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HyperKAN: Hypergraph Representation Learning with Kolmogorov-Arnold Networks

Xiangfei Fang, Boying Wang, Chengying Huan, Shaonan Ma, Heng Zhang, Chen Zhao

TL;DR

HyperKAN tackles imbalanced information aggregation in hypergraph representation learning by combining structural and similarity features. It computes $A = HH^{\top}$ to obtain $k$-hop structural features and uses cosine similarity to derive $S$, which are then refined by a Feature Adjustment module before passing through Kolmogorov-Arnold Networks (KANs) to produce balanced vertex representations. Empirical results on four real-world datasets show HyperKAN outperforms state-of-the-art HNNs, notably achieving about a 9% gain on the Senate dataset, with ablation studies confirming the necessity of FE, FA, and KAN components. The approach offers strong accuracy with competitive runtime, highlighting its practical impact for high-order relationship modeling in hypergraphs.

Abstract

Hypergraph representation learning has garnered increasing attention across various domains due to its capability to model high-order relationships. Traditional methods often rely on hypergraph neural networks (HNNs) employing message passing mechanisms to aggregate vertex and hyperedge features. However, these methods are constrained by their dependence on hypergraph topology, leading to the challenge of imbalanced information aggregation, where high-degree vertices tend to aggregate redundant features, while low-degree vertices often struggle to capture sufficient structural features. To overcome the above challenges, we introduce HyperKAN, a novel framework for hypergraph representation learning that transcends the limitations of message-passing techniques. HyperKAN begins by encoding features for each vertex and then leverages Kolmogorov-Arnold Networks (KANs) to capture complex nonlinear relationships. By adjusting structural features based on similarity, our approach generates refined vertex representations that effectively addresses the challenge of imbalanced information aggregation. Experiments conducted on the real-world datasets demonstrate that HyperKAN significantly outperforms state of-the-art HNN methods, achieving nearly a 9% performance improvement on the Senate dataset.

HyperKAN: Hypergraph Representation Learning with Kolmogorov-Arnold Networks

TL;DR

HyperKAN tackles imbalanced information aggregation in hypergraph representation learning by combining structural and similarity features. It computes to obtain -hop structural features and uses cosine similarity to derive , which are then refined by a Feature Adjustment module before passing through Kolmogorov-Arnold Networks (KANs) to produce balanced vertex representations. Empirical results on four real-world datasets show HyperKAN outperforms state-of-the-art HNNs, notably achieving about a 9% gain on the Senate dataset, with ablation studies confirming the necessity of FE, FA, and KAN components. The approach offers strong accuracy with competitive runtime, highlighting its practical impact for high-order relationship modeling in hypergraphs.

Abstract

Hypergraph representation learning has garnered increasing attention across various domains due to its capability to model high-order relationships. Traditional methods often rely on hypergraph neural networks (HNNs) employing message passing mechanisms to aggregate vertex and hyperedge features. However, these methods are constrained by their dependence on hypergraph topology, leading to the challenge of imbalanced information aggregation, where high-degree vertices tend to aggregate redundant features, while low-degree vertices often struggle to capture sufficient structural features. To overcome the above challenges, we introduce HyperKAN, a novel framework for hypergraph representation learning that transcends the limitations of message-passing techniques. HyperKAN begins by encoding features for each vertex and then leverages Kolmogorov-Arnold Networks (KANs) to capture complex nonlinear relationships. By adjusting structural features based on similarity, our approach generates refined vertex representations that effectively addresses the challenge of imbalanced information aggregation. Experiments conducted on the real-world datasets demonstrate that HyperKAN significantly outperforms state of-the-art HNN methods, achieving nearly a 9% performance improvement on the Senate dataset.

Paper Structure

This paper contains 11 sections, 7 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Proposed HyperKAN Architecture
  4. Hypergraph Feature Extraction Module
  5. Feature Adjustment Module
  6. KAN Layers
  7. Loss Function
  8. Evaluation
  9. Experimental settings
  10. Experiment Results
  11. Conclusion

Figures (2)

  • Figure 1: Architecture of the HyperKAN model where $N$ is the number of vertices, $k$ is the hop number, and $d$ is the dimension of the vertex feature vector. The model comprises three key components: a) the Feature Extraction module, which extracts structural features from the hypergraph structure and similarity features from the raw vertex features; b) the Feature Adjustment module for structural feature adjustment utilizing the similarity features; and c) the KAN layers for further encoding and feature extraction.
  • Figure 2: Comparison of runtime.