# Enhancing Hyperbolic Graph Embeddings via Contrastive Learning

arXiv: https://arxiv.org/abs/2201.08554 · HTML: https://mlsanity.com/paper/2201.08554/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 21 references that are in the map.
- First posted on arXiv 21 Jan 2022.

## Builds on (most cited first, 16 of 16)

- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Contrastive Learning based Hybrid Networks for Long-Tailed Image Classification](https://mlsanity.com/paper/2103.14267/) (2021)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Hyperbolic Graph Attention Network](https://mlsanity.com/paper/1912.03046/) (2019)
- [Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space](https://mlsanity.com/paper/2107.03767/) (2021)
- [Contrastive and Generative Graph Convolutional Networks for Graph-based Semi-Supervised Learning](https://mlsanity.com/paper/2009.07111/) (2020)

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

- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [Improving Fine-tuning of Self-supervised Models with Contrastive Initialization](https://mlsanity.com/paper/2208.00238/) (2022)
- [Understanding Hyperbolic Metric Learning through Hard Negative Sampling](https://mlsanity.com/paper/2404.15523/) (2024)
- [Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learning](https://mlsanity.com/paper/2310.18209/) (2023)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [BSAL: A Framework of Bi-component Structure and Attribute Learning for Link Prediction](https://mlsanity.com/paper/2204.09508/) (2022)
- [L^2GC:Lorentzian Linear Graph Convolutional Networks for Node Classification](https://mlsanity.com/paper/2403.06064/) (2024)
- [Hyperbolic Graph Representation Learning: A Tutorial](https://mlsanity.com/paper/2211.04050/) (2022)
- [Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks](https://mlsanity.com/paper/2303.01724/) (2023)
- [Hyperbolic Multimodal Continual Learning](https://mlsanity.com/paper/2608.09572/) (2026)
- [FlatLand: Personalized Graph Federated Learning via Tailored Lorentz Space](https://mlsanity.com/paper/2608.21096/) (2026)
- [Memory Has Geometry: Non-Uniform Geometric Memory for Long-Horizon Personalized AI](https://mlsanity.com/paper/2609.17969/) (2026)
- [GLADMamba: Unsupervised Graph-Level Anomaly Detection Powered by Selective State Space Model](https://mlsanity.com/paper/2503.17903/) (2025)
- [Metapath-based Hyperbolic Contrastive Learning for Heterogeneous Graph Embedding](https://mlsanity.com/paper/2506.16754/) (2025)
- [Intrinsic Concept Extraction Based on Compositional Interpretability](https://mlsanity.com/paper/2603.11795/) (2026)
- [Hyperbolic Multimodal Continual Learning: A Closest-Admissible Solution](https://mlsanity.com/paper/2609.29329/) (2026)

## Abstract (arXiv)

Recently, hyperbolic space has risen as a promising alternative for semi-supervised graph representation learning. Many efforts have been made to design hyperbolic versions of neural network operations. However, the inspiring geometric properties of this unique geometry have not been fully explored yet. The potency of graph models powered by the hyperbolic space is still largely underestimated. Besides, the rich information carried by abundant unlabelled samples is also not well utilized. Inspired by the recently active and emerging self-supervised learning, in this study, we attempt to enhance the representation power of hyperbolic graph models by drawing upon the advantages of contrastive learning. More specifically, we put forward a novel Hyperbolic Graph Contrastive Learning (HGCL) framework which learns node representations through multiple hyperbolic spaces to implicitly capture the hierarchical structure shared between different views. Then, we design a hyperbolic position consistency (HPC) constraint based on hyperbolic distance and the homophily assumption to make contrastive learning fit into hyperbolic space. Experimental results on multiple real-world datasets demonstrate the superiority of the proposed HGCL as it consistently outperforms competing methods by considerable margins for the node classification task.