BP Algorithm Implementation for XOR Problem

The Backpropagation (BP) algorithm is a neural network learning algorithm designed to solve the XOR problem. It employs a feedforward multi-layer neural network architecture utilizing sigmoid functions as activation functions. The core principle of the BP algorithm involves iterative forward propagation and backward propagation to adjust network weights and biases, enabling the network to better fit training data. In implementation, the forward pass computes outputs through weighted sums and sigmoid activations across hidden layers, while the backward pass calculates error gradients using chain rule differentiation. Key functions typically include weight initialization, forward propagation calculation, error computation, gradient descent updates, and convergence checking. Through repeated iterations, the BP algorithm gradually improves network performance by minimizing the error between predicted and actual outputs, ultimately achieving accurate classification of the XOR problem. The algorithm typically requires proper learning rate selection and stopping criteria to ensure convergence.