] = np.zeros(conv_param['filter_num'])pre_channel_num = conv_param['filter_num']self.params['W7'] = wight_init_scales[6] * np.random.randn(64*4*4, hidden_size)self.params['b7'] = np.zeros(hidden_size)self.params['W8'] = wight_init_scales[7] * np.random.randn(hidden_size, output_size)self.params['b8'] = np.zeros(output_size)# 生成层===========self.layers = []self.layers.append(Convolution(self.params['W1'], self.params['b1'], conv_param_1['stride'], conv_param_1['pad']))self.layers.append(Relu())self.layers.append(Convolution(self.params['W2'], self.params['b2'], conv_param_2['stride'], conv_param_2['pad']))self.layers.append(Relu())self.layers.append(Pooling(pool_h=2, pool_w=2, stride=2))self.layers.append(Convolution(self.params['W3'], self.params['b3'], conv_param_3['stride'], conv_param_3['pad']))self.layers.append(Relu())self.layers.append(Convolution(self.params['W4'], self.params['b4'],conv_param_4['stride'], conv_param_4['pad']))self.layers.append(Relu())self.layers.append(Pooling(pool_h=2, pool_w=2, stride=2))self.layers.append(Convolution(self.params['W5'], self.params['b5'],conv_param_5['stride'], conv_param_5['pad']))self.layers.append(Relu())self.layers.append(Convolution(self.params['W6'], self.params['b6'],conv_param_6['stride'], conv_param_6['pad']))self.layers.append(Relu())self.layers.append(Pooling(pool_h=2, pool_w=2, stride=2))self.layers.append(Affine(self.params['W7'], self.params['b7']))self.layers.append(Relu())self.layers.append(Dropout(0.5))self.layers.append(Affine(self.params['W8'], self.params['b8']))self.layers.append(Dropout(0.5))self.last_layer = SoftmaxWithLoss()def predict(self, x, train_flg=False):for layer in self.layers:if isinstance(layer, Dropout):x = layer.forward(x, train_flg)else:x = layer.forward(x)return xdef loss(self, x, t):y = self.predict(x, train_flg=True)return self.last_layer.forward(y, t)def accuracy(self, x, t, batch_size=100):if t.ndim != 1 : t = np.argmax(t, axis=1)acc = 0.0for 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, train_flg=False)y = np.argmax(y, axis=1)acc += np.sum(y == tt)return acc / x.shape[0]def gradient(self, x, t):# forwardself.loss(x, t)# backwarddout = 1dout = self.last_layer.backward(dout)tmp_layers = self.layers.copy()tmp_layers.reverse()for layer in tmp_layers:dout = layer.backward(dout)# 设定grads = {}for i, layer_idx in enumerate((0, 2, 5, 7, 10, 12, 15, 18)):grads['W' + str(i+1)] = self.layers[layer_idx].dWgrads['b' + str(i+1)] = self.layers[layer_idx].dbreturn gradsdef save_params(self, file_name="params.pkl"):params = {}for key, val in self.params.items():params[key] = valwith 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] = valfor i, layer_idx in enumerate((0, 2, 5, 7, 10, 12, 15, 18)):self.layers[layer_idx].W = self.params['W' + str(i+1)]self.layers[layer_idx].b = self.params['b' + str(i+1)]

解析：

1

    def __init__(self, input_dim=(1, 28, 28),conv_param_1 = {'filter_num':16, 'filter_size':3, 'pad':1, 'stride':1},conv_param_2 = {'filter_num':16, 'filter_size':3, 'pad':1, 'stride':1},conv_param_3 = {'filter_num':32, 'filter_size':3, 'pad':1, 'stride':1},conv_param_4 = {'filter_num':32, 'filter_size':3, 'pad':2, 'stride':1},conv_param_5 = {'filter_num':64, 'filter_size':3, 'pad':1, 'stride':1},conv_param_6 = {'filter_num':64, 'filter_size':3, 'pad':1, 'stride':1},hidden_size=50, output_size=10):

这里我们确定了各个神经网络层的形状，卷积核形状均为3 X 3，步幅为1，填充在第4个卷积层为2，其他为1. 卷积核数量1,2层为16， 3,4层为32， 5,6层为64.最后隐藏层（全连接层）神经元个数50

2

pre_node_nums = np.array([1*3*3, 16*3*3, 16*3*3, 32*3*3, 32*3*3, 64*3*3, 64*4*4, hidden_size])
wight_init_scales = np.sqrt(2.0 / pre_node_nums)  # 使用ReLU的情况下推荐的初始值

这里定义了神经网络各层的神经元个数，以及ReLU函数使用的He初始值的标准差

3

        self.params = {}pre_channel_num = input_dim[0]for idx, conv_param in enumerate([conv_param_1, conv_param_2, conv_param_3, conv_param_4, conv_param_5, conv_param_6]):self.params['W' + str(idx+1)] = wight_init_scales[idx] * np.random.randn(conv_param['filter_num'], pre_channel_num, conv_param['filter_size'], conv_param['filter_size'])self.params['b' + str(idx+1)] = np.zeros(conv_param['filter_num'])pre_channel_num = conv_param['filter_num']self.params['W7'] = wight_init_scales[6] * np.random.randn(64*4*4, hidden_size)self.params['b7'] = np.zeros(hidden_size)self.params['W8'] = wight_init_scales[7] * np.random.randn(hidden_size, output_size)self.params['b8'] = np.zeros(output_size)

这里我们遍历形状参数列表得到各层的形状，并对各层的值进行初始化。其中卷积核与ReLU权重初始值都使用了He初始值，偏置的初始值都为0

3

        # 生成层===========self.layers = []self.layers.append(Convolution(self.params['W1'], self.params['b1'], conv_param_1['stride'], conv_param_1['pad']))self.layers.append(Relu())self.layers.append(Convolution(self.params['W2'], self.params['b2'], conv_param_2['stride'], conv_param_2['pad']))self.layers.append(Relu())self.layers.append(Pooling(pool_h=2, pool_w=2, stride=2))self.layers.append(Convolution(self.params['W3'], self.params['b3'], conv_param_3['stride'], conv_param_3['pad']))self.layers.append(Relu())self.layers.append(Convolution(self.params['W4'], self.params['b4'],conv_param_4['stride'], conv_param_4['pad']))self.layers.append(Relu())self.layers.append(Pooling(pool_h=2, pool_w=2, stride=2))self.layers.append(Convolution(self.params['W5'], self.params['b5'],conv_param_5['stride'], conv_param_5['pad']))self.layers.append(Relu())self.layers.append(Convolution(self.params['W6'], self.params['b6'],conv_param_6['stride'], conv_param_6['pad']))self.layers.append(Relu())self.layers.append(Pooling(pool_h=2, pool_w=2, stride=2))self.layers.append(Affine(self.params['W7'], self.params['b7']))self.layers.append(Relu())self.layers.append(Dropout(0.5))self.layers.append(Affine(self.params['W8'], self.params['b8']))self.layers.append(Dropout(0.5))self.last_layer = SoftmaxWithLoss()

按照神经网络顺序搭建神经网络各层，保存为列表layers。

神经网络结构：
卷积层（16 X 3 X 3）—ReLU—卷积层（16 X 3 X 3）—ReLU—池化层（长2，宽2，步幅2）—卷积层（32 X 3 X 3）—ReLU—卷积层（32 X 3 X 3）—ReLU—池化层（长2，宽2，步幅2）—卷积层（64 X 3 X 3）—ReLU—卷积层（64 X 3 X 3）—ReLU—池化层（长2，宽2，步幅2）—affine—ReLU—dropout（dropout比率0.5）—affine—dropout（dropout比率0.5）—softmax

4

    def predict(self, x, train_flg=False):for layer in self.layers:if isinstance(layer, Dropout):x = layer.forward(x, train_flg)else:x = layer.forward(x)return x

利用神经网络进行预测，其中train_flg为True时代表神经网络处于训练模式，在Dropout层会随机删除神经元。如为False则代表神经网络在预测状态，启用全部神经元

5

    def accuracy(self, x, t, batch_size=100):if t.ndim != 1 : t = np.argmax(t, axis=1)acc = 0.0for 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, train_flg=False)y = np.argmax(y, axis=1)acc += np.sum(y == tt)return acc / x.shape[0]

返回每一轮batch中预测准确率

    def gradient(self, x, t):# forwardself.loss(x, t)# backwarddout = 1dout = self.last_layer.backward(dout)tmp_layers = self.layers.copy()tmp_layers.reverse()for layer in tmp_layers:dout = layer.backward(dout)# 设定grads = {}for i, layer_idx in enumerate((0, 2, 5, 7, 10, 12, 15, 18)):grads['W' + str(i+1)] = self.layers[layer_idx].dWgrads['b' + str(i+1)] = self.layers[layer_idx].dbreturn grads

使用反向传播梯度下降求网络梯度并返回得到的梯度值

训练程序

# coding: utf-8
import sys, os
sys.path.append("D:\AI learning source code")  # 为了导入父目录而进行的设定
import numpy as np
import matplotlib.pyplot as plt
from dataset.mnist import load_mnist
from deep_convnet import DeepConvNet
from common.trainer import Trainer(x_train, t_train), (x_test, t_test) = load_mnist(flatten=False)network = DeepConvNet()  
trainer = Trainer(network, x_train, t_train, x_test, t_test,epochs=20, 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("deep_convnet_params.pkl")
print("Saved Network Parameters!")

在训练程序中，我们调用DeepConvNet，使用Adam权重更新方法，0.001学习率对mnist数据集进行mini-batch训练。其中每一个batch个数为100，进行20个epoch