Frozen slot embeddings show hierarchy-consistent depth under hyperbolic projection

Madan et al. take frozen slot embeddings from three pretrained slot-attention systems (SPOT, VideoSAUR, SlotContrast) and project them onto the Lorentz hyperboloid at fixed curvatures, with no retraining [madan-etal-2026-hyperbolic-object-centric-scene-reps] Coarse scene-level slots sit farther from the origin than fine object-level slots, a consistent depth ordering absent in native Euclidean space [madan-etal-2026-hyperbolic-object-centric-scene-reps] Hyperbolic projection at curvature 0.2 substantially reduces coarse/fine distributional overlap (0.49 to 0.41 SlotContrast, 0.62 to 0.37 VideoSAUR, 0.51 to 0.36 SPOT) [madan-etal-2026-hyperbolic-object-centric-scene-reps] A curvature-task tradeoff holds (low curvature best for retrieval, moderate for separation), the ordering is the opposite of a supervised hyperbolic model's, and no causal intervention is performed [madan-etal-2026-hyperbolic-object-centric-scene-reps]