用Python编写bp神经网络

好的，以下是一个简单的Python实现的bp神经网络：

import numpy as np

class BPNeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.output_size = output_size
        
        # 初始化权重和偏置
        self.weights1 = np.random.randn(self.hidden_size, self.input_size)
        self.bias1 = np.zeros((self.hidden_size, 1))
        self.weights2 = np.random.randn(self.output_size, self.hidden_size)
        self.bias2 = np.zeros((self.output_size, 1))
        
    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))
    
    def forward(self, x):
        hidden = self.sigmoid(self.weights1 @ x + self.bias1)
        output = self.sigmoid(self.weights2 @ hidden + self.bias2)
        return output, hidden
    
    def train(self, x, y, learning_rate=0.1, epochs=1000):
        for epoch in range(epochs):
            output, hidden = self.forward(x)
            
            # 计算误差
            error = y - output
            delta_output = error * output * (1 - output)
            delta_hidden = self.weights2.T @ delta_output * hidden * (1 - hidden)
            
            # 更新权重和偏置
            self.weights2 += learning_rate * delta_output @ hidden.T
            self.bias2 += learning_rate * delta_output.sum(axis=1, keepdims=True)
            self.weights1 += learning_rate * delta_hidden @ x.T
            self.bias1 += learning_rate * delta_hidden.sum(axis=1, keepdims=True)
            
            # 计算损失
            loss = np.mean(np.square(error))
            if epoch % 100 == 0:
                print(f"Epoch: {epoch}, Loss: {loss:.4f}")

这个神经网络具有一个输入层，一个隐藏层和一个输出层。在初始化时，权重和偏置被随机初始化。在前向传播中，输入通过权重和偏置传递到隐藏层和输出层。在反向传播中，通过计算输出误差和隐藏层误差来更新权重和偏置。该函数`sigmoid`用于激活层。`train`函数用于训练神经网络，并在每个时期打印损失。