Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods

Real-world knowledge can take various forms, including structured, semi-structured, and unstructured data. Among these, Knowledge Graphs (KGs) are structured representations that integrate heterogeneous data sources into structured representations. However, KGs typically reduce complex n-ary relations to simple triples, thereby losing higher-order relational details. In contrast, hypergraphs naturally represent n-ary relations with hyperedges that directly connect multiple entities. Recent advances have led to many hypergraph representation learning methods; however, they often overlook entity roles in hyperedges, limiting fine-grained semantic modelling. To address these issues, Knowledge Hypergraphs (KHGs) and Hyper-relational Knowledge Graphs (HKGs) combine the advantages of KGs and hypergraphs to better capture complex relational structures and role-specific semantics of real-world knowledge. This survey provides a structured review of representation learning methods for n-ary relational data, with a primary focus on static KHGs and HKGs. We propose a two-dimensional taxonomy: the first dimension categorises models based on their methodology, including translation-based models, tensor factorisation-based models, deep neural network-based models, logic rule-based models, and hyperedge expansion-based models. The second dimension classifies models according to their awareness of entity roles and positions in n-ary relations, dividing them into position-aware, role-aware, and aware-less approaches. Finally, we summarise benchmark datasets, training settings, negative sampling strategies, and benchmark-style performance comparisons, and outline open challenges to inspire future research.