Bochner integrals and neural networks
Functional Analysis
2023-02-28 v1 Machine Learning
Neural and Evolutionary Computing
Abstract
A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are established, variation-spaces and tensor products are studied, and examples are presented. The paper develops a functional analytic theory of neural networks and shows that variation spaces are Banach spaces.
Cite
@article{arxiv.2302.13228,
title = {Bochner integrals and neural networks},
author = {Paul C. Kainen and A. Vogt},
journal= {arXiv preprint arXiv:2302.13228},
year = {2023}
}
Comments
25 pages