Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning
<|reference_start|>Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning: 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.<|reference_end|>
@article{jacimovic2024conformally,
    title={Conformally Natural Families of Probability Distributions on Hyperbolic
  Disc with a View on Geometric Deep Learning},
    author={Vladimir Jacimovic and Marijan Markovic},
    journal={arXiv preprint arXiv:2407.16733},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.16733},
    primaryClass={cs.LG math.CV}
}