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Neural Computation

Winter 1989, Vol. 1, No. 4, Pages 465-469
(doi: 10.1162/neco.1989.1.4.465)
© 1989 Massachusetts Institute of Technology
Representation Properties of Networks: Kolmogorov's Theorem Is Irrelevant
Article PDF (248.23 KB)
Abstract

Many neural networks can be regarded as attempting to approximate a multivariate function in terms of one-input one-output units. This note considers the problem of an exact representation of nonlinear mappings in terms of simpler functions of fewer variables. We review Kolmogorov's theorem on the representation of functions of several variables in terms of functions of one variable and show that it is irrelevant in the context of networks for learning.