Probabilistic Bounds for Approximation by Neural Networks

0507969 - ÚI 2020 RIV CH eng C - Conference Paper (international conference)
Kůrková, Věra
Probabilistic Bounds for Approximation by Neural Networks.
Artificial Neural Networks and Machine Learning – ICANN 2019: Theoretical Neural Computation. Proceedings, Part I. Cham: Springer, 2019 - (Tetko, I.; Kůrková, V.; Karpov, P.; Theis, F.), s. 418-428. Lecture Notes in Computer Science, 11727. ISBN 978-3-030-30486-7. ISSN 0302-9743.
[ICANN 2019. International Conference on Artificial Neural Networks /28./. Munich (DE), 17.09.2019-19.09.2019]
R&D Projects: GA ČR(CZ) GA19-05704S
Institutional support: RVO:67985807
Keywords : Approximation of random functions * Feedforward networks * Dictionaries of computational units * High-dimensional geometry * Concentration of measure * Azuma-Hoeffding inequalities
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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.
Permanent Link: http://hdl.handle.net/11104/0298932