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.
|Original language||English (US)|
|Journal||Statistical Analysis and Data Mining: The ASA Data Science Journal|
|State||Published - Mar 23 2021|
Bibliographical noteKAUST Repository Item: Exported on 2021-03-25
Acknowledgements: This work was supported by the Nazarbayev University faculty-development competitive research grants program, Grant Number 240919FD3921, and by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan, IRN AP05133700.