# CORE: Cyclic Orthotope Relation Embedding for Knowledge Graph Completion

arXiv: https://arxiv.org/abs/2605.11159 · HTML: https://mlsanity.com/paper/2605.11159/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 19 of 19)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [KG-BERT: BERT for Knowledge Graph Completion](https://mlsanity.com/paper/1909.03193/) (2019)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Learning Attention-based Embeddings for Relation Prediction in Knowledge Graphs](https://mlsanity.com/paper/1906.01195/) (2019)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [SimKGC: Simple Contrastive Knowledge Graph Completion with Pre-trained Language Models](https://mlsanity.com/paper/2203.02167/) (2022)
- [Sequence-to-Sequence Knowledge Graph Completion and Question Answering](https://mlsanity.com/paper/2203.10321/) (2022)
- [TorusE: Knowledge Graph Embedding on a Lie Group](https://mlsanity.com/paper/1711.05435/) (2017)
- [KICGPT: Large Language Model with Knowledge in Context for Knowledge Graph Completion](https://mlsanity.com/paper/2402.02389/) (2024)
- [Differentiating Concepts and Instances for Knowledge Graph Embedding](https://mlsanity.com/paper/1811.04588/) (2018)
- [ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion](https://mlsanity.com/paper/2206.04192/) (2022)
- [Capturing Knowledge Graphs and Rules with Octagon Embeddings](https://mlsanity.com/paper/2401.16270/) (2024)

## Abstract (arXiv)

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 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.