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 fine-grained 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, negative sampling strategies, and outline open challenges to inspire future research.