Complexity of Shallow Networks Representing Finite Mappings

0443724 - ÚI 2016 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Kůrková, Věra
Complexity of Shallow Networks Representing Finite Mappings.
Artificial Intelligence and Soft Computing. Vol. 1. Cham: Springer, 2015 - (Rutkowski, L.; Korytkowski, M.; Scherer, R.; Tadeusiewicz, R.; Zadeh, L.; Zurada, J.), s. 39-48. Lecture Notes in Artificial Intelligence, 9119. ISBN 978-3-319-19323-6. ISSN 0302-9743.
[ICAISC 2015. International Conference on Artificial Intelligence and Soft Computing /14./. Zakopane (PL), 12.06.2015-16.06.2015]
Grant CEP: GA ČR GA15-18108S
Institucionální podpora: RVO:67985807
Klíčová slova: Shallow feedforward networks * Signum perceptrons * Finite mappings * Model complexity * Hadamard matrices
Kód oboru RIV: IN - Informatika

Complexity of shallow (one-hidden-layer) networks representing finite multivariate mappings is investigated. Lower bounds are derived on growth of numbers of network units and sizes of output weights in terms of variational norms of mappings to be represented. Probability distributions of mappings whose computations require large networks are described. It is shown that due to geometrical properties of highdimensional Euclidean spaces, representation of almost any randomly chosen function on a sufficiently large domain by a shallow network with perceptrons requires untractably large network. Concrete examples of such functions are constructed using Hadamard matrices.
Trvalý link: http://hdl.handle.net/11104/0246406