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

arXiv: https://arxiv.org/abs/2603.14022 · HTML: https://mlsanity.com/paper/2603.14022/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 55 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Builds on (most cited first, 30 of 49)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [GroupViT: Semantic Segmentation Emerges from Text Supervision](https://mlsanity.com/paper/2202.11094/) (2022)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Video Instance Segmentation](https://mlsanity.com/paper/1905.04804/) (2019)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [MOSE: A New Dataset for Video Object Segmentation in Complex Scenes](https://mlsanity.com/paper/2302.01872/) (2023)
- [MeViS: A Large-scale Benchmark for Video Segmentation with Motion Expressions](https://mlsanity.com/paper/2308.08544/) (2023)
- [GENESIS: Generative Scene Inference and Sampling with Object-Centric Latent Representations](https://mlsanity.com/paper/1907.13052/) (2019)
- [Bridging the Gap to Real-World Object-Centric Learning](https://mlsanity.com/paper/2209.14860/) (2022)
- [Cut and Learn for Unsupervised Object Detection and Instance Segmentation](https://mlsanity.com/paper/2301.11320/) (2023)
- [SAVi++: Towards End-to-End Object-Centric Learning from Real-World Videos](https://mlsanity.com/paper/2206.07764/) (2022)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Illiterate DALL-E Learns to Compose](https://mlsanity.com/paper/2110.11405/) (2021)
- [Simple Unsupervised Object-Centric Learning for Complex and Naturalistic Videos](https://mlsanity.com/paper/2205.14065/) (2022)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [How to represent part-whole hierarchies in a neural network](https://mlsanity.com/paper/2102.12627/) (2021)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Unsupervised Discovery of Object Radiance Fields](https://mlsanity.com/paper/2107.07905/) (2021)
- [Object Scene Representation Transformer](https://mlsanity.com/paper/2206.06922/) (2022)
- [Stacked Capsule Autoencoders](https://mlsanity.com/paper/1906.06818/) (2019)

## Built on by (most cited first, 1 of 1)

- [HSA: Hierarchical Slot Attention for Multi-granularity Scene-Decomposition](https://mlsanity.com/paper/2607.08249/) (2026)

## Abstract (arXiv)

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 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 hrefhttps://github.com/NeeluMadan/HHSgithub.com/NeeluMadan/HHS.