Convergence Rate of Fourier Neural Networks
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Date
2019-04-26
Authors
Zhumekenov, Abylay
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
Abstract
The paper investigates a convergence rate for 2-layer feedforward Fourier Neural Network
(FNN). Such networks are motivated by the approximation properties of wellknown
Fourier series. Several implementations of FNNs were proposed since 1990’s:
by Gallant and White; A. Silvescu; Tan, Zuo and Cai; Liu. The main focus of this
research is Silvescu’s FNN, because such 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 1989. 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.
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Keywords
Research Subject Categories::MATHEMATICS::Applied mathematics