# On the universal approximation property of radial basis function neural networks

arXiv: https://arxiv.org/abs/2304.02220 · HTML: https://mlsanity.com/paper/2304.02220/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 25 references that are in the map.
- First posted on arXiv 5 Apr 2023.

## Built on by (most cited first, 3 of 3)

- [Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning](https://mlsanity.com/paper/2601.07760/) (2026)
- [Approximating Signed Distance Fields With Sparse Ellipsoidal Radial Basis Function Networks: A Dynamic Multi-Objective Optimization Strategy](https://mlsanity.com/paper/2505.02350/) (2025)
- [Deep Neural Network-Driven Adaptive Filtering](https://mlsanity.com/paper/2508.04258/) (2025)

## Abstract (arXiv)

In this paper we consider a new class of RBF (Radial Basis Function) neural networks, in which smoothing factors are replaced with shifts. We prove under certain conditions on the activation function that these networks are capable of approximating any continuous multivariate function on any compact subset of the d-dimensional Euclidean space. For RBF networks with finitely many fixed centroids we describe conditions guaranteeing approximation with arbitrary precision.