Python实现一个简单的反向传播算法

x输入乘以w1权重，后rulu激活函数，后w2权重，最后输出结果。

# -*- coding: utf-8 -*-
import numpy as np

# N为batch size; D_in 输入维度
# H为隐藏层维度 D_out 输出维度
N, D_in, H, D_out = 64, 1000, 100, 10

# 创建随机输入数据，让网络拟合
x = np.random.randn(N, D_in)
y = np.random.randn(N, D_out)

# Randomly initialize weights
w1 = np.random.randn(D_in, H)
w2 = np.random.randn(H, D_out)

learning_rate = 1e-6
for t in range(500):
    # 前向传播计算y_pre
    h = x.dot(w1)
    h_relu = np.maximum(h, 0)
    y_pred = h_relu.dot(w2)

    # 计算误差
    loss = np.square(y_pred - y).sum()
    print(t, loss)

    # 反向传播计算梯度核心！
    # 计算过程见上图
    grad_y_pred = 2.0 * (y_pred - y)
    grad_w2 = h_relu.T.dot(grad_y_pred)
    grad_h_relu = grad_y_pred.dot(w2.T)
    grad_h = grad_h_relu.copy()
    grad_h[h < 0] = 0
    grad_w1 = x.T.dot(grad_h)

    # 更新权重，向梯度相反的方向下降
    w1 -= learning_rate * grad_w1
    w2 -= learning_rate * grad_w2