# OpenHype: Hyperbolic Embeddings for Hierarchical Open-Vocabulary Radiance Fields

arXiv: https://arxiv.org/abs/2510.21441 · HTML: https://mlsanity.com/paper/2510.21441/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 50 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [ScanNet++: A High-Fidelity Dataset of 3D Indoor Scenes](https://mlsanity.com/paper/2308.11417/) (2023)
- [Language-driven Semantic Segmentation](https://mlsanity.com/paper/2201.03546/) (2022)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [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)
- [GroupViT: Semantic Segmentation Emerges from Text Supervision](https://mlsanity.com/paper/2202.11094/) (2022)
- [Scaling Open-Vocabulary Image Segmentation with Image-Level Labels](https://mlsanity.com/paper/2112.12143/) (2021)
- [LangSplat: 3D Language Gaussian Splatting](https://mlsanity.com/paper/2312.16084/) (2023)
- [Decomposing NeRF for Editing via Feature Field Distillation](https://mlsanity.com/paper/2205.15585/) (2022)
- [Feature 3DGS: Supercharging 3D Gaussian Splatting to Enable Distilled Feature Fields](https://mlsanity.com/paper/2312.03203/) (2023)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Language Embedded 3D Gaussians for Open-Vocabulary Scene Understanding](https://mlsanity.com/paper/2311.18482/) (2023)
- [OpenGaussian: Towards Point-Level 3D Gaussian-based Open Vocabulary Understanding](https://mlsanity.com/paper/2406.02058/) (2024)
- [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)
- [GARField: Group Anything with Radiance Fields](https://mlsanity.com/paper/2401.09419/) (2024)
- [Semantic Gaussians: Open-Vocabulary Scene Understanding with 3D Gaussian Splatting](https://mlsanity.com/paper/2403.15624/) (2024)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)

## Built on by (most cited first, 5 of 5)

- [YOLOE-26: Integrating YOLO26 with YOLOE for Real-Time Open-Vocabulary Instance Segmentation](https://mlsanity.com/paper/2602.00168/) (2026)
- [LatentAM: Real-Time, Large-Scale Latent Gaussian Attention Mapping via Online Dictionary Learning](https://mlsanity.com/paper/2602.12314/) (2026)
- [WildGHand: Learning Anti-Perturbation Gaussian Hand Avatars from Monocular In-the-Wild Videos](https://mlsanity.com/paper/2602.20556/) (2026)
- [H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes](https://mlsanity.com/paper/2605.11967/) (2026)
- [HyperANFIS: Enhancing Rule Representation and Interpretability in Adaptive Neuro-Fuzzy Systems via Hyperbolic Geometry](https://mlsanity.com/paper/2608.11768/) (2026)

## Abstract (arXiv)

Modeling the inherent hierarchical structure of 3D objects and 3D scenes is highly desirable, as it enables a more holistic understanding of environments for autonomous agents. Accomplishing this with implicit representations, such as Neural Radiance Fields, remains an unexplored challenge. Existing methods that explicitly model hierarchical structures often face significant limitations: they either require multiple rendering passes to capture embeddings at different levels of granularity, significantly increasing inference time, or rely on predefined, closed-set discrete hierarchies that generalize poorly to the diverse and nuanced structures encountered by agents in the real world. To address these challenges, we propose OpenHype, a novel approach that represents scene hierarchies using a continuous hyperbolic latent space. By leveraging the properties of hyperbolic geometry, OpenHype naturally encodes multi-scale relationships and enables smooth traversal of hierarchies through geodesic paths in latent space. Our method outperforms state-of-the-art approaches on standard benchmarks, demonstrating superior efficiency and adaptability in 3D scene understanding.