Homogeneous Artificial Neural Network

• URL: http://arxiv.org/abs/2311.17973v1
• Date: Wed, 29 Nov 2023 16:16:32 GMT
• Title: Homogeneous Artificial Neural Network
• Authors: Andrey Polyakov
• Abstract summary: The paper proposes an artificial neural network (ANN) being a global approximator for a special class of functions. The homogeneity means a symmetry of a function with respect to a group of transformations having topological characterization of a dilation.
• Score: 0.6526824510982799
• License: http://creativecommons.org/licenses/by/4.0/
• 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).

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