Neural Network Backpropagation Algorithm

Backpropagation is a widely used training algorithm for neural networks. This method iteratively adjusts the network's weights and biases to minimize the difference between the actual output and the desired target output. The core mechanism involves computing the gradient of the loss function with respect to each parameter through chain rule differentiation, then applying gradient descent optimization to update these parameters. In practical implementation, backpropagation consists of two main phases: the forward pass (computing predictions and loss) and the backward pass (calculating gradients and updating weights). Key operations include matrix multiplications for forward propagation, activation function derivatives (like sigmoid, ReLU, or tanh), and gradient computations using automatic differentiation frameworks in modern deep learning libraries. The algorithm typically runs for multiple epochs until the network converges to an optimal state. Backpropagation's effectiveness has enabled remarkable achievements in various domains including computer vision (image recognition), speech processing, natural language processing, and other machine learning applications. Modern implementations often incorporate enhancements like momentum, adaptive learning rates (Adam optimizer), and regularization techniques to improve training stability and performance.