Neural networks power everything from image recognition to language models, yet most tutorials use Python and hide the mathematics behind library calls. If you are a Java developer, building a neural network from raw arithmetic — no TensorFlow, no DL4J, no dependencies at all — is the single best way to internalise how learning actually works at the weight-and-gradient level.

This post implements a fully connected, multi-layer feedforward neural network in pure Java. The network learns the XOR function, a classic problem that a single-layer perceptron cannot solve, which is exactly why it is the standard benchmark for testing that backpropagation is implemented correctly. Every line is annotated with the mathematics driving it.