HyperVis: Continuous Latent Visual Relational Graphs on the Lorentz Hyperboloid for Compositional Reasoning

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.