GKAN: Graph Kolmogorov-Arnold Networks
Authors: Mehrdad Kiamari, Mohammad Kiamari, Bhaskar Krishnamachari
Summary: We introduce Graph Kolmogorov-Arnold Networks (GKAN), an modern neural community structure that extends the ideas of the lately proposed Kolmogorov-Arnold Networks (KAN) to graph-structured knowledge. By adopting the distinctive traits of KANs, notably the usage of learnable univariate capabilities as a substitute of mounted linear weights, we develop a strong mannequin for graph-based studying duties. In contrast to conventional Graph Convolutional Networks (GCNs) that depend on a set convolutional structure, GKANs implement learnable spline-based capabilities between layers, reworking the way in which data is processed throughout the graph construction. We current two alternative ways to include KAN layers into GKAN: structure 1 — the place the learnable capabilities are utilized to enter options after aggregation and structure 2 — the place the learnable capabilities are utilized to enter options earlier than aggregation. We consider GKAN empirically utilizing a semi-supervised graph studying activity on a real-world dataset (Cora). We discover that structure typically performs higher. We discover that GKANs obtain increased accuracy in semi-supervised studying duties on graphs in comparison with the standard GCN mannequin. For instance, when contemplating 100 options, GCN offers an accuracy of 53.5 whereas a GKAN with a comparable variety of parameters provides an accuracy of 61.76; with 200 options, GCN offers an accuracy of 61.24 whereas a GKAN with a comparable variety of parameters provides an accuracy of 67.66. We additionally current outcomes on the affect of varied parameters such because the variety of hidden nodes, grid-size, and the polynomial-degree of the spline on the efficiency of GKAN.