神经网络算法python程序

以下是一个使用Python实现神经网络算法的示例代码：

import numpy as np

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

#定义神经网络类
class NeuralNetwork:
    
    def __init__(self, layers):
        self.weights = []
        for i in range(1, len(layers)):
            w = np.random.randn(layers[i], layers[i-1])
            self.weights.append(w)
    
    def forward(self, x):
        a = x
        for w in self.weights:
            z = np.dot(w, a)
            a = sigmoid(z)
        return a
    
    def backward(self, x, y, lr):
        a = x
        outputs = [a]
        for w in self.weights:
            z = np.dot(w, a)
            a = sigmoid(z)
            outputs.append(a)
        
        error = y - a
        deltas = [error * sigmoid(outputs[-1], True)]
        
        for i in range(len(outputs)-2, 0, -1):
            delta = np.dot(self.weights[i].T, deltas[-1]) * sigmoid(outputs[i], True)
            deltas.append(delta)
        
        deltas.reverse()
        
        for i in range(len(self.weights)):
            self.weights[i] += lr * np.dot(deltas[i], outputs[i].T)

#测试神经网络
nn = NeuralNetwork([2, 4, 1])

x = np.array([[0,0], [0,1], [1,0], [1,1]])
y = np.array([[0], [1], [1], [0]])

for i in range(10000):
    index = np.random.randint(0, len(x))
    nn.backward(x[index], y[index], 0.1)

print(nn.forward([0,0]))
print(nn.forward([0,1]))
print(nn.forward([1,0]))
print(nn.forward([1,1]))

此示例实现了一个简单的2层神经网络，用于解决XOR问题。它使用随机梯度下降算法来更新权重，并使用sigmoid函数作为激活函数。