# Homogeneous Artificial Neural Network

arXiv: https://arxiv.org/abs/2311.17973 · HTML: https://mlsanity.com/paper/2311.17973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 23 references that are in the map.
- First posted on arXiv 29 Nov 2023.

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

- [Neural Thermodynamics: Entropic Forces in Deep and Universal Representation Learning](https://mlsanity.com/paper/2505.12387/) (2025)

## Abstract (arXiv)

The paper proposes an artificial neural network (ANN) being a global approximator for a special class of functions, which are known as generalized homogeneous. The homogeneity means a symmetry of a function with respect to a group of transformations having topological characterization of a dilation. In this paper, a class of the so-called linear dilations is considered. A homogeneous universal approximation theorem is proven. Procedures for an upgrade of an existing ANN to a homogeneous one are developed. Theoretical results are supported by examples from the various domains (computer science, systems theory and automatic control).