DensE: An Enhanced Non-Abelian Group Representation for Knowledge Graph Embedding

Capturing the composition patterns of relations is a vital task in knowledge graph completion. It also serves as a fundamental step towards multi-hop reasoning over learned knowledge. Previously, rotation-based translational methods, e.g., RotatE, have been developed to model composite relations using the product of a series of complex-valued diagonal matrices. However, RotatE makes several oversimplified assumptions on the composition patterns, forcing the relations to be commutative, independent from entities and fixed in scale. To tackle this problem, we have developed a novel knowledge graph embedding method, named DensE, to provide sufficient modeling capacity for complex composition patterns. In particular, our method decomposes each relation into an SO(3) group-based rotation operator and a scaling operator in the three dimensional (3-D) Euclidean space. The advantages of our method are twofold: (1) For composite relations, the corresponding diagonal relation matrices can be non-commutative and related with entity embeddings; (2) It extends the concept of RotatE to a more expressive setting with lower model complexity and preserves the direct geometrical interpretations, which reveals how relations with distinct patterns (i.e., symmetry/anti-symmetry, inversion and composition) are modeled. Experimental results on multiple benchmark knowledge graphs show that DensE outperforms the current state-of-the-art models for missing link prediction, especially on composite relations.