Hyperbolic Representation Learning

Hyperbolic representation learning studies how negatively curved spaces can encode tree-like hierarchies and scale-free relationships more compactly than flat Euclidean spaces. Common approaches learn embeddings in Poincaré balls or Lorentz hyperboloids, using graph neural networks, entailment cones, contrastive objectives, and curvature-adaptive or manifold-aware layers. Applications span graph prediction, vision-language alignment, time-series forecasting, and biomedical data, with evaluations often testing retrieval, classification, and transfer across levels of a hierarchy. A central open question is when the geometry itself improves results: outcomes depend on objectives, curvature, and optimization stability, and some controlled studies find that hierarchy-aware supervision matters more than the choice of geometry.