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Dual Manifold Regularization Steered Robust Representation Learning for Point Cloud Analysis
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Proposes Dual Manifold Regularization (DMR), combining a hyperbolic hierarchical/contrastive loss on the Poincaré ball with a hyperspherical triplet loss on topology-preserving sine-warped augmentations, to improve point cloud representation learning.
Problem
Learning robust point cloud representations is hard due to irregularity and sparsity; prior hyperbolic regularization (HyCoRe) rests on flawed assumptions about common ancestors and distance thresholds, and single-manifold regularization is limited.
Approach
Regularize point cloud encoders on two manifolds of opposite curvature: a hyperbolic (Poincaré ball) part-whole hierarchy loss without a common-ancestor assumption, plus a hyperspherical contrastive triplet loss using Topological Consistency Augmentation (a sine-based homeomorphic warp) to create positive pairs.
Key results
- DMR achieves 94.8% OA on ModelNet40 with PointMLP backbone (with voting), up from 94.1% baseline, without extra parameters.
- DMR reaches 90.7% OA on ScanObjectNN with DeLA backbone, state of the art per the paper.
- On ShapeNetPart, PointMetaBase-S+DMR improves instance mIoU to 87.1% from 86.7%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add DMR to PointMLP | PointMLP · ModelNet40 | OA: 94.1 -> 94.6 | Helped |
| add DMR to PointMLP | PointMLP · ScanObjectNN | OA: 87.2 -> 89.5 | Helped |
| add DMR to PointMetaBase-S | PointMetaBase-S · ShapeNetPart | Ins. mIoU: 86.7 -> 87.1 | Helped |
| use only hyperspherical SLoss instead of DMR (ablation) | DGCNN · ModelNet40 | OA: 94.3 -> 93.7 | Hurt |
| use only hyperbolic HLoss instead of DMR (ablation) | DGCNN · ModelNet40 | OA: 94.3 -> 94.0 | Hurt |
| add hyperspherical SLoss to DGCNN (ablation) | DGCNN · ModelNet40 | OA: 92.2 -> 93.7 | Helped |
| add hyperbolic HLoss to DGCNN (ablation) | DGCNN · ModelNet40 | OA: 92.2 -> 94.0 | Helped |
| combine hyperbolic HLoss and hyperspherical SLoss (ablation) | DGCNN · ModelNet40 | OA: 93.7 -> 94.3 | Helped |
| replace HyCoRe with DMR (ablation) | PointMLP · ModelNet40 | OA: 94.3 -> 94.6 | Helped |
| replace HyCoRe with DMR (ablation) | PointMLP · ScanObjectNN | OA: 89.5 -> 90.2 | Helped |
| add voting strategy to DMR (ablation) | PointMLP + DMR · ModelNet40 | OA: 94.6 -> 94.8 | Helped |
| add voting strategy to DMR (ablation) | PointMLP + DMR · ScanObjectNN | OA: 89.5 -> 90.2 | Helped |
Surprising findings
- Hyperspherical regularization alone performs comparably to HyCoRe, while hyperbolic regularization alone significantly outperforms HyCoRe.
- The authors' theory suggests probability of different objects sharing a common ancestor is near zero, so cross-object hyperbolic hierarchy is argued to be inappropriate.
Limitations
- Evaluation limited to object classification and part segmentation on three datasets
- Theoretical analysis relies on probabilistic assumptions about sampling; empirical validation of hyperbolic geometry choices is limited
Experimental setup
Datasets: ModelNet40 ScanObjectNN ShapeNetPart
Benchmarks: ModelNet40 ScanObjectNN ShapeNetPart
Metrics: overall accuracy class mean accuracy instance mIoU class mIoU
Baselines: HyCoRe GAM PointMLP DGCNN PointNet++ HGNet PointMetaBase-S
Builds on: HyCoRe SimCLR PointMLP DGCNN
Closest papers by meaning
- DV-Matcher: Deformation-based Non-rigid Point Cloud Matching Guided by Pre-trained Visual Features (CVPR 2025 · similarity 0.86)
- PointCFormer: A Relation-Based Progressive Feature Extraction Network for Point Cloud Completion (AAAI 2025 · similarity 0.85)
- An Explicit Frame Construction for Normalizing 3D Point Clouds (ICML 2024 · similarity 0.85)
- Mixed-curvature decision trees and random forests (ICML 2025 · similarity 0.85)
- Mining and Transferring Feature-Geometry Coherence for Unsupervised Point Cloud Registration (NeurIPS 2024 · similarity 0.85)
- Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embedding (CVPR 2025 · similarity 0.85)
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