# Capturing Knowledge Graphs and Rules with Octagon Embeddings

arXiv: https://arxiv.org/abs/2401.16270 · HTML: https://mlsanity.com/paper/2401.16270/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 20 of 20)

- [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)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [A Survey on Knowledge Graph-Based Recommender Systems](https://mlsanity.com/paper/2003.00911/) (2020)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [Complex Query Answering with Neural Link Predictors](https://mlsanity.com/paper/2011.03459/) (2020)
- [Knowledge Graph Completion via Complex Tensor Factorization](https://mlsanity.com/paper/1702.06879/) (2017)
- [The More You Know: Using Knowledge Graphs for Image Classification](https://mlsanity.com/paper/1612.04844/) (2016)
- [Knowledge Graph Embedding with Iterative Guidance from Soft Rules](https://mlsanity.com/paper/1711.11231/) (2017)
- [A Decade of Knowledge Graphs in Natural Language Processing: A Survey](https://mlsanity.com/paper/2210.00105/) (2022)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [From Knowledge Graph Embedding to Ontology Embedding? An Analysis of the Compatibility between Vector Space Representations and Rules](https://mlsanity.com/paper/1805.10461/) (2018)
- [On Multi-Relational Link Prediction with Bilinear Models](https://mlsanity.com/paper/1709.04808/) (2017)
- [ExpressivE: A Spatio-Functional Embedding For Knowledge Graph Completion](https://mlsanity.com/paper/2206.04192/) (2022)
- [On Inductive Abilities of Latent Factor Models for Relational Learning](https://mlsanity.com/paper/1709.05666/) (2017)

## Built on by (most cited first, 5 of 5)

- [Faithful Differentiable Reasoning with Reshuffled Region-based Embeddings](https://mlsanity.com/paper/2406.09529/) (2024)
- [KGMark: A Diffusion Watermark for Knowledge Graphs](https://mlsanity.com/paper/2505.23873/) (2025)
- [Knowledge Graph Embeddings with Representing Relations as Annular Sectors](https://mlsanity.com/paper/2506.11099/) (2025)
- [CORE: Cyclic Orthotope Relation Embedding for Knowledge Graph Completion](https://mlsanity.com/paper/2605.11159/) (2026)
- [Pattern Over-Generalization of Knowledge Graph Embedding](https://mlsanity.com/paper/2609.03487/) (2026)

## Abstract (arXiv)

Region based knowledge graph embeddings represent relations as geometric regions. This has the advantage that the rules which are captured by the model are made explicit, making it straightforward to incorporate prior knowledge and to inspect learned models. Unfortunately, existing approaches are severely restricted in their ability to model relational composition, and hence also their ability to model rules, thus failing to deliver on the main promise of region based models. With the aim of addressing these limitations, we investigate regions which are composed of axis-aligned octagons. Such octagons are particularly easy to work with, as intersections and compositions can be straightforwardly computed, while they are still sufficiently expressive to model arbitrary knowledge graphs. Among others, we also show that our octagon embeddings can properly capture a non-trivial class of rule bases. Finally, we show that our model achieves competitive experimental results.