Homogeneous Artificial Neural Network
This work addresses a specific mathematical problem in function approximation for researchers in neural networks and control theory, but it appears incremental as it builds on existing ANN frameworks.
The paper tackles the problem of approximating generalized homogeneous functions using artificial neural networks, proving a homogeneous universal approximation theorem and developing procedures to upgrade existing ANNs to homogeneous ones, with theoretical results supported by examples from domains like computer science and control.
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).