Separating Angular Alignment from Radial Ordering in Hyperbolic Vision-Language Models

Large-scale Vision-Language Models (VLMs) such as CLIP learn powerful semantic representations but operate in Euclidean space, which fails to capture the inherent hierarchical structure of visual and linguistic concepts. Hyperbolic geometry, with its exponential volume growth, offers a principled alternative for embedding such hierarchies with low distortion. However, existing hyperbolic VLMs use entailment losses that are unstable: as parent embeddings contract toward the origin, their entailment cones widen toward a half-space, causing catastrophic cone collapse that destroys the intended hierarchy. Additionally, hierarchical evaluation of these models remains unreliable, being largely retrieval-based and correlation-based metrics and prone to taxonomy dependence and ambiguous negatives. To address these limitations, we propose an adaptive entailment loss paired with a norm regularizer that prevents cone collapse without heuristic aperture clipping. We further introduce an angle-based probabilistic entailment protocol (PEP) for evaluating hierarchical understanding, scored with AUC-ROC and Average Precision. This paper introduces a stronger hyperbolic VLM baseline ARGENT, Adaptive hieRarchical imaGe-tExt represeNTation. ARGENT improves the SOTA hyperbolic VLM by 0.7, 1.1, and 0.8 absolute points on image classification, text-to-image retrieval, and proposed hierarchical metrics, respectively.

Whether a hyperbolic representation model uses its geometry cannot be inferred from curvature alone: what matters is the dimensionless operating point $\sqrt{c}ρ$ and whether the radial and cone mechanisms are operational there. We develop necessary-condition diagnostics and audit three published hyperbolic vision-language families -- MERU, HyCoCLIP, and PHyCLIP -- across released checkpoints and matched interventions. All converged checkpoints remain near-Euclidean ($H(u)\approx1$; none reaches $\sqrt{c}ρ>1$), and releasing the curvature floor changes $c$ and norms without leaving this regime or substantially degrading downstream performance. Entailment cones are inactive or saturated, and graded traversal fails under controlled readouts, including the models' native distance metrics. External parent-child ordering shows no shuffle-controlled pair-specific radial signal at quantified sensitivity; the only surviving pair-specific signal, a statistically detectable but small residual on the GRIT box-to-full-caption relation, remains non-operative under the evaluated readouts. Taxonomy correlations show no detectable norm contribution beyond cosine, and coarse-retrieval gains co-vary with box/compositional supervision without establishing an active radial mechanism. Gradient diagnostics expose a low-curvature, wide-cone shortcut in the entailment objective. A closed-form aperture identity places the saturation edge at $\sqrt{c}ρ\le2K$: with the floor released, all trained relation-level parent means lie at or below this edge, leaving the parent cones fully or nearly saturated. Entailment-off runs pass the edge and continue contracting. The shortcut is the dominant accelerator of collapse, not its sole cause. These audited formulations do not show an operative radial/cone mechanism under our diagnostics. We distill the audit into a five-number geometry report for hierarchy claims.

While Vision-Language Models (VLMs) have achieved remarkable performance, their Euclidean embeddings remain limited in capturing hierarchical relationships such as part-to-whole or parent-child structures, and often face challenges in multi-object compositional scenarios. Hyperbolic VLMs mitigate this issue by better preserving hierarchical structures and modeling part-whole relations (i.e., whole scene and its part images) through entailment. However, existing approaches do not model that each part has a different level of semantic representativeness to the whole. We propose UNcertainty-guided Compositional Hyperbolic Alignment (UNCHA) for enhancing hyperbolic VLMs. UNCHA models part-to-whole semantic representativeness with hyperbolic uncertainty, by assigning lower uncertainty to more representative parts and higher uncertainty to less representative ones for the whole scene. This representativeness is then incorporated into the contrastive objective with uncertainty-guided weights. Finally, the uncertainty is further calibrated with an entailment loss regularized by entropy-based term. With the proposed losses, UNCHA learns hyperbolic embeddings with more accurate part-whole ordering, capturing the underlying compositional structure in an image and improving its understanding of complex multi-object scenes. UNCHA achieves state-of-the-art performance on zero-shot classification, retrieval, and multi-label classification benchmarks. Our code and models are available at: https://github.com/jeeit17/UNCHA.git.