RelBall: Relation Ball with Quaternion Rotation for Knowledge Graph Completion

2026-06-26

AI Summary

This work addresses the limitations of existing knowledge graph completion methods in jointly modeling non-commutative composition relations, semantic hierarchies, and diverse relation cardinalities (e.g., one-to-many). The authors propose a unified framework that integrates quaternion rotations, magnitude-based transformations, and relation spheres centered on tail entities. This approach is the first rotation-based model to simultaneously support symmetry, anti-symmetry, inverse relations, and both commutative and non-commutative compositions, while encompassing all four relation cardinality types. By leveraging magnitude-driven representations to encode semantic hierarchies, the method enhances model interpretability and achieves competitive link prediction performance across multiple standard benchmarks, consistently outperforming current state-of-the-art baselines.

Abstract

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.

Problem

• Knowledge Graph Completion
• Relational Patterns
• Semantic Hierarchy
• One-to-Many Relations
• Non-commutative Composition

Innovation

• Relation Ball
• Quaternion Rotation
• Modulus Transformation
• Semantic Hierarchy
• Knowledge Graph Completion