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

arXiv: https://arxiv.org/abs/2409.18132 · HTML: https://mlsanity.com/paper/2409.18132/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 9 Aug 2024.

## Builds on (most cited first, 11 of 11)

- [Breaking the Curse of Dimensionality with Convex Neural Networks](https://mlsanity.com/paper/1412.8690/) (2014)
- [Representation formulas and pointwise properties for Barron functions](https://mlsanity.com/paper/2006.05982/) (2020)
- [Understanding neural networks with reproducing kernel Banach spaces](https://mlsanity.com/paper/2109.09710/) (2021)
- [Characterization of the Variation Spaces Corresponding to Shallow Neural Networks](https://mlsanity.com/paper/2106.15002/) (2021)
- [On Reproducing Kernel Banach Spaces: Generic Definitions and Unified Framework of Constructions](https://mlsanity.com/paper/1901.01002/) (2019)
- [Sparsity of solutions for variational inverse problems with finite-dimensional data](https://mlsanity.com/paper/1809.05045/) (2018)
- [On Representer Theorems and Convex Regularization](https://mlsanity.com/paper/1806.09810/) (2018)
- [A unifying representer theorem for inverse problems and machine learning](https://mlsanity.com/paper/1903.00687/) (2019)
- [Duality for Neural Networks through Reproducing Kernel Banach Spaces](https://mlsanity.com/paper/2211.05020/) (2022)
- [Convex Optimization in Sums of Banach Spaces](https://mlsanity.com/paper/2104.13127/) (2021)
- [Reproducing Kernel Hilbert Spaces Cannot Contain all Continuous Functions on a Compact Metric Space](https://mlsanity.com/paper/2002.03171/) (2020)

## Abstract (arXiv)

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.