AURORA: Separating Angular Alignment from Radial Ordering in Hyperbolic Vision–Language Models

Hyperbolic vision-language models are well suited to modeling the hierarchical structure of multimodal data, because hyperbolic volume grows exponentially with radius, enabling low-distortion representations of tree-like taxonomies from general to specific concepts. However, existing pretraining objectives for hyperbolic vision-language models entangle semantic alignment with entailment modeling, forcing radial coordinates to simultaneously encode semantic matching and hierarchical structure, leading to conflicting geometric constraints. In this paper, we introduce AURORA, a hyperbolic vision-language framework that decouples the objectives through angular alignment and a novel Radial-Angular Order Cone(RAOC) for entailment modeling. Angular alignment captures semantic similarity while preserving the radial structure for representing hierarchies. Unlike conventional entailment cones, RAOC determines angular allowance from relative parent-child radial gaps. It is incorporated into hierarchical entailment contrastive training to capture partial-order relations. We further introduce a norm regularization term that prevents undesirable radial degeneration for stable training. We train models on millions of image-text pairs and evaluate it across zero-shot classification, image-text retrieval, hierarchical reasoning, and compositional understanding. Our model consistently outperforms strong Euclidean and hyperbolic vision-language baselines, demonstrating the effectiveness of decoupling semantic alignment from hierarchical entailment modeling.