# Hyperbolic Geometry in Computer Vision: A Survey

arXiv: https://arxiv.org/abs/2304.10764 · HTML: https://mlsanity.com/paper/2304.10764/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 67 references that are in the map.
- First posted on arXiv 21 Apr 2023.

## Builds on (most cited first, 30 of 34)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Slimmable Neural Networks](https://mlsanity.com/paper/1812.08928/) (2018)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Label-Embedding for Image Classification](https://mlsanity.com/paper/1503.08677/) (2015)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [Hierarchical Clustering: Objective Functions and Algorithms](https://mlsanity.com/paper/1704.02147/) (2017)
- [Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers](https://mlsanity.com/paper/2107.11472/) (2021)
- [Learning the Predictability of the Future](https://mlsanity.com/paper/2101.01600/) (2021)
- [HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems](https://mlsanity.com/paper/1809.01703/) (2018)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [Unsupervised Discovery of the Long-Tail in Instance Segmentation Using Hierarchical Self-Supervision](https://mlsanity.com/paper/2104.01257/) (2021)
- [Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representations](https://mlsanity.com/paper/2012.01644/) (2020)
- [Skin Lesion Recognition with Class-Hierarchy Regularized Hyperbolic Embeddings](https://mlsanity.com/paper/2209.05842/) (2022)

## Built on by (most cited first, 4 of 4)

- [Hyperbolic Audio-visual Zero-shot Learning](https://mlsanity.com/paper/2308.12558/) (2023)
- [SHMamba: Structured Hyperbolic State Space Model for Audio-Visual Question Answering](https://mlsanity.com/paper/2406.09833/) (2024)
- [A Fashion Item Recommendation Model in Hyperbolic Space](https://mlsanity.com/paper/2409.02599/) (2024)
- [Hyperbolic Distillation: Geometry-Guided Cross-Modal Transfer for Robust 3D Object Detection](https://mlsanity.com/paper/2605.09899/) (2026)

## Abstract (arXiv)

Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, eg, natural language processing, graph learning, etc, as a result of its intriguing property of encoding the data's hierarchical structure (like irregular graph or tree-likeness data). Recent studies prove that such data hierarchy also exists in the visual dataset, and investigate the successful practice of hyperbolic geometry in the computer vision (CV) regime, ranging from the classical image classification to advanced model adaptation learning. This paper presents the first and most up-to-date literature review of hyperbolic spaces for CV applications. To this end, we first introduce the background of hyperbolic geometry, followed by a comprehensive investigation of algorithms, with geometric prior of hyperbolic space, in the context of visual applications. We also conclude this manuscript and identify possible future directions.