KAA: Kolmogorov-Arnold Attention for Enhancing Attentive Graph Neural Networks

Taoran Fang, Tianhong Gao, Chunping Wang, YihaoShang, Wei Chow, Lei CHEN, Yang Yang

Keywords: Kolmogorov-Arnold Networks, Attentive Graph Neural Networks

TL;DR: We introduce Kolmogorov-Arnold Attention (KAA), which integrates KAN into the scoring functions of existing attentive GNN models.

Abstract: Graph neural networks (GNNs) with attention mechanisms, often referred to as attentive GNNs, have emerged as a prominent paradigm in advanced GNN models in recent years. However, our understanding of the critical process of scoring neighbor nodes remains limited, leading to the underperformance of many existing attentive GNNs. In this paper, we unify the scoring functions of current attentive GNNs and propose Kolmogorov-Arnold Attention (KAA), which integrates the Kolmogorov-Arnold Network (KAN) architecture into the scoring process. KAA enhances the performance of scoring functions across the board and can be applied to nearly all existing attentive GNNs. To compare the expressive power of KAA with other scoring functions, we introduce Maximum Ranking Distance (MRD) to quantitatively estimate their upper bounds in ranking errors for node importance. Our analysis reveals that, under limited parameters and constraints on width and depth, both linear transformation-based and MLP-based scoring functions exhibit finite expressive power. In contrast, our proposed KAA, even with a single-layer KAN parameterized by zero-order B-spline functions, demonstrates nearly infinite expressive power. Extensive experiments on both node-level and graph-level tasks using various backbone models show that KAA-enhanced scoring functions consistently outperform their original counterparts, achieving performance improvements of over 20% in some cases.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 4073