Kolmogorov's theorem is relevant

Authors:
Vra Krkov
Affiliations:
Institute of Computer Science, Czechoslovak Academy of Sciences, P. O. Box 5, 182 07 Prague 8, Czechoslovakia
Venue:
Neural Computation
Year:
1991

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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.