Limitations of One-Hidden-Layer Perceptron Networks

Authors: Věra Kůrková
Publication year: 2015
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Proceedings ITAT 2015: Information Technologies - Applications and Theory
Projects: Modeling of complex systems for softcomputing methods
Bibliographic citation: KŮRKOVÁ, Věra. Limitations of One-Hidden-Layer Perceptron Networks. In: YAGHOB, J., ed. Proceedings ITAT 2015: Information Technologies - Applications and Theory. Aachen & Charleston: Technical University & CreateSpace Independent Publishing Platform, 2015, S. 167-171. CEUR Workshop Proceedings, V-1422. ISBN 978-1-5151-2065-0. ISSN 1613-0073.
ID: 447921

Abstract

Limitations of one-hidden-layer perceptron networks to represent efficiently finite mappings is investigated. It is shown that almost any uniformly randomly chosen mapping on a sufficiently large finite domain cannot be tractably represented by a one-hidden-layer perceptron network. This existential probabilistic result is complemented by a concrete example of a class of functions constructed using quasi-random sequences. Analogies with central paradox of coding theory and no free lunch theorem are discussed.