人工智能基础 作业2

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。