Balanced Hyperbolic Embeddings are Natural Out-of-Distribution Detectors

Abstract

We study the relationship between hyperbolic geometry and out-of-distribution (OOD) detection. We show that when embeddings in hyperbolic space are balanced — i.e., they respect the natural hierarchical structure of the space — in-distribution and OOD samples separate geometrically without any explicit OOD supervision. The norm of a hyperbolic embedding encodes certainty: in-distribution samples concentrate near the boundary while OOD samples drift toward the origin. This provides a principled, geometry-driven foundation for OOD detection in visual recognition models, requiring no post-hoc scoring or additional training objectives.

BibTeX

@article{kasarla2026balanced,
  title={Balanced Hyperbolic Embeddings are Natural Out-of-Distribution Detectors},
  author={Kasarla, Tejaswi and van Spengler, Max and Mettes, Pascal},
  journal={International Journal of Computer Vision},
  year={2026}
}