# Hyperbolic Contrastive Learning

arXiv: https://arxiv.org/abs/2302.01409 · HTML: https://mlsanity.com/paper/2302.01409/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 91 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 30 of 67)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Self-Supervised Learning of Pretext-Invariant Representations](https://mlsanity.com/paper/1912.01991/) (2019)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)

## Built on by (most cited first, 15 of 15)

- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [HELM: Hyperbolic Large Language Models via Mixture-of-Curvature Experts](https://mlsanity.com/paper/2505.24722/) (2025)
- [Learning Structured Representations with Hyperbolic Embeddings](https://mlsanity.com/paper/2412.01023/) (2024)
- [Hyp-OW: Exploiting Hierarchical Structure Learning with Hyperbolic Distance Enhances Open World Object Detection](https://mlsanity.com/paper/2306.14291/) (2023)
- [Understanding Hyperbolic Metric Learning through Hard Negative Sampling](https://mlsanity.com/paper/2404.15523/) (2024)
- [HMSN: Hyperbolic Self-Supervised Learning by Clustering with Ideal Prototypes](https://mlsanity.com/paper/2305.10926/) (2023)
- [GeoWorld: Geometric World Models](https://mlsanity.com/paper/2602.23058/) (2026)
- [Continual Hyperbolic Learning of Instances and Classes](https://mlsanity.com/paper/2506.10710/) (2025)
- [A streamlined Approach to Multimodal Few-Shot Class Incremental Learning for Fine-Grained Datasets](https://mlsanity.com/paper/2403.06295/) (2024)
- [Leveraging Superfluous Information in Contrastive Representation Learning](https://mlsanity.com/paper/2408.10292/) (2024)
- [Hyperbolic Chamfer Distance for Point Cloud Completion and Beyond](https://mlsanity.com/paper/2412.17951/) (2024)
- [Hgformer: Hyperbolic Graph Transformer for Recommendation](https://mlsanity.com/paper/2502.15693/) (2024)
- [Predicate Hierarchies Improve Few-Shot State Classification](https://mlsanity.com/paper/2502.12481/) (2025)
- [A Mathematical Perspective On Contrastive Learning](https://mlsanity.com/paper/2505.24134/) (2025)
- [Siamese networks for Poincar'e embeddings and the reconstruction of evolutionary trees](https://mlsanity.com/paper/2410.07387/) (2024)

## Abstract (arXiv)

Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has shown competitive performance on several benchmark datasets. The embeddings of contrastive learning are arranged on a hypersphere that results in using the inner (dot) product as a distance measurement in Euclidean space. However, the underlying structure of many scientific fields like social networks, brain imaging, and computer graphics data exhibit highly non-Euclidean latent geometry. We propose a novel contrastive learning framework to learn semantic relationships in the hyperbolic space. Hyperbolic space is a continuous version of trees that naturally owns the ability to model hierarchical structures and is thus beneficial for efficient contrastive representation learning. We also extend the proposed Hyperbolic Contrastive Learning (HCL) to the supervised domain and studied the adversarial robustness of HCL. The comprehensive experiments show that our proposed method achieves better results on self-supervised pretraining, supervised classification, and higher robust accuracy than baseline methods.