Understanding neural networks with reproducing kernel Banach spaces
Abstract
Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper we discuss how the theory of reproducing kernel Banach spaces can be used to tackle this challenge. In particular, we prove a representer theorem for a wide class of reproducing kernel Banach spaces that admit a suitable integral representation and include one hidden layer neural networks of possibly infinite width. Further, we show that, for a suitable class of ReLU activation functions, the norm in the corresponding reproducing kernel Banach space can be characterized in terms of the inverse Radon transform of a bounded real measure, with norm given by the total variation norm of the measure. Our analysis simplifies and extends recent results in [34,29,30].
Keywords
Cite
@article{arxiv.2109.09710,
title = {Understanding neural networks with reproducing kernel Banach spaces},
author = {Francesca Bartolucci and Ernesto De Vito and Lorenzo Rosasco and Stefano Vigogna},
journal= {arXiv preprint arXiv:2109.09710},
year = {2021}
}