Hyperbolic Geometric Inference
Preserve, Analyze, Extract, and Interpret Structures in Latent Data Representations
Time: Thu 2026-11-12 13.00
Location: F3 (Flodis), Lindstedtsvägen 26
Video link: https://kth-se.zoom.us/j/65209779499
Language: English
Subject area: Computer Science
Doctoral student: Aniss Aiman Medbouhi , Robotik, perception och lärande
Opponent: Associate Professor Georgios Arvanitidis, Technical University of Denmark, Denmark
Supervisor: Professor Danica Kragic, Robotik, perception och lärande; Doctor Giovanni Luca Marchetti, Algebra, kombinatorik och topologi; Doctor Anastasiia Varava, Robotik, perception och lärande; Doctor Vladislav Polianskii, Ericsson Research
QC 20261019
Abstract
High-dimensional data are often represented in lower-dimensional latentspaces for analysis. The geometry chosen for such a representation determines how distances, neighborhoods, and other relations between observations are expressed. Hyperbolic geometry is well suited to hierarchical and tree-like data because of its negative curvature and exponential growth. Once a hyperbolic representation has been constructed, a further question arises: what information can be inferred? This thesis studies this question from the perspective of hyperbolic geometric inference: the analysis and extraction of structural information encoded in hyperbolic latent representations, together with their interpretation. We first consider the upstream problem of preserving selected structure during representation learning, using geometric and topological constraints in variational auto-encoders. We then develop methods for geometric inference from hyperbolic latent representations, with applications in single-cell biology and olfactory perception. Hyperbolic Delaunay Geometric Alignment compares predefined subsets through their Delaunay connectivity. A complementary study of olfactory descriptor data investigates radial, directional, and regional organization. Finally, HyperSteiner and Randomized HyperSteiner (RHS) construct approximate solutions to the hyperbolic Steiner minimal tree problem using Delaunay triangulation. RHS broadens the exploration of candidate tree topologies and refines Steiner-point locations through Riemannian optimization. The main contribution of this thesis is a set of methods for geometric inference from hyperbolic latent representations: quantifying geometric relations, analyzing geometric organization, and extracting parsimonious tree structures.