# Neural Embeddings of Graphs in Hyperbolic Space

arXiv: https://arxiv.org/abs/1705.10359 · HTML: https://mlsanity.com/paper/1705.10359/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 30 of 58)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections](https://mlsanity.com/paper/2106.03306/) (2021)
- [Hyperbolic Deep Reinforcement Learning](https://mlsanity.com/paper/2210.01542/) (2022)
- [Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach](https://mlsanity.com/paper/2106.04941/) (2021)
- [Heterogeneous manifolds for curvature-aware graph embedding](https://mlsanity.com/paper/2202.01185/) (2022)
- [Latent Graph Inference using Product Manifolds](https://mlsanity.com/paper/2211.16199/) (2022)
- [Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning](https://mlsanity.com/paper/2305.18962/) (2023)
- [Neural Distance Embeddings for Biological Sequences](https://mlsanity.com/paper/2109.09740/) (2021)
- [Hyperbolic Safety-Aware Vision-Language Models](https://mlsanity.com/paper/2503.12127/) (2025)
- [Word2Box: Capturing Set-Theoretic Semantics of Words using Box Embeddings](https://mlsanity.com/paper/2106.14361/) (2021)
- [Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Space](https://mlsanity.com/paper/2302.06807/) (2023)
- [A Hierarchical Block Distance Model for Ultra Low-Dimensional Graph Representations](https://mlsanity.com/paper/2204.05885/) (2022)
- [Hyperbolic Random Forests](https://mlsanity.com/paper/2308.13279/) (2023)
- [D-HYPR: Harnessing Neighborhood Modeling and Asymmetry Preservation for Digraph Representation Learning](https://mlsanity.com/paper/2112.11734/) (2021)
- [Fast hyperboloid decision tree algorithms](https://mlsanity.com/paper/2310.13841/) (2023)
- [HiCu: Leveraging Hierarchy for Curriculum Learning in Automated ICD Coding](https://mlsanity.com/paper/2208.02301/) (2022)
- [Hyperbolic vs Euclidean Embeddings in Few-Shot Learning: Two Sides of the Same Coin](https://mlsanity.com/paper/2309.10013/) (2023)
- [Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometries](https://mlsanity.com/paper/2310.15003/) (2023)
- [Hyperbolic Large Language Models](https://mlsanity.com/paper/2509.05757/) (2025)
- [tensorflow-riemopt: A Library for Optimization on Riemannian Manifolds](https://mlsanity.com/paper/2105.13921/) (2021)
- [Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchy](https://mlsanity.com/paper/2410.21107/) (2024)
- [HyFI: Hyperbolic Feature Interpolation for Brain-Vision Alignment](https://mlsanity.com/paper/2603.22721/) (2026)
- [Network Representation Learning: From Traditional Feature Learning to Deep Learning](https://mlsanity.com/paper/2103.04339/) (2021)
- [Hyperbolic Genome Embeddings](https://mlsanity.com/paper/2507.21648/) (2025)
- [Incorporating Domain Knowledge into Health Recommender Systems using Hyperbolic Embeddings](https://mlsanity.com/paper/2106.07720/) (2021)
- [Poincar'e Heterogeneous Graph Neural Networks for Sequential Recommendation](https://mlsanity.com/paper/2205.11233/) (2022)
- [Sinhala Sentence Embedding: A Two-Tiered Structure for Low-Resource Languages](https://mlsanity.com/paper/2210.14472/) (2022)
- [Relating graph auto-encoders to linear models](https://mlsanity.com/paper/2211.01858/) (2022)

## Abstract (arXiv)

Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The success of neural embeddings has prompted significant amounts of research into applications in domains other than language. One such domain is graph-structured data, where embeddings of vertices can be learned that encapsulate vertex similarity and improve performance on tasks including edge prediction and vertex labelling. For both NLP and graph based tasks, embeddings have been learned in high-dimensional Euclidean spaces. However, recent work has shown that the appropriate isometric space for embedding complex networks is not the flat Euclidean space, but negatively curved, hyperbolic space. We present a new concept that exploits these recent insights and propose learning neural embeddings of graphs in hyperbolic space. We provide experimental evidence that embedding graphs in their natural geometry significantly improves performance on downstream tasks for several real-world public datasets.