Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object. However, these slots are learned in Euclidean space, which provides no geometric inductive bias for the hierarchical relationships that naturally structure visual scenes. In this work, we propose a simple post-hoc pipeline to project Euclidean slot embeddings onto the Lorentz hyperboloid of hyperbolic space, without modifying the underlying training pipeline. We construct five-level visual hierarchies directly from slot attention masks and analyse whether hyperbolic geometry reveals latent hierarchical structure that remains invisible in Euclidean space. Integrating our pipeline with SPOT (images), VideoSAUR (video), and SlotContrast (video), We find that hyperbolic projection exposes a consistent scene-level to object-level organisation, where coarse slots occupy greater manifold depth than fine slots, which is absent in Euclidean space. We further identify a "curvature--task tradeoff": low curvature ($c{=}0.2$) matches or outperforms Euclidean on parent slot retrieval, while moderate curvature ($c{=}0.5$) achieves better inter-level separation. Together, these findings suggest that slot representations already encode latent hierarchy that hyperbolic geometry reveals, motivating end-to-end hyperbolic training as a natural next step. Code and models are available at \href{https://github.com/NeeluMadan/HHS}{github.com/NeeluMadan/HHS}.

翻译：槽注意力（Slot Attention）已成为无监督面向对象学习的重要框架，它可将视觉场景分解为少量称为“槽”（slots）的紧凑向量表征，每个槽对应一个独立区域或物体。然而，这些槽是在欧氏空间中学习的，无法为自然构建视觉场景的层级关系提供几何归纳偏置。本文提出一个简单的后处理流程，在不修改原有训练流程的前提下，将欧氏槽嵌入投影到双曲空间的洛伦兹双曲面。我们直接从槽注意力掩码构建五级视觉层级，并分析双曲几何能否揭示欧氏空间中不可见的潜在层级结构。将该流程与SPOT（图像）、VideoSAUR（视频）及SlotContrast（视频）集成后，我们发现双曲投影暴露出一致的场景级到物体级组织关系，其中粗粒度槽占据更大的流形深度，而细粒度槽占据较小深度——这一现象在欧氏空间中不存在。我们还识别出“曲率-任务权衡”：低曲率（c=0.2）在父级槽检索中与欧氏空间性能相当或更优，而中等曲率（c=0.5）可实现更好的层间分离。综合这些发现表明，槽表征已编码了潜在层级，而双曲几何可将其揭示，这为端到端双曲训练作为自然下一步研究提供了动机。代码与模型见\href{https://github.com/NeeluMadan/HHS}{github.com/NeeluMadan/HHS}。