**arXiv ID:** 2311.17973 **Authors:** Andrey Polyakov **Published:** 2023-11-29T16:16:32Z **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 univer...
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# Homogeneous Artificial Neural Network
**arXiv ID:** 2311.17973
**Authors:** Andrey Polyakov
**Published:** 2023-11-29T16:16:32Z
**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).
## Skill Description
This skill is generated from the arXiv paper: Homogeneous Artificial Neural Network (2311.17973).
## How to Use
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## References
- [arXiv:2311.17973](http://arxiv.org/abs/2311.17973v1)
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