tesseract led数字识别

《深度学习的数学》给予了我极大的启发，作者阐述的神经网络的思想和数学基础令我受益颇多，但是由于书中使用Excel作为示例向读者展示神经网络，这对我这样一个不精通Excel的人来说很头疼，因此我打算使用Python来实现书中的一个简单的卷积神经网络模型，即识别数字123的模型。
这个网络模型极其简单，比号称机器学习中的“Hello World”的手写数字识别模型更简单，它基本没有实用价值，但是我之所以推崇它，只因为它褪去了神经网络的复杂性，展示了神经网络中最基本、最根本的东西。
模型总共分为四层，第一层为输入层，第二层为卷积层，第三层为最大池化层，第四层为输出层。输入图像为96张66的单值二色图像。
卷积层的过滤器共包含39+3=30个参数，输出层包括12*3+3=39个参数，所以网络模型中总共69个参数。
原理和上篇文章一样，所涉及的数学知识有点改变。具体如下：
首先是卷积层神经单元的加权输入和神经单元的输出
$z_{ij}^{Fk}=w_{11}^{Fk}x_{ij}+w_{12}^{Fk}x_{ij+1}+w_{13}^{Fk}x_{ij+2}+w_{21}^{Fk}x_{i+1j}+w_{22}^{Fk}x_{i+1j+1}+w_{23}^{Fk}x_{i+1j+2}+w_{31}^{Fk}x_{i+2j}+w_{32}^{Fk}x_{i+2j+1}+w_{33}^{Fk}x_{i+2j+2}+b^{Fk}$
$a_{ij}^{Fk}=a(z_{ij}^{Fk}),其中k为卷积层的子层编号,i、j(i,j=1,2,3,4)为扫描的起始行列编号，a(z)表示激活函数$
然后是池化层的加权输入和神经单元的输出:
$z_{ij}^{Pk}=Max(a_{2i-12j-1}^{Fk},a_{2i-12j}^{Fk},a_{2i2j-1}^{Fk},a_{2i2j}^{Fk})$
$a_{ij}^{Pk}=z_{ij}^{Pk}$
然后是输出层的加权输入和神经单元的输出:
$z_n^O=w_{1-11}^{On}a_{11}^{P1}+w_{1-12}^{On}a_{12}^{P1}+w_{1-21}^{On}a_{21}^{P1}+w_{1-22}^{On}a_{22}^{P1}+w_{2-11}^{On}a_{11}^{P2}+w_{2-12}^{On}a_{12}^{P2}+w_{2-21}^{On}a_{21}^{P2}+w_{2-22}^{On}a_{22}^{P2}+w_{3-11}^{On}a_{11}^{P3}+w_{3-12}^{On}a_{12}^{P3}+w_{3-21}^{On}a_{21}^{P3}+w_{3-22}^{On}a_{22}^{P3}+b_n^O$
$a_n^O=a(z_n^O),n为输出层神经单元的编号(n=1,2,3)$
$平方误差C=1/2*((t_1-a_1^O)^2+t_2-a_2^O)^2+t_3-a_3^O)^2)$

	含义	图像为1	图像为2	图像为3
$t_1$	1的正解变量	1	0	0
$t_2$	2的正解变量	0	1	0
$t_3$	3的正解变量	0	0	1

	图像为1	图像为2	图像为3
	接近1的值	接近0的值	接近0的值
	接近0的值	接近1的值	接近0的值
$δ_n^O=(a_n^O-t_n)a$	接近0的值	接近0的值	接近1的值

然后是误差反向传播法中的各层的神经单元误差δ:
输出层的神经单元误差计算:
$δ_n^O=(a_n^O-t_n)a$
卷积层神经单元误差的反向递推关系式:
$δ_{ij}^{Fk}=(δ_1^Ow_{k-i$
下面是平方误差关于过滤器的偏导数:(下面是像素为66、过滤器大小为33时的关系式)
卷积层:
关于权重：
$\frac{\partial C}{\partial w_{ij}^{Fk}}=δ_{11}^{Fk}x_{ij}+δ_{12}^{Fk}x_{ij+1}+...+δ_{44}^{Fk}x_{i+3j+3}$
关于偏置:
$\frac{\partial C}{\partial b^{Fk}}=δ_{11}^{Fk}+δ_{12}^{Fk}+...+δ_{33}^{Fk}+δ_{44}^{Fk}$
输出层:
$\frac{\partial C}{\partial w_{k-ij}^{On}}=δ_n^O，\frac{\partial C}{\partial b_n^O}=δ_n^O$

代价函数(损失函数)$C_T=\sum_{k=1}^{m}C_k,m在这里指的是全部学习数据的数量$
梯度下降法基本式:
$(Δ w_{11}^{F1},...,Δ w_{1-11}^{O1},...,Δ b_1^2,...,Δ b_1^O,...)=-η(\frac{\partial C_T}{\partial w_{11}^{F1}},...,\frac{\partial C_T}{\partial w_{1-11}^{O1}},...,\frac{\partial C_T}{\partial b^{F1}},...,\frac{\partial C_T}{\partial b_1^O}),正的常数η称为学习率$

新的位置：
$(w_{11}^{F1}+Δ w_{11}^{F1},...,w_{1-11}^{O1}+Δ w_{1-11}^{O1},...,b^{F1}+Δ b_1^2,...,b_1^O+Δ b_1^O,...)$
基于上述的数学基础，编写了以下的Python程序。
注意：初始值和学习率对最终结果影响很大，随机的初始值并不一定合适，如果出现这种情况需要初始化。

import numpy as np
import math
#_inputs的形状为(96,6,6)
_inputs = np.array([[[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0]],
    [[0,0,0,1,0,0],[0,0,1,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0]],
    [[0,0,1,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0]],
    [[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,1,1,0,0]],
    [[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,1,1,1,0]],
    [[0,0,1,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,1,1,1,0]],
    [[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,1,1,1,0,0]],
    [[0,1,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0]],
    #10
    [[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,1,1,1,0,0]],
    [[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,1,0]],
    [[0,0,0,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,0,1,0,0]],
    [[0,0,1,1,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,1,0,0]],
    [[0,0,0,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0]],
    [[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,0]],
    [[0,0,1,0,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,0,1,0,0]],
    [[0,0,0,0,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0]],
    [[0,0,0,0,0,0],[0,0,1,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0]],
    [[0,0,0,0,0,0],[0,0,1,1,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,1,0,0]],
    #20
    [[0,0,0,0,0,0],[0,0,1,1,0,0],[0,0,1,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0]],
    [[0,0,1,0,0,0],[0,1,1,0,0,0],[0,1,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0]],
    [[0,0,0,0,1,0],[0,0,0,1,1,0],[0,0,0,1,1,0],[0,0,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0]],
    [[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0]],
    [[0,0,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0]],
    [[0,1,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0]],
    [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0]],
    [[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,0]],
    [[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0],[0,0,1,0,0,0]],
    [[0,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,1,0],[0,0,0,0,1,0],[0,0,0,0,1,0],[0,0,0,0,0,0]],
    #30
    [[0,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,0]],
    [[0,0,0,0,0,0],[0,0,1,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,1,0,0],[0,0,0,0,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,1,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,1,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,1,0,0,0],[0,1,1,1,1,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,1,0,0,0],[0,1,1,1,1,0]],
    [[0,1,1,1,1,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    #40
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,1,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,1,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,1,1,1,1,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,1,1,0,0],[0,1,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,1]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[1,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[1,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[1,0,0,0,1,0],[0,0,0,1,0,0],[0,1,1,0,0,0],[0,1,1,1,1,0]],
    #50
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,1,0,0],[1,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,1]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,1]],
    [[0,0,1,1,0,0],[0,1,0,0,1,1],[0,0,0,0,1,1],[0,0,0,1,1,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,1,1,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,1,0,1,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,1,0,1,0],[0,1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,1,1,0,0],[0,1,1,0,0,0],[1,1,1,1,1,0]],
    [[0,0,1,1,1,0],[0,1,0,0,1,1],[0,0,0,0,1,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,1,1,1,1]],
    #60
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,0],[0,0,0,1,0,0],[0,0,1,1,0,0],[0,1,1,1,1,0]],
    [[0,1,1,1,1,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,0,1,1,0,0],[1,1,1,1,1,0]],
    [[0,1,1,1,0,0],[0,1,0,1,0,0],[0,0,0,1,0,0],[0,0,1,1,0,0],[0,1,1,0,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,1,1,0],[0,0,0,1,1,0],[0,0,0,1,0,0],[0,0,1,1,0,0],[0,1,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,0],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,0,1,1],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,1,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,1,0]],
    #70
    [[0,0,1,1,1,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,1,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,1,1],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,0,1,1],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,1,0],[0,1,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,1,1],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,1,0],[0,1,0,0,1,0],[0,0,0,1,1,1],[0,0,0,0,1,1],[0,1,0,0,0,1],[0,0,1,1,1,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[1,0,0,0,1,0],[0,1,1,1,0,0]],
    [[0,1,1,1,0,0],[1,0,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    #80
    [[0,1,1,1,0,0],[1,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[1,1,0,0,1,0],[0,1,1,1,0,0]],
    [[0,1,1,1,0,0],[1,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[1,1,0,0,1,0],[0,1,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,1],[0,0,0,1,1,0],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,1,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,0],[0,0,0,1,1,0],[0,1,0,0,0,1],[0,0,1,1,1,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,0],[0,0,0,1,1,0],[1,1,0,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[1,1,0,0,1,0],[0,0,1,1,1,0],[0,0,0,1,1,0],[1,1,0,0,1,0],[0,1,1,1,0,0]],
    [[0,1,1,1,0,0],[1,0,0,0,1,0],[0,0,1,1,1,0],[0,0,1,1,1,0],[0,0,0,0,1,0],[1,1,1,1,0,0]],
    [[1,1,1,1,0,0],[0,0,0,0,1,0],[0,0,1,1,1,0],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,1,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,1],[0,0,0,0,1,0],[0,0,0,1,1,0],[1,1,0,0,1,1],[0,1,1,1,1,0]],
    #90
    [[0,1,1,1,0,0],[0,1,1,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[0,1,0,0,1,0],[0,1,1,1,0,0]],
    [[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,1,1,0],[0,0,0,0,1,0],[0,1,1,0,1,0],[0,0,1,1,0,0]],
    [[0,0,1,1,0,0],[0,1,0,0,1,1],[0,0,0,0,1,1],[0,0,0,1,1,0],[1,1,0,0,1,0],[0,1,1,1,1,0]],
    [[1,1,1,1,1,0],[0,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[1,1,0,0,1,0],[0,1,1,1,0,0]],
    [[1,1,1,1,0,0],[1,1,0,0,1,0],[0,0,0,0,1,0],[0,0,0,1,1,0],[1,1,0,0,1,0],[1,1,1,1,0,0]],
    [[0,0,1,1,1,0],[0,1,0,0,1,1],[0,0,0,1,1,0],[0,0,0,0,1,0],[0,1,0,0,1,1],[0,0,1,1,1,0]],])
#对应的标签
#shape = (96,3)
labels = np.array([[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],
                   [1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],
                   [1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],
                   [1,0,0],[1,0,0],
                   [0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],
                   [0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],
                   [0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],[0,1,0],
                   [0,1,0],[0,1,0],
                   [0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],
                   [0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],
                   [0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],[0,0,1],
                   [0,0,1],[0,0,1]])
#激活函数
def a(x):
    return 1.0 / (1 + math.exp(-x))

#激活函数的导数
def aa(x):
    return a(x) * (1 - a(x))

#学习率n
n = 0.2

#初始化权重和偏置 神经网络总共69个参数
#初始化使用的是正态分布随机数
#卷积层
F = np.random.randn(3,3,3)
#输出层
O = np.random.randn(3, 3, 2, 2)
#6个偏置
FB = np.random.randn(3)
OB = np.random.randn(3)


#根据卷积层的i行j列返回神经单元连接的池化层神经单元的位置
def Pij(i,j):
    x = 0 if i <= 1 else 1
    y = 0 if j <= 1 else 1
    return (x,y)

#处理单张图像
def proprecessing(_inputs,t):
    #wi_j代表层i的第j个神经单元，SWi_j代表层i的第j个神经单元的平均误差对权重的偏导，SB代表平均误差对偏置的偏导，Ct为64张图像的平均误差的和
    #最终要得到的权重和偏置保存在wi_j和bs中
    global F,O,FB,OB,C,Wf,Wo,Bf,Bo

    #求加权输入z
    #36个分量
    x = _inputs.flatten()

    #卷积层的48个加权输入和48个神经单元输出
    Z = np.zeros((3,4,4))
    Fa = np.zeros((3,4,4))
    for k in range(3):
        w = F[k].flatten()
        for i in range(4):
            for j in range(4):
               Z[k][i][j] = np.sum(w * _inputs[i:i + 3,j:j + 3].flatten()) + FB[k]
               Fa[k][i][j] = a(Z[k][i][j])
               
    #池化层的12个加权输入和12个神经单元输出
    #池化层的输入和输出相等
    Zp = np.zeros((3,2,2))
    for k in range(3):
        for i in range(2):
            for j in range(2):
               Zp[k][i][j] = np.max([Fa[k][2 * i][2 * j],Fa[k][2 * i][2 * j + 1],Fa[k][2 * i + 1][2 * j],Fa[k][2 * i + 1][2 * j + 1]])
               
    #输出层3个加权输入和3个神经单元的输出
    Zo = np.zeros((3,1))
    Oa = np.zeros((3,1))
    for k in range(3):
        w = O[k].flatten()
        Zo[k] = np.sum(w * Zp.flatten()) + OB[k]
        Oa[k] = a(Zo[k])
        
    #平均误差
    C += 1.0 / 2 * ((t[0] - Oa[0]) ** 2 + (t[1] - Oa[1]) ** 2 + (t[2] - Oa[2]) ** 2)
    
    #输出层的神经单元误差3个
    Do = np.zeros((3,1))
    for k in range(3):
        Do[k] = (Oa[k] - t[k]) * aa(Zo[k])
        
    #卷积层的神经单元误差48个
    Df = np.zeros((3,4,4))
    for k in range(3):
        for i in range(4):
            for j in range(4):
                l = Pij(i,j)
                zeroOrone = 1 if Fa[k][i][j] == Zp[k][l[0]][l[1]] else 0
                Df[k][i][j] = np.sum(Do.flatten() * O[:,k,l[0],l[1]].flatten()) * zeroOrone * aa(Z[k][i][j])
                
    #平方误差关于过滤器的偏导数27个
    for k in range(3):
        for i in range(3):
            for j in range(3):
                Wf[k][i][j] += np.sum(Df[k].flatten() * _inputs[i:i + 4,j:j + 4].flatten())
    #偏置 3个
    for k in range(3):
        Bf[k] += np.sum(Df[k].flatten())
        
    #平方误差关于输出层神经单元的权重的偏导数
    for n in range(3):
        for k in range(3):
            for i in range(2):
                for j in range(2):
                    Wo[n][k][i][j] += Do[n] * Zp[k][i][j]
    #偏置3个
    Bo += Do

#平方误差
for k in range(50):
    C = 0.0
    Wf = np.zeros((3,3,3))
    Wo = np.zeros((3,3,2,2))
    Bf = np.zeros((3,1))
    Bo = Bf
    for i in range(96):
        proprecessing(_inputs[i],labels[i])
    #更新权重和偏置
    F+=(-1 * n * Wf)
    O+=(-1 * n * Wo)
    FB+=(-1 * n * Bf.flatten())
    OB+=(-1 * n * Bo.flatten())
    print('第{0}次神经网络的平均误差:{1}'.format(k + 1,C))
print(F.tolist())
print(O.tolist())
print(FB.tolist())
print(OB.tolist())

得到的权重结果就不贴了，测试程序:

import numpy as np
import math

#预设的测试图像为3
_inputs = np.array([[0,1,1,1,1,0],[0,0,0,0,1,0],[0,0,1,1,0,0],[0,0,0,0,1,0],[0,0,0,0,1,0],[0,1,1,1,0,0]])
#激活函数
def a(x):
    return 1.0 / (1 + math.exp(-x))

#激活函数的导数
def aa(x):
    return a(x) * (1 - a(x))


#初始化权重和偏置 神经网络总共69个参数
#初始化使用的是正态分布随机数
#卷积层
F = np.array(空，此处的值为上面得到的)
##输出层
O = np.array(空，此处的值为上面得到的)
##6个偏置
FB = np.array(空，此处的值为上面得到的)
OB = np.array(空，此处的值为上面得到的)
#根据卷积层的i行j列返回神经单元连接的池化层神经单元的位置
def Pij(i,j):
    x = 0 if i <= 1 else 1
    y = 0 if j <= 1 else 1
    return (x,y)

#处理单张图像
def getResult(_inputs):
    #wi_j代表层i的第j个神经单元，SWi_j代表层i的第j个神经单元的平均误差对权重的偏导，SB代表平均误差对偏置的偏导，Ct为64张图像的平均误差的和
    #最终要得到的权重和偏置保存在wi_j和bs中
    global F,O,FB,OB,C,Wf,Wo,Bf,Bo

    #求加权输入z
    #36个分量
    x = _inputs.flatten()

    #卷积层的48个加权输入和48个神经单元输出
    Z = np.zeros((3,4,4))
    Fa = np.zeros((3,4,4))
    for k in range(3):
        w = F[k].flatten()
        for i in range(4):
            for j in range(4):
               Z[k][i][j] = np.sum(w * _inputs[i:i + 3,j:j + 3].flatten()) + FB[k]
               Fa[k][i][j] = a(Z[k][i][j])
               
    #池化层的12个加权输入和12个神经单元输出
    #池化层的输入和输出相等
    Zp = np.zeros((3,2,2))
    for k in range(3):
        for i in range(2):
            for j in range(2):
               Zp[k][i][j] = np.max([Fa[k][2 * i][2 * j],Fa[k][2 * i][2 * j + 1],Fa[k][2 * i + 1][2 * j],Fa[k][2 * i + 1][2 * j + 1]])
    #输出层3个加权输入和3个神经单元的输出
    Zo = np.zeros((3,1))
    Oa = np.zeros((3,1))
    for k in range(3):
        w = O[k].flatten()
        Zo[k] = np.sum(w * Zp.flatten()) + OB[k]
        Oa[k] = a(Zo[k])
    print('图像中为1的概率为:{0},为2的概率为:{1},为3的概率为:{2}'.format(Oa[0],Oa[1],Oa[2]))
getResult(_inputs)

至此就结束了。