RelBall: Relation Ball with Quaternion Rotation for Knowledge Graph Completion

Computer Science > Artificial Intelligence [Submitted on 26 Jun 2026] RelBall: Relation Ball with Quaternion Rotation for Knowledge Graph Completion Yike Liu, Peijia Xie, Chao He, Huiling Zhu Real-world knowledge graphs are often incomplete, lacking many valid facts. Knowledge Graph Completion (KGC) aims to predict missing links using known triples, thereby enhancing graph coverage. A key challenge is modeling diverse relational patterns such as symmetry, antisymmetry, inversion, composition and semantic hierarchy. Existing models such as RotatE can capture symmetric, antisymmetric, inverse, and commutative composition patterns, yet struggle with non-commutative composition. Rotate3D addresses this by introducing non-commutativity via three-dimensional rotations, but still fails to capture the semantic hierarchies prevalent in knowledge graphs. Moreover, both models cannot effectively model one-to-many relations. To overcome these limitations, we propose RelBall, which extends Rotate3D with two innovations. First, our model introduces modulus transformation to model hierarchies, driving abstract concepts toward smaller moduli and concrete instances toward larger ones. Second, it introduces a tail-centric relation ball to model one-to-one, one-to-many, many-to-one, and many-to-many relations. RelBall offers the following advantages: (1) coverage of all relational patterns, including the ones mentioned above; (2) an interpretable hierarchical representation where the modulus directly reflect semantic levels; (3) support for one-to-one, one-to-many, many-to-one, and many-to-many relations. Experiments on multiple datasets demonstrate RelBall's competitive link prediction performance against various baselines. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2606.27967 [cs.AI]   (or arXiv:2606.27967v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.27967 Focus to learn more Submission history From: Yike Liu [view email] [v1] Fri, 26 Jun 2026 11:15:50 UTC (176 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)