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

• URL: http://arxiv.org/abs/2603.14022v1
• Date: Sat, 14 Mar 2026 16:53:59 GMT
• Title: A Hyperbolic Perspective on Hierarchical Structure in Object-Centric Scene Representations
• Abstract summary: We propose a simple pipeline to project Euclidean slot embeddings onto the Lorentz hyperboloid of hyperbolic space.<n>We construct five-level visual hierarchies directly from slot attention masks.<n>We find that hyperbolic projection exposes a consistent scene-level to object-level organisation.
• Score: 58.143688187023734
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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}.

Related papers

• $\text{H}^2$em: Learning Hierarchical Hyperbolic Embeddings for Compositional Zero-Shot Learning [18.502719006213635]
  Compositional zero-shot learning (CZSL) aims to recognize unseen state-object compositions by generalizing from a training set of their primitives (state and object)<n>Current methods often overlook the rich hierarchical structures, such as the semantic hierarchy of primitives and the conceptual hierarchy between primitives and compositions.<n>We propose H2em, a new framework that learns Hierarchical Hyperbolic EMs for CZSL.
  arXiv  Detail & Related papers  (2025-12-23T03:46:04Z)
• HLFormer: Enhancing Partially Relevant Video Retrieval with Hyperbolic Learning [77.434558721499]
  Partially Relevant Video Retrieval (PRVR) addresses the challenge of matching untrimmed videos with text queries describing only partial content.<n>We propose the first hyperbolic modeling framework for PRVR, namely HLFormer, which leverages hyperbolic space learning to compensate for the suboptimal hierarchical modeling capabilities of Euclidean space.
  arXiv  Detail & Related papers  (2025-07-23T10:59:46Z)
• GGBall: Graph Generative Model on Poincaré Ball [10.796246797823557]
  GGBall is a novel hyperbolic framework for graph generation that integrates geometric inductive biases with modern generative paradigms.<n>Our model reduces degree MMD by over 75% on Community-Small and over 40% on Ego-Small compared to state-of-the-art baselines.
  arXiv  Detail & Related papers  (2025-06-08T15:43:21Z)
• Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learning [70.0681902472251]
  We propose a novel contrastive learning framework to learn high-quality graph embeddings in hyperbolic space.<n>Specifically, we design the alignment metric that effectively captures the hierarchical data-invariant information.<n>We show that in the hyperbolic space one has to address the leaf- and height-level uniformity related to properties of trees.
  arXiv  Detail & Related papers  (2023-10-27T15:31:42Z)
• HMSN: Hyperbolic Self-Supervised Learning by Clustering with Ideal Prototypes [7.665392786787577]
  We use hyperbolic representation space for self-supervised representation learning for prototype-based clustering approaches. We extend the Masked Siamese Networks to operate on the Poincar'e ball model of hyperbolic space. Unlike previous methods we project to the hyperbolic space at the output of the encoder network and utilise a hyperbolic projection head to ensure that the representations used for downstream tasks remain hyperbolic.
  arXiv  Detail & Related papers  (2023-05-18T12:38:40Z)
• Flattening-Net: Deep Regular 2D Representation for 3D Point Cloud Analysis [66.49788145564004]
  We present an unsupervised deep neural architecture called Flattening-Net to represent irregular 3D point clouds of arbitrary geometry and topology. Our methods perform favorably against the current state-of-the-art competitors.
  arXiv  Detail & Related papers  (2022-12-17T15:05:25Z)
• Geometry Interaction Knowledge Graph Embeddings [153.69745042757066]
  We propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities.
  arXiv  Detail & Related papers  (2022-06-24T08:33:43Z)
• Hyperbolic Hierarchical Knowledge Graph Embeddings for Link Prediction in Low Dimensions [11.260501547769636]
  We propose a novel KGE model called $textbfHyp$erbolic $textbfH$ierarchical $textbfKGE$ (HypHKGE) This model introduces attention-based learnable curvatures for hyperbolic space, which helps preserve rich semantic hierarchies. Experiments demonstrate the effectiveness of the proposed HypHKGE model on the three benchmark datasets.
  arXiv  Detail & Related papers  (2022-04-28T03:41:41Z)
• HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization [52.369435664689995]
  We introduce a textitHyperbolic Regularization powered Collaborative Filtering (HRCF) and design a geometric-aware hyperbolic regularizer. Specifically, the proposal boosts optimization procedure via the root alignment and origin-aware penalty. Our proposal is able to tackle the over-smoothing problem caused by hyperbolic aggregation and also brings the models a better discriminative ability.
  arXiv  Detail & Related papers  (2022-04-18T06:11:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.