# Bochner integrals and neural networks

arXiv: https://arxiv.org/abs/2302.13228 · HTML: https://mlsanity.com/paper/2302.13228/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 47 references that are in the map.
- First posted on arXiv 26 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces](https://mlsanity.com/paper/2312.08461/) (2023)

## Abstract (arXiv)

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.