APPROXIMATION ERROR OF FOURIER NEURAL NETWORKS

dc.contributor.authorZhumekenov, Abylay
dc.contributor.authorTakhanov, Rustem
dc.contributor.authorCastro, Alejandro J.
dc.contributor.authorAssylbekov, Zhenisbek
dc.date.accessioned2021-08-27T03:20:09Z
dc.date.available2021-08-27T03:20:09Z
dc.date.issued2021-03-23
dc.description.abstractThe paper investigates approximation error of two-layer feedforward Fourier Neural Networks (FNNs). Such networks are motivated by the approximation properties of Fourier series. Several implementations of FNNs were proposed since 1980s: by Gallant and White, Silvescu, Tan, Zuo and Cai, and Liu. The main focus of our work is Silvescu's FNN, because its activation function does not fit into the category of networks, where the linearly transformed input is exposed to activation. The latter ones were extensively described by Hornik. In regard to non-trivial Silvescu's FNN, its convergence rate is proven to be of order O(1/n). The paper continues investigating classes of functions approximated by Silvescu FNN, which appeared to be from Schwartz space and space of positive definite functions.en_US
dc.identifier.citationZhumekenov, A., Takhanov, R., Castro, A. J., & Assylbekov, Z. (2021). Approximation error of Fourier neural networks. Statistical Analysis and Data Mining: The ASA Data Science Journal, 14(3), 258–270. https://doi.org/10.1002/sam.11506en_US
dc.identifier.issn1932-1864
dc.identifier.urihttps://doi.org/10.1002/sam.11506
dc.identifier.urihttps://onlinelibrary.wiley.com/doi/10.1002/sam.11506
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/5713
dc.language.isoenen_US
dc.publisherJohn Wiley and Sons Incen_US
dc.relation.ispartofseriesStatistical Analysis and Data Mining;Volume 14, Issue 3, June 2021, Pages 258-270
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectType of access: Open Accessen_US
dc.subjectapproximation erroren_US
dc.subjectconvergenceen_US
dc.subjectFourieren_US
dc.subjectneural networksen_US
dc.titleAPPROXIMATION ERROR OF FOURIER NEURAL NETWORKSen_US
dc.typeArticleen_US
workflow.import.sourcescience

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