Approximation of functionals on Korobov spaces with Fourier Functional Networks

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

View graph of relations

Author(s)

Detail(s)

Original languageEnglish
Article number106922
Journal / PublicationNeural Networks
Volume182
Online published20 Nov 2024
Publication statusPublished - Feb 2025

Link(s)

Abstract

Learning from functional data with deep neural networks has become increasingly useful, and numerous neural network architectures have been developed to tackle high-dimensional problems raised in practical domains. Despite the impressive practical achievements, theoretical foundations underpinning the ability of neural networks to learn from functional data largely remain unexplored. In this paper, we investigate the approximation capacity of a functional neural network, called Fourier Functional Network, consisting of Fourier neural operators and deep convolutional neural networks with a great reduction in parameters. We establish rates of approximating by Fourier Functional Networks nonlinear continuous functionals defined on Korobov spaces of periodic functions. Finally, our results demonstrate dimension-independent convergence rates, which overcomes the curse of dimension. © 2024 The Authors.

Research Area(s)

  • Approximation theory, Convolutional neural network, Fourier neural operator, Korobov space, Neural network

Download Statistics

No data available