Bi-DaR4D: a distance-adaptive quaternion embedding with bidirectional rotation for knowledge graph completion

Abstract

Knowledge graph embedding (KGE) models encode entities and relations in continuous spaces, but existing translation-, rotation-, and quaternion-based methods still struggle to jointly represent relational directionality and semantic distance. We propose Bi-DaR4D, a quaternion embedding framework that combines bidirectional isoclinic rotation with a distance-adaptive translation mechanism. The model uses paired unit quaternions to perform coordinated rotations in four-dimensional space, strengthening the representation of inverse and multi-relational structures. It further learns relation-specific distance adjustments that balance directional transformation with geometric sensitivity. Experiments on WN18RR and FB15k-237 show that Bi-DaR4D achieves competitive or superior link prediction performance across ranking metrics, including MRR, Hits@3, and Hits@10. Ablation results indicate that the distance-adaptive module provides the clearest contribution, while bidirectional rotation contributes to relational expressiveness with smaller changes across the tested metrics. These results support Bi-DaR4D as a geometrically interpretable framework for knowledge graph completion in settings with complex relational patterns.