APPROXIMATION ERROR OF FOURIER NEURAL NETWORKS
| dc.contributor.author | Zhumekenov, Abylay | |
| dc.contributor.author | Takhanov, Rustem | |
| dc.contributor.author | Castro, Alejandro J. | |
| dc.contributor.author | Assylbekov, Zhenisbek | |
| dc.date.accessioned | 2021-08-27T03:20:09Z | |
| dc.date.available | 2021-08-27T03:20:09Z | |
| dc.date.issued | 2021-03-23 | |
| dc.description.abstract | The 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.citation | Zhumekenov, 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.11506 | en_US |
| dc.identifier.issn | 1932-1864 | |
| dc.identifier.uri | https://doi.org/10.1002/sam.11506 | |
| dc.identifier.uri | https://onlinelibrary.wiley.com/doi/10.1002/sam.11506 | |
| dc.identifier.uri | http://nur.nu.edu.kz/handle/123456789/5713 | |
| dc.language.iso | en | en_US |
| dc.publisher | John Wiley and Sons Inc | en_US |
| dc.relation.ispartofseries | Statistical Analysis and Data Mining;Volume 14, Issue 3, June 2021, Pages 258-270 | |
| dc.rights | Attribution-NonCommercial-ShareAlike 3.0 United States | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/us/ | * |
| dc.subject | Type of access: Open Access | en_US |
| dc.subject | approximation error | en_US |
| dc.subject | convergence | en_US |
| dc.subject | Fourier | en_US |
| dc.subject | neural networks | en_US |
| dc.title | APPROXIMATION ERROR OF FOURIER NEURAL NETWORKS | en_US |
| dc.type | Article | en_US |
| workflow.import.source | science |