python人工智能算法之人工神经网络怎么使用

import numpy as npclass NeuralNetwork():    def __init__(self, layers):        """        layers: 数组，包含每个层的神经元数量，例如 [2, 3, 1] 表示 3 层神经网络，第一层 2 个神经元，第二层 3 个神经元，第三层 1 个神经元。        weights: 数组，包含每个连接的权重矩阵，默认值随机生成。        biases: 数组，包含每个层的偏差值，默认值为 0。        """        self.layers = layers        self.weights = [np.random.randn(a, b) for a, b in zip(layers[1:], layers[:-1])]        self.biases = [np.zeros((a, 1)) for a in layers[1:]]    def sigmoid(self, z):        """Sigmoid 激活函数."""        return 1 / (1 + np.exp(-z))    def forward_propagation(self, a):        """前向传播."""        for w, b in zip(self.weights, self.biases):            z = np.dot(w, a) + b            a = self.sigmoid(z)        return a    def backward_propagation(self, x, y):        """反向传播."""        nabla_w = [np.zeros(w.shape) for w in self.weights]        nabla_b = [np.zeros(b.shape) for b in self.biases]        a = x        activations = [x]        zs = []        for w, b in zip(self.weights, self.biases):            z = np.dot(w, a) + b            zs.append(z)            a = self.sigmoid(z)            activations.append(a)        delta = self.cost_derivative(activations[-1], y) * self.sigmoid_prime(zs[-1])        nabla_b[-1] = delta        nabla_w[-1] = np.dot(delta, activations[-2].transpose())        for l in range(2, len(self.layers)):            z = zs[-l]            sp = self.sigmoid_prime(z)            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp            nabla_b[-l] = delta            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())        return (nabla_w, nabla_b)    def train(self, x_train, y_train, epochs, learning_rate):        """训练网络."""        for epoch in range(epochs):            nabla_w = [np.zeros(w.shape) for w in self.weights]            nabla_b = [np.zeros(b.shape) for b in self.biases]            for x, y in zip(x_train, y_train):                delta_nabla_w, delta_nabla_b = self.backward_propagation(np.array([x]).transpose(), np.array([y]).transpose())                nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]                nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]            self.weights = [w-(learning_rate/len(x_train))*nw for w, nw in zip(self.weights, nabla_w)]            self.biases = [b-(learning_rate/len(x_train))*nb for b, nb in zip(self.biases, nabla_b)]    def predict(self, x_test):        """预测."""        y_predictions = []        for x in x_test:            y_predictions.append(self.forward_propagation(np.array([x]).transpose())[0][0])        return y_predictions    def cost_derivative(self, output_activations, y):        """损失函数的导数."""        return output_activations - y    def sigmoid_prime(self, z):        """Sigmoid 函数的导数."""        return self.sigmoid(z) * (1 - self.sigmoid(z))

x_train = [[0, 0], [1, 0], [0, 1], [1, 1]]y_train = [0, 1, 1, 0]# 创建神经网络nn = NeuralNetwork([2, 3, 1])# 训练神经网络nn.train(x_train, y_train, 10000, 0.1)# 测试神经网络x_test = [[0, 0], [1, 0], [0, 1], [1, 1]]y_test = [0, 1, 1, 0]y_predictions = nn.predict(x_test)print("Predictions:", y_predictions)print("Actual:", y_test)