Universal Approximation Using Radial-Basis-Function Networks

TLDR

Recent studies have examined feedforward networks for approximating arbitrary functionals, including cases with non‑sigmoidal hidden‑layer units motivated by successful applications. This study demonstrates that one‑hidden‑layer radial‑basis‑function networks possess universal approximation capability. The results confirm that typical RBF networks with a uniform smoothing factor across kernel nodes are sufficiently expressive for universal approximation.

Abstract

There have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables. Some of these studies deal with cases in which the hidden-layer nonlinearity is not a sigmoid. This was motivated by successful applications of feedforward networks with nonsigmoidal hidden-layer units. This paper reports on a related study of radial-basis-function (RBF) networks, and it is proved that RBF networks having one hidden layer are capable of universal approximation. Here the emphasis is on the case of typical RBF networks, and the results show that a certain class of RBF networks with the same smoothing factor in each kernel node is broad enough for universal approximation.