Kolmogorov's Theorem Is Relevant

Abstract

We show that Kolmogorov's theorem on representations of continuous functions of n-variables by sums and superpositions of continuous functions of one variable is relevant in the context of neural networks. We give a version of this theorem with all of the one-variable functions approximated arbitrarily well by linear combinations of compositions of affine functions with some given sigmoidal function. We derive an upper estimate of the number of hidden units.

Identifiers

DOI

10.1162/neco.1991.3.4.617

Citations and references