代码

# -*- coding: utf-8 -*-
"""
Created on Wed Feb 23 20:37:01 2022

@author: koneko
"""
import numpy as np
import matplotlib.pyplot as plt


def sigmoid(x):
    return 1 / (1 + np.exp(-x))


def mean_squared_error(y, t):
    return 0.5 * np.sum((y-t)**2)


class Sigmoid:
    def __init__(self):
        self.out = None
        
    def forward(self, x):
        out = sigmoid(x)
        self.out = out
        return out
    
    def backward(self, dout):
        dx = dout * (1.0 - self.out) * self.out 
        return dx
    
 
    
x = np.linspace(-np.pi, np.pi, 1000)
y = np.sin(x)
plt.plot(x,y)
x = x.reshape(1, x.size)
y = y.reshape(1, y.size)

# 初始化权重
W1 = np.random.randn(3,1)
b1 = np.random.randn(3,1)

W2 = np.random.randn(2,3)
b2 = np.random.randn(2,1)

W3 = np.random.randn(1,2)
b3 = np.random.randn(1,1)


sig1 = Sigmoid()

sig2 = Sigmoid()

lr = 0.001


for i in range(30000):
    a1 = W1 @ x + b1
    c1 = sig1.forward(a1)
    
    a2 = W2 @ c1 + b2
    c2 = sig2.forward(a2)
    
    y_pred = W3 @ c2 + b3
    
    #y_pred = W2 @ c1 + b2
    
    Loss = mean_squared_error(y, y_pred)
    print(f"Loss[{i}]: {Loss}")
    
    dy_pred = y_pred - y
    
    dc2 = W3.T @ dy_pred
    da2 = sig2.backward(dc2)
    
    dc1 = W2.T @ da2
    da1 = sig1.backward(dc1)
    
    # 计算Loss对各层参数的偏导数

    dW3 = dy_pred @ c2.T
    db3 = np.sum(dy_pred)
    
    dW2 = da2 @ c1.T
    db2 = np.sum(da2, axis=1)
    db2 = db2.reshape(db2.size, 1)
    
    dW1 = da1 @ x.T
    db1 = np.sum(da1, axis=1)
    db1 = db1.reshape(db1.size, 1)
    
    W3 -= lr*dW3
    b3 -= lr*db3
    W2 -= lr*dW2
    b2 -= lr*db2
    W1 -= lr*dW1
    b1 -= lr*db1
    
    if i % 100 == 99:
        plt.cla()
        plt.plot(x.T,y.T)
        plt.plot(x.T,y_pred.T)
    

    

效果