# H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes

arXiv: https://arxiv.org/abs/2605.11967 · HTML: https://mlsanity.com/paper/2605.11967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 27 of 27)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [OpenScene: 3D Scene Understanding with Open Vocabularies](https://mlsanity.com/paper/2211.15654/) (2022)
- [LERF: Language Embedded Radiance Fields](https://mlsanity.com/paper/2303.09553/) (2023)
- [In-Place Scene Labelling and Understanding with Implicit Scene Representation](https://mlsanity.com/paper/2103.15875/) (2021)
- [Decomposing NeRF for Editing via Feature Field Distillation](https://mlsanity.com/paper/2205.15585/) (2022)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Panoptic Neural Fields: A Semantic Object-Aware Neural Scene Representation](https://mlsanity.com/paper/2205.04334/) (2022)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Panoptic Lifting for 3D Scene Understanding with Neural Fields](https://mlsanity.com/paper/2212.09802/) (2022)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Weakly Supervised 3D Open-vocabulary Segmentation](https://mlsanity.com/paper/2305.14093/) (2023)
- [Distilled Feature Fields Enable Few-Shot Language-Guided Manipulation](https://mlsanity.com/paper/2308.07931/) (2023)
- [NeSF: Neural Semantic Fields for Generalizable Semantic Segmentation of 3D Scenes](https://mlsanity.com/paper/2111.13260/) (2021)
- [GARField: Group Anything with Radiance Fields](https://mlsanity.com/paper/2401.09419/) (2024)
- [OmniSeg3D: Omniversal 3D Segmentation via Hierarchical Contrastive Learning](https://mlsanity.com/paper/2311.11666/) (2023)
- [OpenNeRF: Open Set 3D Neural Scene Segmentation with Pixel-Wise Features and Rendered Novel Views](https://mlsanity.com/paper/2404.03650/) (2024)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Contrastive Lift: 3D Object Instance Segmentation by Slow-Fast Contrastive Fusion](https://mlsanity.com/paper/2306.04633/) (2023)
- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [View-Consistent Hierarchical 3D Segmentation Using Ultrametric Feature Fields](https://mlsanity.com/paper/2405.19678/) (2024)
- [OpenHype: Hyperbolic Embeddings for Hierarchical Open-Vocabulary Radiance Fields](https://mlsanity.com/paper/2510.21441/) (2025)

## Abstract (arXiv)

Hierarchical 3D grouping aims to recover scene groups across multiple granularities, from fine object parts to complete objects, without relying on semantic labels or a fixed vocabulary. The main challenge is to transform 2D foundation-model cues into coherent hierarchy supervision and embed that hierarchy in a 3D representation. We propose H2G, a hyperbolic affinity field for hierarchical 3D grouping. Our method derives semantically organized tree supervision by interpreting foundation-model affinities through Dasgupta's objective for similarity-based hierarchical clustering. This supervision is distilled into a single Lorentz hyperbolic feature field, whose geometry is well suited for tree-like branching structures. A hierarchy-aware objective aligns the field with fine-level assignments, coarse object structure, compact feature clusters, and LCA (Lowest Common Ancestor) ordering. This formulation represents multiple grouping levels in one feature space, enabling semantic hierarchical grouping grounded in 2D foundation-model knowledge.