# HyperKAN: Hypergraph Representation Learning with Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2503.12365 · HTML: https://mlsanity.com/paper/2503.12365/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 16 Mar 2025.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Vision GNN: An Image is Worth Graph of Nodes](https://mlsanity.com/paper/2206.00272/) (2022)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs](https://mlsanity.com/paper/2010.04558/) (2020)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [Generative hypergraph clustering: from blockmodels to modularity](https://mlsanity.com/paper/2101.09611/) (2021)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [Kolmogorov-Arnold Graph Neural Networks](https://mlsanity.com/paper/2406.18354/) (2024)
- [Semi-supervised Hypergraph Node Classification on Hypergraph Line Expansion](https://mlsanity.com/paper/2005.04843/) (2020)
- [HypeBoy: Generative Self-Supervised Representation Learning on Hypergraphs](https://mlsanity.com/paper/2404.00638/) (2024)
- [A nonlinear diffusion method for semi-supervised learning on hypergraphs](https://mlsanity.com/paper/2103.14867/) (2021)
- [Classification in biological networks with hypergraphlet kernels](https://mlsanity.com/paper/1703.04823/) (2017)
- [Hypergraph Transformer for Semi-Supervised Classification](https://mlsanity.com/paper/2312.11385/) (2023)

## Abstract (arXiv)

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.