Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning
This work offers a novel mathematical tool for handling uncertainties in hyperbolic data, with potential applications in Geometric Deep Learning and bioinformatics, though it appears incremental as it builds on existing concepts in hyperbolic geometry.
The authors introduced a new family of probability distributions on the hyperbolic disc that is invariant under disc-preserving conformal mappings, providing a tractable model for encoding uncertainties in hyperbolic data.
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.