# HMSN: Hyperbolic Self-Supervised Learning by Clustering with Ideal Prototypes

arXiv: https://arxiv.org/abs/2305.10926 · HTML: https://mlsanity.com/paper/2305.10926/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 58 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 30 of 43)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [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)
- [SimMIM: A Simple Framework for Masked Image Modeling](https://mlsanity.com/paper/2111.09886/) (2021)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [iBOT: Image BERT Pre-Training with Online Tokenizer](https://mlsanity.com/paper/2111.07832/) (2021)
- [Self-Supervised Learning of Pretext-Invariant Representations](https://mlsanity.com/paper/1912.01991/) (2019)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Muse: Text-To-Image Generation via Masked Generative Transformers](https://mlsanity.com/paper/2301.00704/) (2023)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Masked Siamese Networks for Label-Efficient Learning](https://mlsanity.com/paper/2204.07141/) (2022)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Local Aggregation for Unsupervised Learning of Visual Embeddings](https://mlsanity.com/paper/1903.12355/) (2019)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)

## Built on by (most cited first, 6 of 6)

- [Hyperbolic Random Forests](https://mlsanity.com/paper/2308.13279/) (2023)
- [Semantic Positive Pairs for Enhancing Visual Representation Learning of Instance Discrimination Methods](https://mlsanity.com/paper/2306.16122/) (2023)
- [Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applications](https://mlsanity.com/paper/2311.13883/) (2023)
- [Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicing](https://mlsanity.com/paper/2510.04579/) (2025)
- [Multi-Scale Representation of Follicular Lymphoma Pathology Images in a Single Hyperbolic Space](https://mlsanity.com/paper/2506.18523/) (2025)
- [On the Geometry of Multimodal Saturation: Riemannian VICReg](https://mlsanity.com/paper/2610.06096/) (2026)

## Abstract (arXiv)

Hyperbolic manifolds for visual representation learning allow for effective learning of semantic class hierarchies by naturally embedding tree-like structures with low distortion within a low-dimensional representation space. The highly separable semantic class hierarchies produced by hyperbolic learning have shown to be powerful in low-shot tasks, however, their application in self-supervised learning is yet to be explored fully. In this work, we explore the use of hyperbolic representation space for self-supervised representation learning for prototype-based clustering approaches. First, we extend the Masked Siamese Networks to operate on the Poincar'e ball model of hyperbolic space, secondly, we place prototypes on the ideal boundary of the Poincar'e ball. Unlike previous methods we project to the hyperbolic space at the output of the encoder network and utilise a hyperbolic projection head to ensure that the representations used for downstream tasks remain hyperbolic. Empirically we demonstrate the ability of these methods to perform comparatively to Euclidean methods in lower dimensions for linear evaluation tasks, whilst showing improvements in extreme few-shot learning tasks.