CORE: Cyclic Orthotope Relation Embedding for Knowledge Graph Completion

2026-05-11

AI Summary

This work addresses the limitations of existing region-based embedding models for knowledge graph completion, which either suffer from optimization difficulties due to hard boundary constraints or uncontrolled region expansion in the absence of constraints. To overcome these issues, the authors propose the first approach that embeds entities and relations on an unbounded toroidal manifold. They introduce relation regions modeled as cyclic orthants, enabling smooth transitions across boundaries, and incorporate an adaptive width regularization mechanism to effectively control region expansion. The proposed method simultaneously ensures topological continuity and region controllability, theoretically supporting complex relational patterns such as inclusion and intersection. Experimental results demonstrate significant improvements in link prediction performance across four benchmark datasets, with particularly strong gains in densely semantic scenarios.

Abstract

Knowledge graph completion (KGC) aims to automatically infer missing facts in multi-relational data by mapping entities and relations into continuous representation spaces. Recent region-based embedding models have shown great promise in capturing complex logical patterns by representing relations as geometric regions. However, these models inevitably suffer from absolute boundary constraints during optimization. Conversely, without such constraints, relation regions expand indefinitely. To address the limitation, we propose \textbf{CORE} (Cyclic Orthotope Relation Embedding), a novel KGC model that embeds entities and relations onto a boundary-less torus manifold.CORE represents relations as cyclic orthotopes on the torus manifold, allowing regions to seamlessly wrap around spatial boundaries to ensure smooth gradient conduction. Furthermore, an adaptive width regularization is introduced to prevent unconditional region expansion. Theoretical analysis proves that CORE can capture various complex relation patterns such as subsumption and intersection. Extensive experiments on four benchmark datasets demonstrate that CORE achieves highly competitive performance, significantly improving link prediction accuracy in dense semantic environments.

Problem

• Knowledge Graph Completion
• Region-based Embedding
• Boundary Constraints
• Relation Modeling
• Geometric Representation

Innovation

• Cyclic Orthotope
• Torus Manifold
• Region-based Embedding
• Adaptive Width Regularization
• Knowledge Graph Completion