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Neural Computation

Winter 1991, Vol. 3, No. 4, Pages 617-622
(doi: 10.1162/neco.1991.3.4.617)
© 1991 Massachusetts Institute of Technology
Kolmogorov's Theorem Is Relevant
Article PDF (292.25 KB)
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.