Uncertainty-guided Compositional Alignment with Part-to-Whole Semantic Representativeness in Hyperbolic Vision-Language Models

Vision-Language Models (VLMs) struggle with compositional reasoning that requires understanding inter-object relationships. A natural remedy is to inject explicit scene graph triplets $\langle s, p, o \rangle$ from an off-the-shelf scene graph generator (SGG), but we show this backfires: discrete text labels collide with the continuous visual modality, degrading GQA accuracy from 60.38% to 58.86%. We propose \textbf{HyperVis}, which bypasses the SGG semantic bottleneck entirely. From $N$ class-agnostic region proposals, we compute a dense $O(N^2)$ visual relation tensor via spatially-biased cross-attention, project it onto a Lorentz hyperboloid, and enforce hierarchy through spatial physics, namely IoA-driven entailment cones and exterior-angle repulsion. We discover that HyperVis contributes in two complementary ways: (1) as a \emph{training-time regularizer}, the hyperbolic relational losses shape LoRA representations that improve generative VQA (GQA 61.03% vs.\ 57.21% for LoRA fine-tuning without relational losses, recovering and surpassing the baseline); and (2) as an \emph{inference-time relational encoder}, hyperbolic prefix tokens boost discriminative compositional scoring (SugarCrepe 79.94%, $+$6.25pp over baseline). The learned curvature stabilises at $κ{=}4.0$, an order of magnitude above prior hyperbolic VLMs where $κ$ typically collapses toward zero, indicating that continuous visual features genuinely require the exponential volume of strongly curved space. A controlled Euclidean ablation confirms this decomposition: the relational pipeline regularises LoRA comparably in flat space (GQA 60.81%), but the compositionality gain is specifically hyperbolic (SugarCrepe $+$4.58pp over Euclidean), with entailment loss ${\sim}6{\times}$ higher in Euclidean training. Codes are available at TBA.

Hyperbolic vision-language models (VLMs) represent image and text features in a geometry naturally suited to hierarchy, but their adaptation to downstream tasks has largely relied on fixed prompts. Existing prompt learning methods, meanwhile, treat class labels as a flat set and do not exploit available taxonomic structure. We address this gap with a hierarchical prompt learning plug-in for frozen hyperbolic VLMs. Given a fixed offline parent-class hierarchy, it augments a class prompt learner with a separate parent prompt learner, parent-level supervision, hyperbolic entailment regularization, and parent-feedback logit fusion. We instantiate the method with CoOp, CoCoOp and MaPLe, yielding HyPLO, CoHyPLO and MaHyPLO. Across the standard 11-dataset benchmark, all variants improve base-to-new generalization and cross-dataset transfer, and remain comparable to their prompt learning baselines under domain shift. Six hierarchical metrics and embedding analyses show that the method produces more taxonomically consistent predictions and induces a hierarchy-consistent organization of parent, class, and image embeddings in hyperbolic space. Its gains are largest when novel classes must be placed within a fixed taxonomy, and smallest for fine-grained confusions among sibling classes or shifts affecting only the image distribution.

Open-vocabulary semantic segmentation requires adapting image-level vision-language models such as CLIP to dense pixel-level prediction, which is challenging due to the mismatch between hierarchical structure and semantic alignment in the embedding space. While recent works leverage hyperbolic geometry to model hierarchical relationships, they align embeddings across hierarchical levels but overlook semantic misalignment among embeddings within the same level. In this work, we propose HyRo, a hyperbolic fine-tuning framework that decouples hierarchical and semantic alignment in the Poincaré ball model. HyRo aligns hierarchical levels by adjusting the hyperbolic radius and refines semantic relationships through angular alignment using an orthogonal transformation that theoretically preserves the hyperbolic radius. Experiments on standard open-vocabulary semantic segmentation benchmarks demonstrate that HyRo achieves state-of-the-art performance over prior methods.