KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning
Roman Bresson, Giannis Nikolentzos, George Panagopoulos, Michail Chatzianastasis, Jun Pang, Michalis Vazirgiannis
TL;DR
The paper tackles the expressiveness and efficiency trade-offs of replacing MLPs with Kolmogorov-Arnold Networks (KANs) in graph neural networks. By implementing three KAN-based layers (KAGIN, KAGCN, KAGAT) and using BS-splines and Radial Basis Functions, it provides a comprehensive, task-spanning evaluation (node classification, link prediction, graph classification, graph regression). The empirical results show KAN-based layers are on par with or surpass MLP-based counterparts in several tasks, with regression tasks particularly benefitting from KANs, especially BS-splines, albeit with higher computational cost for some variants. Overall, the work demonstrates the viability of KANs as a flexible, potentially more interpretable alternative to traditional MLP-based GNNs, and highlights trade-offs between performance, model size, and training efficiency.
Abstract
In recent years, Graph Neural Networks (GNNs) have become the de facto tool for learning node and graph representations. Most GNNs typically consist of a sequence of neighborhood aggregation (a.k.a., message-passing) layers, within which the representation of each node is updated based on those of its neighbors. The most expressive message-passing GNNs can be obtained through the use of the sum aggregator and of MLPs for feature transformation, thanks to their universal approximation capabilities. However, the limitations of MLPs recently motivated the introduction of another family of universal approximators, called Kolmogorov-Arnold Networks (KANs) which rely on a different representation theorem. In this work, we compare the performance of KANs against that of MLPs on graph learning tasks. We implement three new KAN-based GNN layers, inspired respectively by the GCN, GAT and GIN layers. We evaluate two different implementations of KANs using two distinct base families of functions, namely B-splines and radial basis functions. We perform extensive experiments on node classification, link prediction, graph classification and graph regression datasets. Our results indicate that KANs are on-par with or better than MLPs on all tasks studied in this paper. We also show that the size and training speed of RBF-based KANs is only marginally higher than for MLPs, making them viable alternatives. Code available at https://github.com/RomanBresson/KAGNN.