1 def update(self): 按照梯度下降，更新权重 filter in self.filters: 6 filter.update(self.learning_rate)

　　6.MaxPooling层的训练

　　1).定义MaxPooling类

1 class MaxPoolingLayer(object): (self, input_width, input_height, 3 channel_number, filter_width, 4 filter_height, stride): 5 self.input_width = input_width 6 self.input_height = input_height 7 self.channel_number = channel_number 8 self.filter_width = filter_width 9 self.filter_height = filter_height 10 self.stride = stride 11 self.output_width = (input_width - 12 filter_width) / self.stride + 1 13 self.output_height = (input_height - 14 filter_height) / self.stride + 1 15 self.output_array = np.zeros((self.channel_number, 16 self.output_height, self.output_width))

　　2).前向传播计算

forward(self, input_array): 3 for d in range(self.channel_number): 4 for i in range(self.output_height): 5 for j in range(self.output_width): 6 self.output_array[d,i,j] = ( 7 get_patch(input_array[d], i, j, 8 self.filter_width, 9 self.filter_height, 10 self.stride).max())

　　3).反向传播计算

backward(self, input_array, sensitivity_array): 3 self.delta_array = np.zeros(input_array.shape) 4 for d in range(self.channel_number): 5 for i in range(self.output_height): 6 for j in range(self.output_width): 7 patch_array = get_patch( 8 input_array[d], i, j, 9 self.filter_width, 10 self.filter_height, 11 self.stride) 12 k, l = get_max_index(patch_array) 13 self.delta_array[d, 14 i * self.stride + k, 15 j * self.stride + l] = \ 16 sensitivity_array[d,i,j]

　　完整代码请见：cnn.py (https://github.com/huxiaoman7/PaddlePaddle_code/blob/master/1.mnist/cnn.py)

Created by huxiaoman 2017.11.22 numpy as np 8 from activators import ReluActivator,IdentityActivator ConvLayer(object): (self,input_width,input_weight, 12 channel_number,filter_width, 13 filter_height,filter_number, 14 zero_padding,stride,activator, 15 learning_rate): 16 self.input_width = input_width 17 self.input_height = input_height 18 self.channel_number = channel_number 19 self.filter_width = filter_width 20 self.filter_height = filter_height 21 self.filter_number = filter_number 22 self.zero_padding = zero_padding self.output_width = ConvLayer.calculate_output_size( 25 self.input_width,filter_width,zero_padding, 26 stride) 27 self.output_height = ConvLayer.calculate_output_size( 28 self.input_height,filter_height,zero_padding, 29 stride) 30 self.output_array = np.zeros((self.filter_number, 31 self.output_height,self.output_width)) 32 self.filters = [] 33 for i in range(filter_number): 34 self.filters.append(Filter(filter_width, 35 filter_height,self.channel_number)) 36 self.activator = activator 37 self.learning_rate = learning_rate 38 def forward(self,input_array): 计算卷积层的输出 41 输出结果保存在self.output_array self.input_array = input_array 44 self.padded_input_array = padding(input_array, 45 self.zero_padding) 46 for i in range(self.filter_number): 47 filter = self.filters[f] 48 conv(self.padded_input_array, 49 filter.get_weights(), self.output_array[f], 50 self.stride, filter.get_bias()) 51 element_wise_op(self.output_array, 52 self.activator.forward) get_batch(input_array, i, j, filter_width,filter_height,stride): 从输入数组中获取本次卷积的区域， 57 自动适配输入为2D和3D的情况 start_i = i * stride 60 start_j = j * stride 61 if input_array.ndim == 2: 62 return input_array[ 63 start_i : start_i + filter_height, 64 start_j : start_j + filter_width] 65 elif input_array.ndim == 3: 66 return input_array[ 67 start_i : start_i + filter_height, 68 start_j : start_j + filter_width] get_max_index(array): 72 max_i = 0 73 max_j = 0 74 max_value = array[0,0] 75 for i in range(array.shape[0]): 76 for j in range(array.shape[1]): 77 if array[i,j] > max_value: 78 max_value = array[i,j] 79 max_i, max_j = i, j 80 return max_i, max_j conv(input_array,kernal_array, 83 output_array,stride,bias): 计算卷积，自动适配输入2D,3D的情况 channel_number = input_array.ndim 88 output_width = output_array.shape[1] 89 output_height = output_array.shape[0] 90 kernel_width = kernel_array.shape[-1] 91 kernel_height = kernel_array.shape[-2] 92 for i in range(output_height): 93 for j in range(output_width): 94 output_array[i][j] = ( 95 get_patch(input_array, i, j, kernel_width, 96 kernel_height,stride) * kernel_array).sum() +bias element_wise_op(array, op): 100 for i in np.nditer(array, ]): 102 i[...] = op(i) ReluActivators(object): 106 def forward(self, weighted_input): max(0, weighted_input) backward(self,output): 111 return 1 if output > 0 else 0 SigmoidActivator(object): forward(self,weighted_input): 116 return 1 / (1 + math.exp(- weighted_input)) backward(self,output): 119 return output * (1 - output)

 　　最后，我们用之前的4 * 4的image数据检验一下通过一次卷积神经网络进行前向传播和反向传播后的输出结果：