Sparsity of Shallow Networks Representing Finite Mappings

Authors: Věra Kůrková
Publication year: 2017
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: EANN 2017
Projects: Model complexity of neural, radial, and kernel networks
Bibliographic citation: KŮRKOVÁ, Věra. Sparsity of Shallow Networks Representing Finite Mappings. In: BORACCHI, G., ILIADIS, L., JAYNE, C., LIKAS, A., eds. EANN 2017. Cham: Springer, 2017, S. 337-348. Communications in Computer and Information Science, 744. ISBN 978-3-319-65171-2. ISSN 1865-0929
Dostupné z: doi:10.1007/978-3-319-65172-9_29
DOI: 10.1007/978-3-319-65172-9_29
ID: 476509

Abstract

Limitations of capabilities of shallow networks to represent sparsely real-valued functions on finite domains is investigated. Influence of sizes of function domains and of sizes dictionaries of computational units on sparsity of networks computing finite mappings is explored. It is shown that when dictionary is not sufficiently large with respect to the size of the finite domain, then almost any uniformly randomly chosen function on the domain either cannot be sparsely represented or its computation is unstable.