提出无边界环面嵌入模型，解决知识图谱补全中关系区域膨胀问题。
CORE: Cyclic Orthotope Relation Embedding for Knowledge Graph Completion
- 在环面流形上用循环长方体表示关系，实现边界无缝衔接。
- 引入自适应宽度正则化，防止关系区域无限扩张。
- 理论证明可捕捉子类、交集等复杂逻辑关系，适合密集语义场景。
知识图谱补全（KGC）旨在通过将实体和关系映射到连续表示空间，自动推断多关系数据中的缺失事实。近年来基于区域的嵌入模型通过将关系表示为几何区域，在捕捉复杂逻辑模式方面展现出巨大潜力。然而，这些模型在优化过程中不可避免地受到绝对边界约束的影响；若无此约束，关系区域将无限扩张。为此，本文提出新颖的KGC模型CORE（Cyclic Orthotope Relation Embedding），将实体和关系嵌入无边界的环面流形。CORE在环面流形上将关系表示为循环长方体，使区域能无缝绕过空间边界，确保梯度平滑传导。此外，引入自适应宽度正则化，有效防止关系区域无限制扩展。理论分析表明，CORE能够捕捉子类、交集等多种复杂关系模式。在四个基准数据集上的大量实验显示，CORE在密集语义环境下显著提升了链接预测准确率，表现极具竞争力。
原文摘要 · Abstract (English)
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.
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