RelBall: Relation Ball with Quaternion Rotation for... | AI Research

Knowledge graphs are essential for organizing facts, but they are often incomplete, missing many connections between entities. The paper "RelBall: Relation Ball with Quaternion Rotation for Knowledge Graph Completion" introduces a new model designed to predict these missing links more accurately. While previous models have struggled to capture the full complexity of real-world data—such as hierarchical structures and the various ways entities relate to one another—RelBall provides a more flexible and expressive framework for mapping these relationships.

Modeling Complex Relationships

A primary challenge in knowledge graph completion is handling different types of mappings, such as one-to-one, one-to-many, and many-to-many relations. Existing rotation-based models often struggle with these variations. RelBall addresses this by introducing a "tail-centric relation ball." By mapping entities into a spherical space centered at the tail entity, the model can naturally accommodate complex, multi-entity relationships without needing extra parameters. This allows the system to be much more versatile when dealing with the diverse patterns found in real-world data.

Capturing Semantic Hierarchies

Beyond simple connections, knowledge graphs often contain hierarchical information, where some concepts are abstract and others are concrete. RelBall introduces a "modulus transformation" to represent these levels. In this system, abstract concepts are pushed toward smaller moduli, while concrete instances are pushed toward larger ones. This creates an interpretable structure where the distance from the center directly reflects the semantic level of an entity, allowing the model to understand the "depth" of information within the graph.

Leveraging Quaternion Rotation

To handle the directionality and composition of relations, the model utilizes quaternion space. Quaternions are a type of hypercomplex number that excel at representing three-dimensional rotations. By using these rotations, RelBall can effectively model non-commutative composition patterns—where the order of relations matters—without the technical limitations (such as gimbal lock) that affect other methods. This ensures that the model remains stable and expressive when calculating how different entities interact.

Performance and Versatility

By combining quaternion rotations, modulus scaling, and the relation ball mechanism, RelBall creates a unified geometric framework for knowledge graph completion. The model is capable of covering all major relational patterns, including symmetry, antisymmetry, inversion, and composition. Experimental results on standard benchmarks show that this approach is highly competitive, offering a robust solution for predicting missing links while maintaining a clear, interpretable representation of the underlying semantic hierarchy.