On Hypergraph Neural Networks and Their Stability Towards Higher-Order Knowledge Representation and Learning

Hypergraph neural networks (HGNNs) have emerged as a powerful extension of traditional graph neural networks, enabling the capture of higher-order relationships beyond pairwise connections. This paper explores the potential of HGNNs for advanced knowledge representation and learning. We introduce stability criteria for hyperedge selection, utilize hypergraph Laplacians, and construct higher-order knowledge graphs (HOKGs) for improved vertex classification. Through experiments on datasets such as Citeseer, Pubmed, and Cora, we demonstrate that integrating stability criteria significantly enhances the robustness and accuracy of HGNN models. Our results highlight the importance of stable hyperedges in maintaining consistent performance across diverse datasets.