Homogeneous Artificial Neural Network
Machine Learning
2023-12-01 v1 Artificial Intelligence
Numerical Analysis
Neural and Evolutionary Computing
Systems and Control
Systems and Control
Numerical Analysis
Optimization and Control
Abstract
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).
Cite
@article{arxiv.2311.17973,
title = {Homogeneous Artificial Neural Network},
author = {Andrey Polyakov},
journal= {arXiv preprint arXiv:2311.17973},
year = {2023}
}