Backpropagation Neural Network Routine

This is a backpropagation neural network routine implementing a single hidden layer BP network with straightforward, easy-to-understand code structure. Through this routine, we can thoroughly understand the principles and implementation process of backpropagation neural networks. The code demonstrates how to construct each layer of the neural network, implement forward propagation and backpropagation algorithms, and provides practical examples showing the network's training and prediction processes. Key implementation aspects include weight initialization methods, activation function selection (typically using sigmoid or tanh functions), error calculation, and gradient descent optimization for weight updates. This routine helps solidify fundamental concepts of backpropagation neural networks and establishes a strong foundation for further learning and research by providing hands-on experience with core neural network operations like matrix-based computations for layer connections and derivative calculations during backward pass.