# Approximation by superpositions of a sigmoidal function

@article{Cybenko1989ApproximationBS,
title={Approximation by superpositions of a sigmoidal function},
author={George V. Cybenko},
journal={Mathematics of Control, Signals and Systems},
year={1989},
volume={2},
pages={303-314}
}
• G. Cybenko
• Published 1989
• Mathematics, Computer Science
• Mathematics of Control, Signals and Systems
In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well… Expand
5,423 Citations

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