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 are a form of structured human knowledge that integrate heterogeneous data sources into structured representations but 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, which directly connect multiple entities together. Yet hypergraph representation learning often overlooks entity roles in hyperedges, limiting the finegrained semantic modelling. To address these issues, knowledge hypergraphs and hyper-relational knowledge graphs combine the advantages of knowledge graphs and hypergraphs to better capture the complex structures and role-specific semantics of real world knowledge. This survey provides a comprehensive review of methods handling n-ary relational data, covering both knowledge hypergraphs and hyper-relational knowledge graphs literatures. We propose a two-dimensional taxonomy: the first dimension categorises models based on their methodology, i.e., translation-based models, tensor factorisation-based models, deep neural network-based models, logic rules-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 aware-less, position-aware, and role-aware approaches. Finally, we discuss existing datasets, training settings and strategies, and outline open challenges to inspire future research.