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).

翻译：本文提出一种人工神经网络（ANN），该网络作为一类被称为广义齐次函数的全局逼近器。齐次性是指函数在具有膨胀拓扑表征的变换群作用下具备对称性。本文考虑一类所谓的线性膨胀变换，并证明了齐次通用逼近定理。此外，还开发了将现有ANN升级为齐次网络的方法。来自不同领域（计算机科学、系统理论与自动控制）的实例验证了理论成果。