说明
实现手动实现反向传播更新模型权重
构造一个2层的全连接神经网络,有2个输入,隐藏层和输出层分别有2个神经元
训练数据:输入 x1, x2 = 0.5, 0.3 期望输出 y1, y2 =0.23, -0.07
激活函数:sigmod
优化方法:梯度下降
损失函数:均方差损失
代码
加了自己理解的注释
import numpy as np
# 激活函数
def sigmoid(z):
a = 1 / (1 + np.exp(-z))
return a
# 前向传播,使用给定的权值进行预测
def 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) ** 2
print("损失函数:均方误差")
print(round(error, 5))
return out_o1, out_o2, out_h1, out_h2
# 反向传播,根据各层输出计算各权重张量反向传播中的梯度值
# 以下这个是错误代码,梯度公式错了
# def 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_w8
# 以下这个是正确的
def back_propagate(out_o1, out_o2, out_h1, out_h2):
# 反向传播
d_o1 = out_o1 - y1
d_o2 = out_o2 - y2
d_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_h2
d_w1 = (d_o1 * out_h1 * (1 - out_h1) * w5 + d_o2 * out_o2 * (1 - out_o2) * w6) * out_h1 * (1 - out_h1) * x1
d_w3 = (d_o1 * out_h1 * (1 - out_h1) * w5 + d_o2 * out_o2 * (1 - out_o2) * w6) * out_h1 * (1 - out_h1) * x2
d_w2 = (d_o1 * out_h1 * (1 - out_h1) * w7 + d_o2 * out_o2 * (1 - out_o2) * w8) * out_h2 * (1 - out_h2) * x1
d_w4 = (d_o1 * out_h1 * (1 - out_h1) * w7 + d_o2 * out_o2 * (1 - out_o2) * w8) * out_h2 * (1 - out_h2) * x2
print("w的梯度:",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_w8
# 使用梯度下降法更新模型各权重参数
def update_w(w1, w2, w3, w4, w5, w6, w7, w8):
# 学习率
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, w8
if __name__ == "__main__":
# 初始化权重
w1, w2, w3, w4, w5, w6, w7, w8 = 0.2, -0.4, 0.5, 0.6, 0.1, -0.5, -0.3, 0.8
# 数据集
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))
# 训练1000轮
for i in range(1000):
print("=====第" + str(i) + "轮=====")
# 前向传播 y_hat = net(x)
out_o1, out_o2, out_h1, out_h2 = forward_propagate(x1, x2, y1, y2, w1, w2, w3, w4, w5, w6, w7, w8)
# 反向传播计算梯度 loss.backward()
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)
# 根据梯度信息更新模型各权重 optimizer.step()
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))
训练结果
模型优化迭代了1000次后,在给定输入 x1, x2 = 0.5, 0.3 的情况下输出 y1`, y2` = 0.23038, 0.00954,可以看到和期望输出的 y1, y2 =0.23, -0.07 已经很接近了。