Homogeneous Artificial Neural Network
Andrey Polyakov
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).