Approximation of RKHS Functionals by Neural Networks

arXiv:2403.12187v1 Announce Type: cross
Abstract: Motivated by the abundance of functional data such as time series and images, there has been a growing interest in integrating such data into neural networks and learning maps from function spaces to R (i.e., functionals). In this paper, we study the approximation of functionals on reproducing kernel Hilbert spaces (RKHS's) using neural networks. We establish the universality of the approximation of functionals on the RKHS's. Specifically, we derive explicit error bounds for those induced …

abstract approximation arxiv cs.lg data function functional images kernel maps math.st networks neural networks paper series spaces stat.ml stat.th study time series type