What Drives Hierarchy-Aware Image Retrieval? Taxonomy Alignment, Objective Choice, and Geometry

Foundation vision models provide strong generic representations, yet high class-level retrieval accuracy does not necessarily imply that an embedding respects a target semantic taxonomy. We study strict explicit-taxonomy image retrieval on frozen DINOv2 features and ask: when hierarchical retrieval improves, how much of the change is associated with the organization of taxonomy-aware supervision, and how much with the Euclidean-hyperbolic geometry choice? We evaluate higher levels with strict cross-class criteria that exclude finer-grained matches, and compare Euclidean and hyperbolic projections trained with taxonomy-distance regression or a taxonomy-aware supervised contrastive objective. A compute-matched 2 x 2 Geometry x Loss factorial uses the same 768-256-32 projector capacity, optimization schedule, batch order, and fixed 100-epoch budget; the Loss axis denotes the Regression-to-Taxonomy-SupCon objective-family contrast. On CUB, the objective-family contrasts in mean hierarchy mAP (strict middle/high average, excluding Class/Leaf) are +0.0487 in Euclidean space and +0.0414 in hyperbolic space, compared with geometry contrasts of +0.0102 and +0.0030. On NABirds Parent-disjoint retrieval, the corresponding objective-family contrasts are +0.0467 and +0.0440, whereas geometry contrasts are +0.0017 and -0.0009. A semantic-alignment control shows that the true taxonomy substantially outperforms a structure-preserving shuffled hierarchy, while a NABirds curvature/radius control does not support stronger negative curvature as the explanation for the observed hierarchy gains. Across the two taxonomies, the Regression-to-Taxonomy-SupCon contrasts are larger in aggregate than the evaluated geometry contrasts; semantic alignment also matters separately, while geometry remains hierarchy-dependent.