GAHE: Geometry-Aware Embedding for Hyper-Relational Knowledge Graph Representation
Zongsheng Cao, Qianqian Xu, Zhiyong Yang, Yuan He, Xiaochun Cao, Qingming Huang · ACM Transactions on Multimedia Computing Communications and Applications · 2025
Knowledge graphs have proven highly effective for learning representations of entities and relations, with hyper-relational knowledge graphs (HKGs) gaining increased attention due to their enhanced representation capabilities. Each fact in an HKG consists of a main triple supplemented by attribute-value qualifiers that provide additional contextual information. Due to the complexity of hyper-relations, HKGs typically contain complex geometric structures, such as hierarchical, ring, and chain structures, often mixed together. However, previous work mainly embeds HKGs into Euclidean space, limiting their ability to capture these complex geometric structures simultaneously. To address this challenge, we propose a novel model called geometry-aware hyper-relational embedding (GAHE). Specifically, GAHE adopts a multi-curvature geometry-aware approach by modeling HKGs in Euclidean space (zero curvature), hyperbolic space (negative curvature), and hyperspherical space (positive curvature) in a unified framework. In this way, it can integrate space-invariant and space-specific features to accurately capture the diverse structures in HKGs. In addition, GAHE introduces a module termed hyper-relational subspace learning, which allocates multiple sub-relations for each hyper-relation. It enables the exploitation of abundant latent semantic interactions and facilitates the exploration of fine-grained semantics between attribute-value pairs and hyper-relations across multiple subspaces. Furthermore, we provide theoretical guarantees that GAHE is fully expressive and capable of modeling a wide range of semantic patterns for hyper-relations. Empirical evaluations demonstrate that GAHE achieves state-of-the-art results on both hyper-relational and binary-relational benchmarks.