Approximation error of Fourier neural networks

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)258-270
Number of pages13
JournalStatistical Analysis and Data Mining
Issue number3
Publication statusAccepted/In press - 2021


  • approximation error
  • convergence
  • Fourier
  • neural networks

ASJC Scopus subject areas

  • Analysis
  • Information Systems
  • Computer Science Applications

Fingerprint Dive into the research topics of 'Approximation error of Fourier neural networks'. Together they form a unique fingerprint.

Cite this