Approximation error of Fourier neural networks
Zhumekenov A. Takhanov R. Castro A.J. Assylbekov Z.
June 2021John Wiley and Sons Inc
Statistical Analysis and Data Mining
2021#14Issue 3258 - 270 pp.
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 Silvescus 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 Silvescus 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.
approximation error , convergence , Fourier , neural networks
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Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Nur-Sultan, Kazakhstan
Computer
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
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