# Curvature-Aware Captioning:Leveraging Geodesic Attention for 3D Scene Understanding

arXiv: https://arxiv.org/abs/2605.08808 · HTML: https://mlsanity.com/paper/2605.08808/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 54 references that are in the map.
- First posted on arXiv 9 May 2026.

## Builds on (most cited first, 30 of 38)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Flamingo: a Visual Language Model for Few-Shot Learning](https://mlsanity.com/paper/2204.14198/) (2022)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [CIDEr: Consensus-based Image Description Evaluation](https://mlsanity.com/paper/1411.5726/) (2014)
- [DINO: DETR with Improved DeNoising Anchor Boxes for End-to-End Object Detection](https://mlsanity.com/paper/2203.03605/) (2022)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Executing your Commands via Motion Diffusion in Latent Space](https://mlsanity.com/paper/2212.04048/) (2022)
- [Self-critical Sequence Training for Image Captioning](https://mlsanity.com/paper/1612.00563/) (2016)
- [ScanRefer: 3D Object Localization in RGB-D Scans using Natural Language](https://mlsanity.com/paper/1912.08830/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [ScanQA: 3D Question Answering for Spatial Scene Understanding](https://mlsanity.com/paper/2112.10482/) (2021)
- [An End-to-End Transformer Model for 3D Object Detection](https://mlsanity.com/paper/2109.08141/) (2021)
- [PointGroup: Dual-Set Point Grouping for 3D Instance Segmentation](https://mlsanity.com/paper/2004.01658/) (2020)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Scan2Cap: Context-aware Dense Captioning in RGB-D Scans](https://mlsanity.com/paper/2012.02206/) (2020)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Hunyuan3D 2.5: Towards High-Fidelity 3D Assets Generation with Ultimate Details](https://mlsanity.com/paper/2506.16504/) (2025)
- [End-to-End 3D Dense Captioning with Vote2Cap-DETR](https://mlsanity.com/paper/2301.02508/) (2023)
- [X-Trans2Cap: Cross-Modal Knowledge Transfer using Transformer for 3D Dense Captioning](https://mlsanity.com/paper/2203.00843/) (2022)
- [UniT3D: A Unified Transformer for 3D Dense Captioning and Visual Grounding](https://mlsanity.com/paper/2212.00836/) (2022)
- [D3Net: A Unified Speaker-Listener Architecture for 3D Dense Captioning and Visual Grounding](https://mlsanity.com/paper/2112.01551/) (2021)
- [MORE: Multi-Order RElation Mining for Dense Captioning in 3D Scenes](https://mlsanity.com/paper/2203.05203/) (2022)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [3D Question Answering](https://mlsanity.com/paper/2112.08359/) (2021)
- [Spatiality-guided Transformer for 3D Dense Captioning on Point Clouds](https://mlsanity.com/paper/2204.10688/) (2022)
- [Vote2Cap-DETR++: Decoupling Localization and Describing for End-to-End 3D Dense Captioning](https://mlsanity.com/paper/2309.02999/) (2023)

## Abstract (arXiv)

Accurate 3D scene description is fundamental to robotic navigation and augmented reality, yet current dense captioning methods face significant limitations in processing sparse point cloud data. % Existing approaches that apply Euclidean embedding spaces struggle to simultaneously preserve fine-grained local geometric details and model exponentially growing global semantic hierarchies, leading to either inaccurate localization or disjointed, shallow scene descriptions. % In this work, we propose a novel textbftextscCurvature-Aware Captioning framework, integrating novel non-Euclidean geodesic attention mechanisms, to resolve the localization-contextualization conflict. % Specifically, self-attention within Oblique space enforces dimensional homogeneity while establishing long-range dependencies. Bidirectional geodesic cross-attention within Lorentz space models hierarchical semantic relationships across scene instances, enabling simultaneous precision in object localization and coherence in scene descriptions. % Theoretical analysis confirms that the curvature complementarity between the Oblique manifold and Lorentz hyperboloid resolves the Euclidean-hyperbolic conflict, ensuring feature stability via isotropic optimization while preserving inherent hierarchical relationships. Extensive experiments on ScanRefer and Nr3D benchmarks demonstrate state-of-the-art performance, with significant gains in both localization accuracy and descriptive richness.