# HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion

arXiv: https://arxiv.org/abs/1908.04895 · HTML: https://mlsanity.com/paper/1908.04895/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2019.

## Built on by (most cited first, 20 of 20)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [Small Transformers Compute Universal Metric Embeddings](https://mlsanity.com/paper/2209.06788/) (2022)
- [Dual-Geometric Space Embedding Model for Two-View Knowledge Graphs](https://mlsanity.com/paper/2209.08767/) (2022)
- [Construction of Knowledge Graphs: State and Challenges](https://mlsanity.com/paper/2302.11509/) (2023)
- [Hyperbolic Geometry is Not Necessary: Lightweight Euclidean-Based Models for Low-Dimensional Knowledge Graph Embeddings](https://mlsanity.com/paper/2103.14930/) (2021)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Low-distortion and GPU-compatible Tree Embeddings in Hyperbolic Space](https://mlsanity.com/paper/2502.17130/) (2025)
- [Hyperbolic Large Language Models](https://mlsanity.com/paper/2509.05757/) (2025)
- [Augmenting the User-Item Graph with Textual Similarity Models](https://mlsanity.com/paper/2109.09358/) (2021)
- [Hyperbolic Hierarchical Knowledge Graph Embeddings for Link Prediction in Low Dimensions](https://mlsanity.com/paper/2204.13704/) (2022)
- [Hyperbolic Graph Neural Networks Under the Microscope: The Role of Geometry-Task Alignment](https://mlsanity.com/paper/2602.01828/) (2026)
- [Multi-Hop Reasoning for Question Answering with Hyperbolic Representations](https://mlsanity.com/paper/2507.03612/) (2025)
- [Minimizing Hyperbolic Embedding Distortion with LLM-Guided Hierarchy Restructuring](https://mlsanity.com/paper/2511.20679/) (2025)
- [A Statistical Relational Approach to Learning Distance-based GCNs](https://mlsanity.com/paper/2102.07007/) (2021)
- [What can knowledge graph alignment gain with Neuro-Symbolic learning approaches?](https://mlsanity.com/paper/2310.07417/) (2023)
- [HyperComplEx: Adaptive Multi-Space Knowledge Graph Embeddings](https://mlsanity.com/paper/2511.10842/) (2025)

## Abstract (arXiv)

Learning embeddings of entities and relations existing in knowledge bases allows the discovery of hidden patterns in data. In this work, we examine the geometrical space's contribution to the task of knowledge base completion. We focus on the family of translational models, whose performance has been lagging, and propose a model, dubbed HyperKG, which exploits the hyperbolic space in order to better reflect the topological properties of knowledge bases. We investigate the type of regularities that our model can capture and we show that it is a prominent candidate for effectively representing a subset of Datalog rules. We empirically show, using a variety of link prediction datasets, that hyperbolic space allows to narrow down significantly the performance gap between translational and bilinear models.