A1214
Title: KLAN: Kolmogorov-Lorentz-Arnold neural networks
Authors: Miguel de Carvalho - University of Edinburgh and Universidade de Aveiro (Portugal)
Clemente Ferrer - USM (Chile)
Fengxiang He - University of Edinburgh (United Kingdom)
Johnny Lee - University of Edinburgh (United Kingdom)
William Wu - The University of Edinburgh (United Kingdom)
Andrej Svetlosak - The University of Edinburgh (United Kingdom) [presenting]
Abstract: Kolmogorov-Arnold neural networks (KANs) have been investigated as an alternative to multilayer perceptron networks. Based on the Kolmogorov-Arnold (KA) representation theorem, weights are replaced with non-linear learnable activation functions. This gives KANs flexibility and interpretability. A novel network architecture based on Lorentz's version of the KA theorem is proposed, which is called Kolmogorov-Laurenz-Arnold networks (KLAN). Under certain conditions, the outer function of the KAN architecture can be replaced with a single function. The result is an equally powerful, but sparser network, requiring fewer parameters and less computational effort. The properties of the proposed methods are demonstrated in a series of real and simulated experiments, and their performance is compared to state-of-the-art versions of KAN. It is concluded by discussing the advantages and shortcomings of the proposed approach.
