# Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoders

arXiv: https://arxiv.org/abs/2103.16046 · HTML: https://mlsanity.com/paper/2103.16046/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 79 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (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)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Contrastive Learning with Hard Negative Samples](https://mlsanity.com/paper/2010.04592/) (2020)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [On Mutual Information Maximization for Representation Learning](https://mlsanity.com/paper/1907.13625/) (2019)
- [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)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Joint Unsupervised Learning of Deep Representations and Image Clusters](https://mlsanity.com/paper/1604.03628/) (2016)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)

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

- [Hyperbolic Contrastive Learning for Visual Representations beyond Objects](https://mlsanity.com/paper/2212.00653/) (2022)
- [The Euclidean Space is Evil: Hyperbolic Attribute Editing for Few-shot Image Generation](https://mlsanity.com/paper/2211.12347/) (2022)
- [Multimodal Data Integration for Oncology in the Era of Deep Neural Networks: A Review](https://mlsanity.com/paper/2303.06471/) (2023)
- [Graph Neural Networks: Methods, Applications, and Opportunities](https://mlsanity.com/paper/2108.10733/) (2021)
- [Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections](https://mlsanity.com/paper/2211.10066/) (2022)
- [Curved Geometric Networks for Visual Anomaly Recognition](https://mlsanity.com/paper/2208.01188/) (2022)
- [Hyp-OW: Exploiting Hierarchical Structure Learning with Hyperbolic Distance Enhances Open World Object Detection](https://mlsanity.com/paper/2306.14291/) (2023)
- [Hyperbolic Graph Diffusion Model](https://mlsanity.com/paper/2306.07618/) (2023)
- [HypDAE: Hyperbolic Diffusion Autoencoders for Hierarchical Few-shot Image Generation](https://mlsanity.com/paper/2411.17784/) (2024)
- [Relating tSNE and UMAP to Classical Dimensionality Reduction](https://mlsanity.com/paper/2306.11898/) (2023)
- [Hyperbolic Metric Learning for Visual Outlier Detection](https://mlsanity.com/paper/2403.15260/) (2024)
- [Seg-HGNN: Unsupervised and Light-Weight Image Segmentation with Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/2409.06589/) (2024)
- [Towards Effective, Efficient and Unsupervised Social Event Detection in the Hyperbolic Space](https://mlsanity.com/paper/2412.10712/) (2024)
- [Breaking the Euclidean Barrier: Hyperboloid-Based Biological Sequence Analysis](https://mlsanity.com/paper/2510.01118/) (2025)
- [Hyperbolic Graph Embeddings: a Survey and an Evaluation on Anomaly Detection](https://mlsanity.com/paper/2512.18826/) (2025)

## Abstract (arXiv)

Most of the existing literature regarding hyperbolic embedding concentrate upon supervised learning, whereas the use of unsupervised hyperbolic embedding is less well explored. In this paper, we analyze how unsupervised tasks can benefit from learned representations in hyperbolic space. To explore how well the hierarchical structure of unlabeled data can be represented in hyperbolic spaces, we design a novel hyperbolic message passing auto-encoder whose overall auto-encoding is performed in hyperbolic space. The proposed model conducts auto-encoding the networks via fully utilizing hyperbolic geometry in message passing. Through extensive quantitative and qualitative analyses, we validate the properties and benefits of the unsupervised hyperbolic representations. Codes are available at https://github.com/junhocho/HGCAE.