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arXiv · 2407.16733

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

Vladimir Jacimovic·Marijan Markovic
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Abstract

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.

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Vladimir Jacimovic, Marijan Markovic. 2024-07-23. Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning. https://arxiv.org/abs/2407.16733

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