Is the Geometry Doing the Work? An Operating-Point Audit of Hierarchy in Hyperbolic Vision-Language Models
2026-07-06 • Computer Vision and Pattern Recognition
Computer Vision and Pattern RecognitionMachine Learning
AI summaryⓘ
The authors examine hyperbolic models used in vision-language tasks and find that their special geometry isn’t effectively used in current versions. They show that the models mostly behave like regular Euclidean space rather than true hyperbolic space, with key mechanisms like entailment cones being inactive or ineffective. Their analysis suggests that some supposed benefits of hyperbolic geometry come from simpler shortcuts and supervision signals, not the intended geometric features. They propose a simple numerical report to evaluate future models’ use of hyperbolic geometry more accurately.
hyperbolic geometrycurvature parametervision-language modelsentailment conesradial depthGRIT datasettaxonomy correlationsoperating pointEuclidean spacehierarchical representations
Authors
Jaeyoung Kim, Eunseok Kim, Dongsuk Jang
Abstract
Whether a hyperbolic representation model uses its geometry cannot be read off its curvature parameter: what matters is the dimensionless operating point $\sqrt{c}ρ$ and whether the radial and cone machinery is active there. We develop a battery of necessary-condition diagnostics and audit three published hyperbolic vision-language families -- MERU, HyCoCLIP, and PHyCLIP -- across released checkpoints and controlled interventions on a fixed GRIT snapshot, identifying three failure modes. First, curvature is not an active resource: the operating point stays near-Euclidean ($H(u)\approx 1$; no audited converged checkpoint reaches $\sqrt{c}ρ>1$), and releasing the curvature floor moves curvature and norms but keeps the operating point near-Euclidean, without substantial downstream degradation. Second, the cone and traversal machinery is measured inoperative: entailment cones are inactive, saturated, or misaligned, and graded traversal fails under controlled readouts, while directed radial depth is a bounded non-detection above shuffle-null controls at quantified sensitivity; the one surviving native-relation residual remains non-operative. Third, hierarchy-looking evaluations are underdetermined: taxonomy correlations are carried by angular distance, and coarse-retrieval gains track box/compositional supervision, not curvature. A mechanistic account explains why: the entailment objective admits a low-curvature, wide-cone shortcut, and a parameter-free aperture identity (cones saturate iff $\sqrt{c}ρ\le 2K$) locates the edge where every entailment-trained unclamped run settles; entailment-off runs show no arrest there. The shortcut is the dominant accelerator of collapse, not its sole cause. These formulations, as released, do not instantiate the radial/cone mechanism their geometry motivates; we distill the audit into a five-number geometry report for future hierarchy claims.