---
title: "Low-Dimensional Hyperbolic Knowledge Graph Embeddings (2020)"
description: "The authors propose a family of hyperbolic models (RefH, RotH and AttH) built in the Poincaré ball… 33 references, cited by 63 papers here."
authors: ["Ines Chami", "Adva Wolf", "Da-Cheng Juan", "Frederic Sala", "Sujith Ravi", "Christopher Ré"]
year: 2020
venue: "Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics"
source: "https://aclanthology.org/2020.acl-main.617/"
doi: "10.18653/v1/2020.acl-main.617"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/chami-2020-low-dimensional-hyperbolic-knowledge-graph/"
---
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# Low-Dimensional Hyperbolic Knowledge Graph Embeddings

**Authors:** Ines Chami, Adva Wolf, [Da-Cheng Juan](https://md.research.elamur.ai/free/en/authors/da-cheng-juan/), Frederic Sala, [Sujith Ravi](https://md.research.elamur.ai/free/en/authors/sujith-ravi/) and [Christopher Ré](https://md.research.elamur.ai/free/en/authors/christopher-re/) · **Year:** 2020 · **Venue:** [Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2020](https://md.research.elamur.ai/free/en/venues/acl/2020/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2020.acl-main.617/) · [PDF](https://aclanthology.org/2020.acl-main.617.pdf) · [DOI 10.18653/v1/2020.acl-main.617](https://doi.org/10.18653/v1/2020.acl-main.617) · [OpenAlex](https://openalex.org/W3023009950)

**Citations:** 363 citations (OpenAlex, 2026-10-14) · [63](https://md.research.elamur.ai/free/en/papers/chami-2020-low-dimensional-hyperbolic-knowledge-graph/cited-by/) in our library, of the 141,840 papers whose bibliographies we read

## Summary
Knowledge graphs (KGs) are typically incomplete, so missing links are often predicted with entity and relation embeddings. KGs mix tree-like hierarchies with logical relation patterns such as symmetry, anti-symmetry and inversion. Euclidean and complex-space models usually need very high dimensions, which is costly in memory. The earlier hyperbolic model MuRP handles hierarchies but cannot express many of these logical patterns.

The authors propose a family of hyperbolic models (RefH, RotH and AttH) built in the Poincaré ball, with a separately learned curvature for each relation. Relations act as hyperbolic isometries made from Givens reflections and rotations. AttH uses hyperbolic attention to blend the two transformations. Training happens in tangent space, so Riemannian optimization is unnecessary.

Evaluated on WN18RR, FB15k-237 and YAGO3-10, the method clearly beats Euclidean and hyperbolic baselines at 32 dimensions. At high dimensions, the model family sets new state-of-the-art results. This matters because compact embeddings that preserve hierarchy make link prediction on large KGs cheaper.

## Key points
- At 32 dimensions, MRR rises by up to 6.1% over previous Euclidean and hyperbolic methods. Hierarchical WordNet relations (hypernym, member meronym) gain 16–24% relative to Euclidean baselines.
- Reflections tend to model symmetric relations, while rotations capture anti-symmetric ones. AttH's attention learns to select the appropriate operator for each relation.
- At high dimensions (up to 500), the family reaches new SotA MRR scores of 49.6% on WN18RR (RotH) and 57.7% on YAGO3-10.
- Trainable curvature is essential: learned curvatures shrink toward zero as dimension grows. With fixed curvature, embeddings crowd near the ball boundary and performance drops, which may explain MuRP's weakness at high dimensions.
- Visualizations of a WN18RR sub-tree show that RotH preserves the hierarchy, whereas the Euclidean RotE does not.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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## Cite

Cite as: Ines Chami, Adva Wolf, Da-Cheng Juan, Frederic Sala, Sujith Ravi and Christopher Ré. 2020. Low-Dimensional Hyperbolic Knowledge Graph Embeddings. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{chami2020low,
  title = {{Low-Dimensional Hyperbolic Knowledge Graph Embeddings}},
  author = {Ines Chami, Adva Wolf, Da-Cheng Juan, Frederic Sala, Sujith Ravi and Christopher Ré},
  booktitle = {Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics},
  year = {2020},
  doi = {10.18653/v1/2020.acl-main.617},
  url = {https://doi.org/10.18653/v1/2020.acl-main.617}
}
```

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*Updated 24 October 2026*