Homogeneous Artificial Neural Network

TL;DR

This paper introduces a new class of artificial neural networks designed to approximate generalized homogeneous functions, providing a theoretical foundation and methods for upgrading existing ANNs to this homogeneous form, supported by practical examples.

Contribution

It presents the first homogeneous universal approximation theorem and procedures for transforming existing ANNs into homogeneous ones, expanding the theoretical understanding of neural network capabilities.

Findings

Proven homogeneous universal approximation theorem

Development of procedures to upgrade existing ANNs

Validated with examples from multiple domains

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).