Kolmogorov-Arnold Graph Neural Networks

TL;DR

<3-5 sentence high-level summary> The paper tackles the interpretability gap in graph neural networks by introducing Graph Kolmogorov-Arnold Network (GKAN), which leverages spline-based (or RBF) activations within a Kolmogorov-Arnold framework to enable transparent, data-adaptive message passing on graphs. It presents KANG and KAND as core components, with KANGConvolution enabling data-driven nonlinearities in graph updates and a data-aligned initialisation strategy for spline control points. Across node classification, link prediction, and graph classification on five datasets, KANG demonstrates competitive or superior performance to established GNNs while providing intrinsic interpretability through learnable activations and their evolution during training. The work also analyzes oversmoothing robustness and scalability, acknowledging memory trade-offs for high-complexity activations and outlining future improvements for scalable, self-explanatory KAN-based graph models.

Abstract

Graph neural networks (GNNs) excel in learning from network-like data but often lack interpretability, making their application challenging in domains requiring transparent decision-making. We propose the Graph Kolmogorov-Arnold Network (GKAN), a novel GNN model leveraging spline-based activation functions on edges to enhance both accuracy and interpretability. Our experiments on five benchmark datasets demonstrate that GKAN outperforms state-of-the-art GNN models in node classification, link prediction, and graph classification tasks. In addition to the improved accuracy, GKAN's design inherently provides clear insights into the model's decision-making process, eliminating the need for post-hoc explainability techniques. This paper discusses the methodology, performance, and interpretability of GKAN, highlighting its potential for applications in domains where interpretability is crucial.

Figures (12)

• Figure 1: Illustration of the KANG architecture. The input graph is processed through multiple KANG convolutional layers, where spline-based transformations dynamically aggregate and update node embeddings. A KAND layer refines the final node embeddings for specific downstream tasks.
• Figure 2: Comparison of feature distributions after the first KANG layer for a selected feature dimension. Left: although the distribution visually appears Gaussian-like, the evenly spaced spline control points (red dots) do not accurately reflect the underlying density of the feature values. This rigid placement may limit the spline's flexibility in adapting to the regions of highest feature density. Right: applying LN produces a standardized and more compact Gaussian-like distribution. The spline control points sampled according to a Gaussian distribution, align closely with the density of feature values, thus improving representational flexibility and expressiveness of the spline activations within KANG layers.
• Figure 3: Sensitivity analysis on the Cora dataset for node classification. Left: Test accuracy decreases with more control points. Right: Epoch time increases with additional control points. Means and standard deviations computed over 10 runs per setting.
• Figure 4: Left: Dirichlet Energy. Right: Test accuracy. Results obtained averaging over 10 runs with different random seed at each run. Additional results on the CiteSeer and PubMed datasets in Appendix \ref{['A:over']}
• Figure 5: Computational scaling analysis across different subgraph ratios of the Cora dataset. Results obtained by averaging the results on 5 runs, with different random seeds.