Exploring Kolmogorov-Arnold Networks for Graph Learning

Kolmogorov-Arnold Networks (KANs) have recently gained significant attention in the machine learning community as a promising alternative to Multi-Layer Perceptrons (MLPs). These models are theoretically founded on the Kolmogorov-Arnold representation theorem, and promise greater interpretability, generalization, and accuracy compared to MLPs. Recently, they have been studied across different domains, such as images and text processing, time-series analysis, physics-informed problems, etc. The aim of this work is to explore the applicability of KAN models in the graph domain. Specifically, we study an extension of Graph Neural Networks (GNNs), denoted as Graph Kolmogorov-Arnold Networks (GKANs), which relies on the message-passing framework, but replaces the MLP-based update function with a KAN-based architecture. Our study focuses on two key aspects: the predictive accuracy of GKANs and their interpretability, particularly in the context of spatial-temporal graphs. We first compare GKANs performance with that of state-of-the-art GNN approaches in graph classification tasks, involving static graph datasets. Additionally, we introduce the GKAN Ordinary Differential Equation (GKAN-ODE) framework, in which we leverage the interpretable nature of GKANs to model the evolution of graphs over time and to extract symbolic formulas representing these dynamics. Our experiments highlight the promising capabilities of GKANs, especially in terms of interpretability, while also discussing the limitations and future potential of this approach.