An Algorithm for Approximating Continuous Functions on Compact Subsets with a Neural Network with one Hidden Layer
Machine Learning
2019-02-12 v1 Functional Analysis
Machine Learning
Abstract
George Cybenko's landmark 1989 paper showed that there exists a feedforward neural network, with exactly one hidden layer (and a finite number of neurons), that can arbitrarily approximate a given continuous function on the unit hypercube. The paper did not address how to find the weight/parameters of such a network, or if finding them would be computationally feasible. This paper outlines an algorithm for a neural network with exactly one hidden layer to reconstruct any continuous scalar or vector valued continuous function.
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Cite
@article{arxiv.1902.03638,
title = {An Algorithm for Approximating Continuous Functions on Compact Subsets with a Neural Network with one Hidden Layer},
author = {Elliott Zaresky-Williams},
journal= {arXiv preprint arXiv:1902.03638},
year = {2019}
}
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6 pages