人工智能|人工智能基础作业2 pycharm|python

文章目录

前言
一、反向传播1轮，检验PPT数值
二、增加到5轮，测试收敛
三、改变步长（1变为50），看收敛速度
四、扩展到N轮，步长=5，训练N=1000次，查看效果
五、代码优化
总结
参考博客

前言

反向传播（英语：Backpropagation，缩写为BP）是“误差反向传播”的简称，是一种与最优化方法（如梯度下降法）结合使用的，用来训练人工神经网络的常见方法。该方法对网络中所有权重计算损失函数的梯度。这个梯度会反馈给最优化方法，用来更新权值以最小化损失函数。

文章图片

输入值：x1, x2 = 0.5，0.3
输出值：y1, y2 =0.23， -0.07
激活函数：sigmoid
损失函数：MSE
初始权值：0.2 -0.4 0.5 0.6 0.1 -0.5 -0.3 0.8
目标：通过反向传播优化权值
一、反向传播1轮，检验PPT数值 =正向计算：h1, h2, o1 ,o2=
0.56 0.5 0.48 0.53
=损失函数：均方误差=
0.21
=反向传播：误差传给每个权值=
0.01 0.01 0.01 0.01 0.03 0.08 0.03 0.07
=更新前的权值=
0.2 -0.4 0.5 0.6 0.1 -0.5 -0.3 0.8
=更新后的权值=
0.19 -0.41 0.49 0.59 0.07 -0.58 -0.33 0.73
代码如下：

import numpy as npdef sigmoid(z): a = 1 / (1 + np.exp(-z)) return aif __name__ == "__main__": w1 = 0.2 w2 = -0.4 w3 = 0.5 w4 = 0.6 w5 = 0.1 w6 = -0.5 w7 = -0.3 w8 = 0.8x1 = 0.5 x2 = 0.3y1 = 0.23 y2 = -0.07print("=====输入值：x1, x2；真实输出值：y1, y2=====") print(x1, x2, y1, y2)in_h1 = w1 * x1 + w3 * x2 out_h1 = sigmoid(in_h1) in_h2 = w2 * x1 + w4 * x2 out_h2 = sigmoid(in_h2)in_o1 = w5 * out_h1 + w7 * out_h2 out_o1 = sigmoid(in_o1) in_o2 = w6 * out_h1 + w8 * out_h2 out_o2 = sigmoid(in_o2)print("=====正向计算：h1, h2, o1 ,o2=====") print(round(out_h1, 2), round(out_h2, 2), round(out_o1, 2), round(out_o2, 2))error = (1 / 2) * (out_o1 - y1)**2 + (1 / 2) * (out_o2 - y2)**2print("=====损失函数：均方误差=====") print(round(error, 2))# 反向传播 d_o1 = out_o1 - y1 d_o2 = out_o2 - y2 # print(round(d_o1, 2), round(d_o2, 2))d_w5 = d_o1 * out_o1 * (1 - out_o1) * out_h1 d_w7 = d_o1 * out_o1 * (1 - out_o1) * out_h2 # print(round(d_w5, 2), round(d_w7, 2)) d_w6 = d_o2 * out_o2 * (1 - out_o2) * out_h1 d_w8 = d_o2 * out_o2 * (1 - out_o2) * out_h2 # print(round(d_w6, 2), round(d_w8, 2))d_w1 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x1 d_w3 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x2 # print(round(d_w1, 2), round(d_w3, 2))d_w2 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x1 d_w4 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x2 # print(round(d_w2, 2), round(d_w4, 2)) print("=====反向传播：误差传给每个权值=====") print(round(d_w1, 2), round(d_w2, 2), round(d_w3, 2), round(d_w4, 2), round(d_w5, 2), round(d_w6, 2), round(d_w7, 2), round(d_w8, 2))print("=====更新前的权值=====") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))w1 = w1 - d_w1 w2 = w2 - d_w2 w3 = w3 - d_w3 w4 = w4 - d_w4 w5 = w5 - d_w5 w6 = w6 - d_w6 w7 = w7 - d_w7 w8 = w8 - d_w8print("=====更新后的权值=====") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))

输出结果：

文章图片

二、增加到5轮，测试收敛 =第6轮=
正向计算：h1, h2, o1 ,o2
0.55 0.48 0.44 0.43
损失函数：均方误差
0.15
代码如下：

import numpy as npdef sigmoid(z): a = 1 / (1 + np.exp(-z)) return adef forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8): in_h1 = w1 * x1 + w3 * x2 out_h1 = sigmoid(in_h1) in_h2 = w2 * x1 + w4 * x2 out_h2 = sigmoid(in_h2)in_o1 = w5 * out_h1 + w7 * out_h2 out_o1 = sigmoid(in_o1) in_o2 = w6 * out_h1 + w8 * out_h2 out_o2 = sigmoid(in_o2)print("正向计算：h1, h2, o1 ,o2") print(round(out_h1, 2), round(out_h2, 2), round(out_o1, 2), round(out_o2, 2))error = (1 / 2) * (out_o1 - y1) ** 2 + (1 / 2) * (out_o2 - y2) ** 2print("损失函数：均方误差") print(round(error, 2))return out_o1, out_o2, out_h1, out_h2def back_propagate(out_o1, out_o2, out_h1, out_h2): # 反向传播 d_o1 = out_o1 - y1 d_o2 = out_o2 - y2 # print(round(d_o1, 2), round(d_o2, 2))d_w5 = d_o1 * out_o1 * (1 - out_o1) * out_h1 d_w7 = d_o1 * out_o1 * (1 - out_o1) * out_h2 # print(round(d_w5, 2), round(d_w7, 2)) d_w6 = d_o2 * out_o2 * (1 - out_o2) * out_h1 d_w8 = d_o2 * out_o2 * (1 - out_o2) * out_h2 # print(round(d_w6, 2), round(d_w8, 2))d_w1 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x1 d_w3 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x2 # print(round(d_w1, 2), round(d_w3, 2))d_w2 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x1 d_w4 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x2 # print(round(d_w2, 2), round(d_w4, 2)) print("反向传播：误差传给每个权值") print(round(d_w1, 2), round(d_w2, 2), round(d_w3, 2), round(d_w4, 2), round(d_w5, 2), round(d_w6, 2), round(d_w7, 2), round(d_w8, 2))return d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8if __name__ == "__main__": w1 = 0.2 w2 = -0.4 w3 = 0.5 w4 = 0.6 w5 = 0.1 w6 = -0.5 w7 = -0.3 w8 = 0.8 x1 = 0.5 x2 = 0.3 y1 = 0.23 y2 = -0.07 print("=====输入值：x1, x2；真实输出值：y1, y2=====") print(x1, x2, y1, y2) print("=====更新前的权值=====") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2)# 步长 step = 1w1 = w1 - step * d_w1 w2 = w2 - step * d_w2 w3 = w3 - step * d_w3 w4 = w4 - step * d_w4 w5 = w5 - step * d_w5 w6 = w6 - step * d_w6 w7 = w7 - step * d_w7 w8 = w8 - step * d_w8print("第1轮更新后的权值") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))print("=====第2轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1 = w1 - step * d_w1 w2 = w2 - step * d_w2 w3 = w3 - step * d_w3 w4 = w4 - step * d_w4 w5 = w5 - step * d_w5 w6 = w6 - step * d_w6 w7 = w7 - step * d_w7 w8 = w8 - step * d_w8print("=====第3轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1 = w1 - step * d_w1 w2 = w2 - step * d_w2 w3 = w3 - step * d_w3 w4 = w4 - step * d_w4 w5 = w5 - step * d_w5 w6 = w6 - step * d_w6 w7 = w7 - step * d_w7 w8 = w8 - step * d_w8print("=====第4轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1 = w1 - step * d_w1 w2 = w2 - step * d_w2 w3 = w3 - step * d_w3 w4 = w4 - step * d_w4 w5 = w5 - step * d_w5 w6 = w6 - step * d_w6 w7 = w7 - step * d_w7 w8 = w8 - step * d_w8print("=====第5轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1 = w1 - step * d_w1 w2 = w2 - step * d_w2 w3 = w3 - step * d_w3 w4 = w4 - step * d_w4 w5 = w5 - step * d_w5 w6 = w6 - step * d_w6 w7 = w7 - step * d_w7 w8 = w8 - step * d_w8print("=====第6轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) print("更新后的权值") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))

输出结果：

文章图片

文章图片

三、改变步长（1变为50），看收敛速度 =第6轮=
正向计算：o1 ,o2
0.23 0.03
损失函数：均方误差
0.01
代码如下：

import numpy as npdef sigmoid(z): a = 1 / (1 + np.exp(-z)) return adef forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8): in_h1 = w1 * x1 + w3 * x2 out_h1 = sigmoid(in_h1) in_h2 = w2 * x1 + w4 * x2 out_h2 = sigmoid(in_h2)in_o1 = w5 * out_h1 + w7 * out_h2 out_o1 = sigmoid(in_o1) in_o2 = w6 * out_h1 + w8 * out_h2 out_o2 = sigmoid(in_o2)print("正向计算：o1 ,o2") print(round(out_o1, 2), round(out_o2, 2))error = (1 / 2) * (out_o1 - y1) ** 2 + (1 / 2) * (out_o2 - y2) ** 2print("损失函数：均方误差") print(round(error, 2))return out_o1, out_o2, out_h1, out_h2def back_propagate(out_o1, out_o2, out_h1, out_h2): # 反向传播 d_o1 = out_o1 - y1 d_o2 = out_o2 - y2 # print(round(d_o1, 2), round(d_o2, 2))d_w5 = d_o1 * out_o1 * (1 - out_o1) * out_h1 d_w7 = d_o1 * out_o1 * (1 - out_o1) * out_h2 # print(round(d_w5, 2), round(d_w7, 2)) d_w6 = d_o2 * out_o2 * (1 - out_o2) * out_h1 d_w8 = d_o2 * out_o2 * (1 - out_o2) * out_h2 # print(round(d_w6, 2), round(d_w8, 2))d_w1 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x1 d_w3 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x2 # print(round(d_w1, 2), round(d_w3, 2))d_w2 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x1 d_w4 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x2 # print(round(d_w2, 2), round(d_w4, 2)) print("反向传播：误差传给每个权值") print(round(d_w1, 2), round(d_w2, 2), round(d_w3, 2), round(d_w4, 2), round(d_w5, 2), round(d_w6, 2), round(d_w7, 2), round(d_w8, 2))return d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8def update_w(w1, w2, w3, w4, w5, w6, w7, w8): # 步长 step = 50 w1 = w1 - step * d_w1 w2 = w2 - step * d_w2 w3 = w3 - step * d_w3 w4 = w4 - step * d_w4 w5 = w5 - step * d_w5 w6 = w6 - step * d_w6 w7 = w7 - step * d_w7 w8 = w8 - step * d_w8 return w1, w2, w3, w4, w5, w6, w7, w8if __name__ == "__main__": w1 = 0.2 w2 = -0.4 w3 = 0.5 w4 = 0.6 w5 = 0.1 w6 = -0.5 w7 = -0.3 w8 = 0.8 x1 = 0.5 x2 = 0.3 y1 = 0.23 y2 = -0.07 print("=====输入值：x1, x2；真实输出值：y1, y2=====") print(x1, x2, y1, y2) print("=====更新前的权值=====") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)print("第1轮更新后的权值") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))print("=====第2轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)print("=====第3轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)print("=====第4轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)print("=====第5轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)print("=====第6轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) print("更新后的权值") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))

输出结果：

文章图片

文章图片

四、扩展到N轮，步长=5，训练N=1000次，查看效果 =第999轮=
正向计算：o1 ,o2
0.23038 0.00954
损失函数：均方误差
0.00316
代码如下：

import numpy as npdef sigmoid(z): a = 1 / (1 + np.exp(-z)) return adef forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8): in_h1 = w1 * x1 + w3 * x2 out_h1 = sigmoid(in_h1) in_h2 = w2 * x1 + w4 * x2 out_h2 = sigmoid(in_h2)in_o1 = w5 * out_h1 + w7 * out_h2 out_o1 = sigmoid(in_o1) in_o2 = w6 * out_h1 + w8 * out_h2 out_o2 = sigmoid(in_o2)print("正向计算：o1 ,o2") print(round(out_o1, 5), round(out_o2, 5))error = (1 / 2) * (out_o1 - y1) ** 2 + (1 / 2) * (out_o2 - y2) ** 2print("损失函数：均方误差") print(round(error, 5))return out_o1, out_o2, out_h1, out_h2def back_propagate(out_o1, out_o2, out_h1, out_h2): # 反向传播 d_o1 = out_o1 - y1 d_o2 = out_o2 - y2 # print(round(d_o1, 2), round(d_o2, 2))d_w5 = d_o1 * out_o1 * (1 - out_o1) * out_h1 d_w7 = d_o1 * out_o1 * (1 - out_o1) * out_h2 # print(round(d_w5, 2), round(d_w7, 2)) d_w6 = d_o2 * out_o2 * (1 - out_o2) * out_h1 d_w8 = d_o2 * out_o2 * (1 - out_o2) * out_h2 # print(round(d_w6, 2), round(d_w8, 2))d_w1 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x1 d_w3 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x2 # print(round(d_w1, 2), round(d_w3, 2))d_w2 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x1 d_w4 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x2 # print(round(d_w2, 2), round(d_w4, 2)) print("反向传播：误差传给每个权值") print(round(d_w1, 5), round(d_w2, 5), round(d_w3, 5), round(d_w4, 5), round(d_w5, 5), round(d_w6, 5), round(d_w7, 5), round(d_w8, 5))return d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8def update_w(w1, w2, w3, w4, w5, w6, w7, w8): # 步长 step = 5 w1 = w1 - step * d_w1 w2 = w2 - step * d_w2 w3 = w3 - step * d_w3 w4 = w4 - step * d_w4 w5 = w5 - step * d_w5 w6 = w6 - step * d_w6 w7 = w7 - step * d_w7 w8 = w8 - step * d_w8 return w1, w2, w3, w4, w5, w6, w7, w8if __name__ == "__main__": w1, w2, w3, w4, w5, w6, w7, w8 = 0.2, -0.4, 0.5, 0.6, 0.1, -0.5, -0.3, 0.8 x1, x2 = 0.5, 0.3 y1, y2 = 0.23, -0.07 print("=====输入值：x1, x2；真实输出值：y1, y2=====") print(x1, x2, y1, y2) print("=====更新前的权值=====") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))for i in range(1000): print("=====第" + str(i) + "轮=====") out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)print("更新后的权值") print(round(w1, 2), round(w2, 2), round(w3, 2), round(w4, 2), round(w5, 2), round(w6, 2), round(w7, 2), round(w8, 2))

输出结果：

文章图片

五、代码优化 【人工智能|人工智能基础作业2】修改输出值y2为正，收敛效果很好。
原因是：sigmoid，输出值应在（0,1）区间，所以最开始的假设 y2=-0.07，在这个模型里，无法很好的拟合。
优化后的代码：

import numpy as np import matplotlib.pyplot as pltdef sigmoid(z): a = 1 / (1 + np.exp(-z)) return adef forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8): # 正向传播 in_h1 = w1 * x1 + w3 * x2 out_h1 = sigmoid(in_h1) in_h2 = w2 * x1 + w4 * x2 out_h2 = sigmoid(in_h2)in_o1 = w5 * out_h1 + w7 * out_h2 out_o1 = sigmoid(in_o1) in_o2 = w6 * out_h1 + w8 * out_h2 out_o2 = sigmoid(in_o2)error = (1 / 2) * (out_o1 - y1) ** 2 + (1 / 2) * (out_o2 - y2) ** 2return out_o1, out_o2, out_h1, out_h2, errordef back_propagate(out_o1, out_o2, out_h1, out_h2):# 反向传播 d_o1 = out_o1 - y1 d_o2 = out_o2 - y2d_w5 = d_o1 * out_o1 * (1 - out_o1) * out_h1 d_w7 = d_o1 * out_o1 * (1 - out_o1) * out_h2 d_w6 = d_o2 * out_o2 * (1 - out_o2) * out_h1 d_w8 = d_o2 * out_o2 * (1 - out_o2) * out_h2d_w1 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x1 d_w3 = (d_w5 + d_w6) * out_h1 * (1 - out_h1) * x2 d_w2 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x1 d_w4 = (d_w7 + d_w8) * out_h2 * (1 - out_h2) * x2return d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8def update_w(step,w1, w2, w3, w4, w5, w6, w7, w8):#梯度下降，更新权值 w1 = w1 - step * d_w1 w2 = w2 - step * d_w2 w3 = w3 - step * d_w3 w4 = w4 - step * d_w4 w5 = w5 - step * d_w5 w6 = w6 - step * d_w6 w7 = w7 - step * d_w7 w8 = w8 - step * d_w8 return w1, w2, w3, w4, w5, w6, w7, w8if __name__ == "__main__": w1, w2, w3, w4, w5, w6, w7, w8 = 0.2, -0.4, 0.5, 0.6, 0.1, -0.5, -0.3, 0.8 # 可以给随机值，为配合PPT，给的指定值 x1, x2 = 0.5, 0.3# 输入值 y1, y2 = 0.23, -0.07 # 正数可以准确收敛；负数不行。why? 因为用sigmoid输出，y1, y2 在（0,1）范围内。 N = 10# 迭代次数 step = 10# 步长print("输入值：x1, x2；",x1, x2, "输出值：y1, y2:", y1, y2) eli = [] lli = [] for i in range(N): print("=====第" + str(i) + "轮=====") # 正向传播 out_o1, out_o2, out_h1, out_h2, error = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8) print("正向传播:", round(out_o1, 5), round(out_o2, 5)) print("损失函数：", round(error, 2)) # 反向传播 d_w1, d_w2, d_w3, d_w4, d_w5, d_w6, d_w7, d_w8 = back_propagate(out_o1, out_o2, out_h1, out_h2) # 梯度下降，更新权值 w1, w2, w3, w4, w5, w6, w7, w8 = update_w(step,w1, w2, w3, w4, w5, w6, w7, w8) eli.append(i) lli.append(error)plt.plot(eli, lli) plt.ylabel('Loss') plt.xlabel('w') plt.show()

输出结果：

文章图片

总结输出误差（某种形式）－>隐层（逐层）－>输入层其主要目的是通过将输出误差反传，将误差分摊给各层所有单元，从而获得各层单元的误差信号，进而修正各单元的权值（其过程，是一个权值调整的过程）。
注2：权值调整的过程，也就是网络的学习训练过程（学习也就是这么的由来，权值调整）。
1）初始化
2）输入训练样本对，计算各层输出
3）计算网络输出误差
4）计算各层误差信号
5）调整各层权值
6）检查网络总误差是否达到精度要求
满足，则训练结束；不满足，则返回步骤2。
参考博客【人工智能导论：模型与算法】MOOC 8.3 误差后向传播(BP) 例题编程验证
误差反向传播算法