多层感知机（MLP）代码

多层感知机（Multilayer Perceptron，简称MLP）是一种常见的人工神经网络模型，它由多个神经元层组成，每个神经元层与下一层之间都有连接。以下是一个简单的MLP代码示例：

import numpy as np

class MLP:
    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
        self.weights1 = np.random.randn(self.input_size, self.hidden_size)
        self.weights2 = np.random.randn(self.hidden_size, self.output_size)
        
        # 初始化偏置
        self.bias1 = np.zeros((1, self.hidden_size))
        self.bias2 = np.zeros((1, self.output_size))
        
    def forward(self, X):
        # 前向传播
        self.hidden_layer = np.dot(X, self.weights1) + self.bias1
        self.hidden_activation = self.sigmoid(self.hidden_layer)
        self.output_layer = np.dot(self.hidden_activation, self.weights2) + self.bias2
        self.output_activation = self.sigmoid(self.output_layer)
        
        return self.output_activation
    
    def backward(self, X, y, learning_rate):
        # 反向传播
        error = y - self.output_activation
        delta_output = error * self.sigmoid_derivative(self.output_activation)
        
        error_hidden = delta_output.dot(self.weights2.T)
        delta_hidden = error_hidden * self.sigmoid_derivative(self.hidden_activation)
        
        # 更新权重和偏置
        self.weights2 += self.hidden_activation.T.dot(delta_output) * learning_rate
        self.bias2 += np.sum(delta_output, axis=0, keepdims=True) * learning_rate
        self.weights1 += X.T.dot(delta_hidden) * learning_rate
        self.bias1 += np.sum(delta_hidden, axis=0, keepdims=True) * learning_rate
        
    def train(self, X, y, epochs, learning_rate):
        for epoch in range(epochs):
            output = self.forward(X)
            self.backward(X, y, learning_rate)
            
    def predict(self, X):
        output = self.forward(X)
        predictions = np.round(output)
        return predictions
    
    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))
    
    def sigmoid_derivative(self, x):
        return x * (1 - x)

这段代码实现了一个简单的MLP模型，包括初始化权重和偏置、前向传播、反向传播、训练和预测等功能。你可以根据自己的需求进行修改和扩展。