# Rethinking the compositionality of point clouds through regularization in the hyperbolic space

arXiv: https://arxiv.org/abs/2209.10318 · HTML: https://mlsanity.com/paper/2209.10318/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 43 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 30 of 34)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Spatio-temporal Self-Supervised Representation Learning for 3D Point Clouds](https://mlsanity.com/paper/2109.00179/) (2021)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [Revisiting Point Cloud Shape Classification with a Simple and Effective Baseline](https://mlsanity.com/paper/2106.05304/) (2021)
- [MVTN: Multi-View Transformation Network for 3D Shape Recognition](https://mlsanity.com/paper/2011.13244/) (2020)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Hyperbolic Vision Transformers: Combining Improvements in Metric Learning](https://mlsanity.com/paper/2203.10833/) (2022)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [Global-Local Bidirectional Reasoning for Unsupervised Representation Learning of 3D Point Clouds](https://mlsanity.com/paper/2003.12971/) (2020)
- [Info3D: Representation Learning on 3D Objects using Mutual Information Maximization and Contrastive Learning](https://mlsanity.com/paper/2006.02598/) (2020)
- [PRA-Net: Point Relation-Aware Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2112.04903/) (2021)
- [Self-Contrastive Learning with Hard Negative Sampling for Self-supervised Point Cloud Learning](https://mlsanity.com/paper/2107.01886/) (2021)
- [End-to-End Learning Local Multi-view Descriptors for 3D Point Clouds](https://mlsanity.com/paper/2003.05855/) (2020)
- [Unsupervised Discovery of the Long-Tail in Instance Segmentation Using Hierarchical Self-Supervision](https://mlsanity.com/paper/2104.01257/) (2021)

## Built on by (most cited first, 18 of 18)

- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [HypLiLoc: Towards Effective LiDAR Pose Regression with Hyperbolic Fusion](https://mlsanity.com/paper/2304.00932/) (2023)
- [Transfer Learning in Robotics: An Upcoming Breakthrough? A Review of Promises and Challenges](https://mlsanity.com/paper/2311.18044/) (2023)
- [Hyperbolic Contrastive Learning](https://mlsanity.com/paper/2302.01409/) (2023)
- [Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifolds](https://mlsanity.com/paper/2210.01672/) (2022)
- [Dynamic Hyperbolic Attention Network for Fine Hand-object Reconstruction](https://mlsanity.com/paper/2309.02965/) (2023)
- [Understanding Hyperbolic Metric Learning through Hard Negative Sampling](https://mlsanity.com/paper/2404.15523/) (2024)
- [HyperSDFusion: Bridging Hierarchical Structures in Language and Geometry for Enhanced 3D Text2Shape Generation](https://mlsanity.com/paper/2403.00372/) (2024)
- [Hyperbolic-constraint Point Cloud Reconstruction from Single RGB-D Images](https://mlsanity.com/paper/2412.09055/) (2024)
- [GPr-Net: Geometric Prototypical Network for Point Cloud Few-Shot Learning](https://mlsanity.com/paper/2304.06007/) (2023)
- [GeoFormer: Learning Point Cloud Completion with Tri-Plane Integrated Transformer](https://mlsanity.com/paper/2408.06596/) (2024)
- [Hyperbolic Image-and-Pointcloud Contrastive Learning for 3D Classification](https://mlsanity.com/paper/2409.15810/) (2024)
- [Graph-Convolutional-Beta-VAE for Synthetic Abdominal Aorta Aneurysm Generation](https://mlsanity.com/paper/2506.13628/) (2025)
- [Geometry-aware Distance Measure for Diverse Hierarchical Structures in Hyperbolic Spaces](https://mlsanity.com/paper/2506.18533/) (2025)
- [HyPCV-Former: Hyperbolic Spatio-Temporal Transformer for 3D Point Cloud Video Anomaly Detection](https://mlsanity.com/paper/2508.00473/) (2025)
- [Mamba Learns in Context: Structure-Aware Domain Generalization for Multi-Task Point Cloud Understanding](https://mlsanity.com/paper/2603.20739/) (2026)
- [Curvature-Aware Captioning:Leveraging Geodesic Attention for 3D Scene Understanding](https://mlsanity.com/paper/2605.08808/) (2026)
- [PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification](https://mlsanity.com/paper/2607.24052/) (2026)

## Abstract (arXiv)

Point clouds of 3D objects exhibit an inherent compositional nature where simple parts can be assembled into progressively more complex shapes to form whole objects. Explicitly capturing such part-whole hierarchy is a long-sought objective in order to build effective models, but its tree-like nature has made the task elusive. In this paper, we propose to embed the features of a point cloud classifier into the hyperbolic space and explicitly regularize the space to account for the part-whole hierarchy. The hyperbolic space is the only space that can successfully embed the tree-like nature of the hierarchy. This leads to substantial improvements in the performance of state-of-art supervised models for point cloud classification.