Editing Perceptron (section)

===Universal approximation theorem===

* {{main|Universal approximation theorem}}

A single perceptron can learn to classify any half-space. It cannot solve any linearly nonseparable vectors, such as the Boolean [[exclusive-or]] problem (the famous "XOR problem").

A perceptron network with '''one hidden layer''' can learn to classify any compact subset arbitrarily closely. Similarly, it can also approximate any [[Compactly supported|compactly-supported]] [[continuous function]] arbitrarily closely. This is essentially a special case of the [[Universal approximation theorem#Arbitrary-width case|theorems by George Cybenko and Kurt Hornik]].