Probabilistic Bounds for Approximation by Neural Networks

Authors: Věra Kůrková
Publication year: 2019
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation. Proceedings, Part I
Projects: FoNeCo: Analytical Foundations of Neurocomputing
Bibliographic citation: KŮRKOVÁ, Věra. Probabilistic Bounds for Approximation by Neural Networks. In: TETKO, I. V., KŮRKOVÁ, V., KARPOV, P., THEIS, F., eds. Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation. Proceedings, Part I. Cham: Springer, 2019, S. 418-428. Lecture Notes in Computer Science, 11727. ISBN 978-3-030-30486-7. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-030-30487-4_33
DOI: 10.1007/978-3-030-30487-4_33
ID: 507969

Abstract

A probabilistic model describing relevance of tasks to be computed by a class of feedforward networks is studied. Bounds on correlations of network input-output functions with almost all randomly-chosen functions are derived. Impact of sizes of function domains on correlations are analyzed from the point of view of the concentration of measure phenomenon. It is shown that on large domains, errors of approximation of randomly chosen functions by fixed input-output functions are almost deterministic.