XOR Problem

The XOR problem is a classic example showing why a single linear classifier cannot solve every pattern. XOR outputs true when two binary inputs differ and false when they match. Plotting the four cases reveals that no single straight line separates the true points from the false ones. Early criticism of simple perceptrons highlighted this limitation. A multilayer neural network with a hidden layer and nonlinear activation can represent the required boundary, making XOR a compact demonstration of why depth and nonlinearity matter. The problem is now easy for modern networks, but it remains useful for teaching representation, hidden units, backpropagation, and the difference between linear and nonlinear decision surfaces.