bp神经网络回归relu激活函数

下面是使用 ReLU 激活函数实现的 BP 神经网络回归的代码示例：

import numpy as np

class NeuralNetwork:
    def __init__(self, input_dim, hidden_dim, output_dim):
        self.input_dim = input_dim
        self.hidden_dim = hidden_dim
        self.output_dim = output_dim
        self.weights1 = np.random.randn(input_dim, hidden_dim)
        self.bias1 = np.zeros((1, hidden_dim))
        self.weights2 = np.random.randn(hidden_dim, output_dim)
        self.bias2 = np.zeros((1, output_dim))

    def relu(self, x):
        return np.maximum(0, x)

    def relu_derivative(self, x):
        return np.where(x >= 0, 1, 0)

    def forward(self, x):
        self.z1 = np.dot(x, self.weights1) + self.bias1
        self.a1 = self.relu(self.z1)
        self.z2 = np.dot(self.a1, self.weights2) + self.bias2
        self.y_hat = self.z2

    def backward(self, x, y, learning_rate):
        error = self.y_hat - y
        delta2 = error
        delta1 = np.dot(delta2, self.weights2.T) * self.relu_derivative(self.a1)
        grad_weights2 = np.dot(self.a1.T, delta2)
        grad_bias2 = np.sum(delta2, axis=0, keepdims=True)
        grad_weights1 = np.dot(x.T, delta1)
        grad_bias1 = np.sum(delta1, axis=0)

        self.weights2 -= learning_rate * grad_weights2
        self.bias2 -= learning_rate * grad_bias2
        self.weights1 -= learning_rate * grad_weights1
        self.bias1 -= learning_rate * grad_bias1

    def train(self, X, y, epochs, learning_rate):
        for i in range(epochs):
            self.forward(X)
            self.backward(X, y, learning_rate)

    def predict(self, x):
        self.forward(x)
        return self.y_hat

在这个示例中，`NeuralNetwork` 类的构造函数接收输入层、隐藏层和输出层的维度作为参数，并且随机初始化了神经网络的参数。`relu` 方法实现了 ReLU 激活函数，`relu_derivative` 方法实现了 ReLU 激活函数的导数。

`forward` 方法实现了神经网络的前向传播过程，`backward` 方法实现了神经网络的反向传播过程。在反向传播过程中，使用 `self.relu_derivative` 方法计算了隐藏层的 delta 值，以便计算隐藏层到输入层之间的权重矩阵的梯度。最后，`train` 方法实现了神经网络的训练过程，`predict` 方法实现了神经网络的预测过程。