arXiv:2603.14022cs.CV2026-03中稿 · CVPR被引 1

用双曲几何揭示视觉场景中隐藏的层级结构,让对象表示更合理。

A Hyperbolic Perspective on Hierarchical Structure in Object-Centric Scene Representations

  • 将槽注意力的欧氏嵌入投影到双曲空间,不改训练流程。
  • 低曲率(c=0.2)时父级槽检索性能优于或等于欧氏空间。
  • 中等曲率(c=0.5)能更好分离层级间关系,适合发现隐含层次。

槽注意力已成为无监督对象中心学习的强大框架,将视觉场景分解为少量紧凑的向量表示(称为槽),每个槽捕捉一个独立区域或对象。然而,这些槽在欧氏空间中学习,缺乏对自然存在的层级关系的几何归纳偏置。本文提出一种简单的后处理流程,将欧氏槽嵌入投影到双曲空间的洛伦兹双曲面,不修改原有训练流程。我们直接从槽注意力掩码构建五级视觉层级,并分析双曲几何是否揭示了在欧氏空间中不可见的潜在层级结构。将该方法集成至SPOT(图像)、VideoSAUR(视频)和SlotContrast(视频),发现双曲投影展现出一致的从场景级到对象级的组织结构:粗粒度槽占据更大的流形深度,而欧氏空间中无此现象。进一步发现“曲率-任务权衡”:低曲率(c=0.2)在父槽检索上表现匹配或超越欧氏空间,中等曲率(c=0.5)实现更优的层间分离。这些结果表明,槽表示已编码潜在层级,双曲几何可将其揭示,支持端到端双曲训练作为下一步方向。代码与模型可在github.com/NeeluMadan/HHS获取。

原文摘要 · Abstract (English)

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}.

双曲几何对象中心层级结构槽注意力

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