# Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning

arXiv: https://arxiv.org/abs/2407.16733 · HTML: https://mlsanity.com/paper/2407.16733/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 5 of 5)

- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Skip-gram word embeddings in hyperbolic space](https://mlsanity.com/paper/1809.01498/) (2018)
- [Recent advances in directional statistics](https://mlsanity.com/paper/2005.06889/) (2020)

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

- [A group-theoretic framework for machine learning in hyperbolic spaces](https://mlsanity.com/paper/2501.06934/) (2025)
- [Emotion Collider: Dual Hyperbolic Mirror Manifolds for Sentiment Recovery via Anti Emotion Reflection](https://mlsanity.com/paper/2602.16161/) (2026)
- [Reinforcement Learning in Hyperbolic Spaces: Models and Experiments](https://mlsanity.com/paper/2410.09466/) (2024)
- [Busemann energy-based attention for emotion analysis in Poincar'e discs](https://mlsanity.com/paper/2604.06752/) (2026)

## Abstract (arXiv)

We introduce the novel family of probability distributions on hyperbolic disc. The distinctive property of the proposed family is invariance under the actions of the group of disc-preserving conformal mappings. The group-invariance property renders it a convenient and tractable model for encoding uncertainties in hyperbolic data. Potential applications in Geometric Deep Learning and bioinformatics are numerous, some of them are briefly discussed. We also emphasize analogies with hyperbolic coherent states in quantum physics.