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Hyperbolic Contrastive Learning for Hierarchical 3D Point Cloud Embedding

Yingjie Liu, Pengyu Zhang, Ziyao He, Mingsong Chen, Xuan Tang, Xian Wei

TL;DR

The paper addresses the challenge of modeling hierarchical structure across language, 2D images, and 3D Point Clouds by extending hyperbolic contrastive learning to the 3D modality. It introduces hierarchy-enhancing regularizers, including hyperbolic entailment and alignment losses, and employs a reconstruction-guided framework to transfer hyperbolic language–image knowledge to 3D Point Clouds. By leveraging the Lorentz hyperboloid model, the method explicitly enforces intra- and inter-modal hierarchies and analyzes hyperbolicity with delta-based metrics. Experimental results on ModelNet and ShapeNetPart show improved 3D embeddings and downstream task performance, demonstrating the practical value of hyperbolic, multi-modal learning for 3D understanding. The work advances interpretable, hierarchical cross-modal representations and opens avenues for more robust 3D scene understanding and few-shot/segmentation tasks.

Abstract

Hyperbolic spaces allow for more efficient modeling of complex, hierarchical structures, which is particularly beneficial in tasks involving multi-modal data. Although hyperbolic geometries have been proven effective for language-image pre-training, their capabilities to unify language, image, and 3D Point Cloud modalities are under-explored. We extend the 3D Point Cloud modality in hyperbolic multi-modal contrastive pre-training. Additionally, we explore the entailment, modality gap, and alignment regularizers for learning hierarchical 3D embeddings and facilitating the transfer of knowledge from both Text and Image modalities. These regularizers enable the learning of intra-modal hierarchy within each modality and inter-modal hierarchy across text, 2D images, and 3D Point Clouds. Experimental results demonstrate that our proposed training strategy yields an outstanding 3D Point Cloud encoder, and the obtained 3D Point Cloud hierarchical embeddings significantly improve performance on various downstream tasks.

Hyperbolic Contrastive Learning for Hierarchical 3D Point Cloud Embedding

TL;DR

The paper addresses the challenge of modeling hierarchical structure across language, 2D images, and 3D Point Clouds by extending hyperbolic contrastive learning to the 3D modality. It introduces hierarchy-enhancing regularizers, including hyperbolic entailment and alignment losses, and employs a reconstruction-guided framework to transfer hyperbolic language–image knowledge to 3D Point Clouds. By leveraging the Lorentz hyperboloid model, the method explicitly enforces intra- and inter-modal hierarchies and analyzes hyperbolicity with delta-based metrics. Experimental results on ModelNet and ShapeNetPart show improved 3D embeddings and downstream task performance, demonstrating the practical value of hyperbolic, multi-modal learning for 3D understanding. The work advances interpretable, hierarchical cross-modal representations and opens avenues for more robust 3D scene understanding and few-shot/segmentation tasks.

Abstract

Hyperbolic spaces allow for more efficient modeling of complex, hierarchical structures, which is particularly beneficial in tasks involving multi-modal data. Although hyperbolic geometries have been proven effective for language-image pre-training, their capabilities to unify language, image, and 3D Point Cloud modalities are under-explored. We extend the 3D Point Cloud modality in hyperbolic multi-modal contrastive pre-training. Additionally, we explore the entailment, modality gap, and alignment regularizers for learning hierarchical 3D embeddings and facilitating the transfer of knowledge from both Text and Image modalities. These regularizers enable the learning of intra-modal hierarchy within each modality and inter-modal hierarchy across text, 2D images, and 3D Point Clouds. Experimental results demonstrate that our proposed training strategy yields an outstanding 3D Point Cloud encoder, and the obtained 3D Point Cloud hierarchical embeddings significantly improve performance on various downstream tasks.
Paper Structure (20 sections, 15 equations, 3 figures, 4 tables)

This paper contains 20 sections, 15 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Hyperbolic Geometry for Point Clouds
  4. Contrastive Pre-training for Hierarchy Multi-Modal Embeddings
  5. Preliminary
  6. Hyperbolic Geometry & Lorentz Embeddings
  7. Language-Vision Contrastive Learning Loss
  8. Approach
  9. Overall Architecture and Hierarchy Relations
  10. Hyperbolic Entailment Regularization
  11. Alignment Loss and Hyperbolicity Analysis
  12. Contention Between Modal and Tasks
  13. Experimental Results
  14. Hierarchical Embedding Analysis
  15. Dictionary Learning Analysis
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Hyperbolicity coverage curves and distribution of embedding distances of text embeddings, image embeddings, and point cloud embeddings.
  • Figure 2: Analysis of Embedding Distances for Text, Image, and Point Cloud Data via our approach (MERU (modified)).
  • Figure 3: Disentangled analysis for our obtained 3D Point Cloud embeddings by dictionary learning approach.