RelBall Enhances Knowledge Graph Completion with Quaternion Rotations

Knowledge graphs, while powerful, are often incomplete, missing many valid connections between entities. Knowledge Graph Completion (KGC) aims to fill these gaps by predicting missing links. Existing models like RotatE and Rotate3D have made progress in capturing various relational patterns, but they struggle with complex scenarios such as non-commutative compositions, semantic hierarchies, and one-to-many relationships. This research proposes RelBall, an innovative model that builds upon Rotate3D by introducing two key advancements. First, it incorporates a modulus transformation, which allows it to model semantic hierarchies by representing abstract concepts with smaller moduli and concrete instances with larger ones. Second, RelBall utilizes a tail-centric relation ball, enabling it to effectively capture all types of relations: one-to-one, one-to-many, many-to-one, and many-to-many. RelBall offers several advantages, including comprehensive coverage of diverse relational patterns, an interpretable hierarchical representation, and robust support for various relation cardinalities. Empirical evaluations on multiple datasets demonstrate that RelBall achieves competitive link prediction performance, significantly advancing the state-of-the-art in knowledge graph completion.