Hypergraph Neural Networks: Theoretical Foundations and Applications.

Hypergraphs, as advanced mathematical constructs, are adept at modeling complex, multi-faceted relationships across diverse disciplines, including data mining, computer vision, and life sciences. Hypergraph Neural Networks (HGNNs) represent a significant advancement over traditional graph neural networks by efficiently capturing high-order dependencies, which are prevalent in intricate systems such as biological networks, visual data structures, and large-scale relational datasets. This capability enables more precise modeling of interactions involving multiple entities, such as gene-term associations in life sciences, multi-modal data fusion in computer vision, and collaborative patterns in data mining. This article provides a systematic introduction to HGNNs, presenting the latest advancements in their theoretical foundations, architectural designs, and interpretability analysis. We elaborate on how HGNNs address the limitations of traditional graph-based models by leveraging hyperedge-based aggregation mechanisms to encode higher-order semantics. Beyond theoretical frameworks, we highlight their versatile applications across interdisciplinary fields, including drug discovery, protein interaction prediction, visual recognition, and knowledge graph completion. Particular emphasis is placed on identifying critical theoretical challenges, discussing innovative solutions to improve model efficiency and interpretability, and offering practical guidelines for deploying HGNNs in real-world research scenarios. By bridging theoretical rigor with empirical insights, this article aims to serve as a foundational resource for both researchers and practitioners seeking to engage with HGNNs in diverse domains.