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

Seungcheol Shin, Myungjoo Kang

Keywords: Neural networks, Reproducing kernel Banach spaces, Class of Integral RKBSs

TL;DR: Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces

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 $\mathcal{F}\_{\sigma}(\mathcal{X},\Omega)$ into the sum of $p$-norm RKBSs $\\{\mathcal{L}\_{\sigma}^{1}(\mu\_{i})\\}\_{i\in I}$. Finally, we provide some applications to enhance the structural understanding of the integral RKBS class.

Primary Area: learning theory

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Submission Number: 4117