Representations of Highly-Varying Functions by One-Hidden-Layer Networks

Authors: Věra Kůrková
Publication year: 2014
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Artificial Intelligence and Soft Computing Part I
Projects: Modeling of complex systems for softcomputing methods
Bibliographic citation: KŮRKOVÁ, Věra. Representations of Highly-Varying Functions by One-Hidden-Layer Networks. In: RUTKOWSKI, L., KORYTKOWSKI, M., SCHERER, R., TADEUSIEWICZ, R., ZADEH, L.A., ZURADA, J.M., eds. Artificial Intelligence and Soft Computing Part I. Cham: Springer, 2014, S. 67-76. Lecture Notes in Artificial Intelligence, 8467. ISBN 978-3-319-07172-5. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-319-07173-2_7
DOI: 10.1007/978-3-319-07173-2_7
ID: 427584

Abstract

Limitations of capabilities of one-hidden-layer networks are investigated. It is shown that for networks with Heaviside perceptrons as well as for networks with kernel units used in SVM, there exist large sets of d-variable functions which cannot be tractably represented by these networks, i.e., their representations require numbers of units or sizes of weighs depending on d exponentially. Our results are derived using the concept of variational norm from nonlinear approximation theory and the concentration of measure property of high dimensional Euclidean spaces.