On the Kolmogorov neural networks

TL;DR

This paper demonstrates that Kolmogorov two-hidden-layer neural networks can exactly represent a wide class of multivariate functions, including continuous, discontinuous, bounded, and unbounded functions, depending on the activation functions used.

Contribution

It establishes the expressive power of Kolmogorov neural networks with various activation functions in representing diverse multivariate functions.

Findings

Networks can represent continuous functions precisely.

Networks can represent discontinuous bounded functions.

Networks can represent all unbounded functions.

Abstract

In this paper, we show that the Kolmogorov two hidden layer neural network model with a continuous, discontinuous bounded or unbounded activation function in the second hidden layer can precisely represent continuous, discontinuous bounded and all unbounded multivariate functions, respectively.