Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces

TL;DR

This paper explores the decomposition of one-layer neural networks through the lens of reproducing kernel Banach spaces, providing a mathematical framework for understanding their structure and sum representations.

Contribution

It introduces a novel decomposition method of integral RKBSs into sums of p-norm RKBSs, enhancing the structural understanding of these spaces.

Findings

Decomposition of integral RKBS into p-norm RKBSs.

Compatibility of sum of RKBSs with direct sum of feature spaces.

Applications for structural analysis of RKBS classes.

Abstract

In this paper, we define the sum of RKBSs using the characterization theorem of RKBSs and show that the sum of RKBSs is compatible with the direct sum of feature spaces. Moreover, we decompose the integral RKBS into the sum of $p$-norm RKBSs. Finally, we provide applications for the structural understanding of the integral RKBS class.