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Spectral Informed Mamba for Robust Point Cloud Processing
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Adapts Mamba for point clouds with Laplacian-spectrum-based token traversal (SAST), recursive spectral partitioning for segmentation (HLT), and token repositioning for MAE pretraining (TAR).
Problem
Mamba's sequence-based processing of point clouds depends on token traversal order, and grid-based 3D traversals are view-dependent and fail to keep surface-adjacent patches adjacent; MAE pretraining also breaks because masked tokens are appended rather than placed in their original order.
Approach
Order point patches by the non-constant smallest eigenvectors of a random-walk Laplacian of a patch-kNN graph (isometry-invariant), use recursive binary splits over the spectrum for segmentation, and reinsert masked MAE tokens at their original positions to preserve Mamba's order sensitivity.
Key results
- Ours achieves 94.32% on ScanObjectNN OBJ-BG and 93.4% on ModelNet40 after pretraining with TAR and fine-tuning, versus 92.77% for Point-MAE and 93.29% for PointMamba on OBJ-BG.
- Part segmentation mIoU of 86.1 with HLT in the pretrained setting, vs 86.0 for PointMamba and 86.5 for Point-M2AE.
- Few-shot 10-way 10-shot accuracy 98.5% vs 98.3% for Point-M2AE (5-way 10-shot 96.4% vs 96.8% for Point-M2AE).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add spectral token traversal (SAST) to Point-Mamba | Point-Mamba · ScanObjectNN OBJ-BG, training from scratch | accuracy: 90.87 -> 92.25 | Helped |
| Add spectral token traversal (SAST) to Point-Mamba | Point-Mamba · ScanObjectNN OBJ-ONLY, training from scratch | accuracy: 90.18 -> 91.39 | Helped |
| Add spectral token traversal (SAST) to Point-Mamba | Point-Mamba · ScanObjectNN PB-T50-RS, training from scratch | accuracy: 87.7 -> 87.30 | Hurt |
| Add hierarchical local traversal (HLT) for segmentation | Point-Mamba · ShapeNetPart, training from pretrained | mIoU (Inst.): 86.0 -> 86.1 | Helped |
| Use SAST instead of HLT for segmentation (ablation) | Point-Mamba · ShapeNetPart, training from pretrained | mIoU (Inst.): 86.1 -> 85.7 | Hurt |
| Use four non-constant smallest eigenvectors for traversal (ablation) | SAST · ScanObjectNN OBJ-BG | overall accuracy | Helped |
| Increase the number of non-constant smallest eigenvectors beyond four (ablation) | SAST · ScanObjectNN OBJ-BG | overall accuracy | Hurt |
| Use 20 nearest neighbors to construct the adjacency matrix (ablation) | SAST · ScanObjectNN OBJ-BG | overall accuracy | Helped |
| Increase nearest neighbors beyond 20 (ablation) | SAST · ScanObjectNN OBJ-BG | overall accuracy | Hurt |
| Add TAR during pretraining (ablation) | Point-Mamba · ModelNet40 linear evaluation | overall accuracy | Helped |
| Add TAR during pretraining (ablation) | Point-Mamba · ScanObjectNN OBJ-BG | accuracy: 93.12 -> 94.32 | Helped |
| Add TAR during pretraining (ablation) | Point-Mamba · ScanObjectNN OBJ-ONLY | accuracy: 91.04 -> 91.91 | Helped |
Surprising findings
- In part segmentation, SAST (85.7) performs slightly below the Point-Mamba baseline (85.8) when trained from scratch, while HLT is needed for gains.
- Few-shot 5-way 10-shot result (96.4) is below Point-M2AE (96.8) and Point-MAE (96.3 vs 96.4 is above), showing mixed few-shot gains.
Limitations
- Neighborhood size K is a per-dataset hyperparameter that may limit generalizability.
- Gains over strong transformer baselines are small or mixed on some benchmarks (e.g., few-shot and SAST segmentation).
Experimental setup
Datasets: ShapeNet ModelNet40 ScanObjectNN ShapeNetPart
Benchmarks: ModelNet40 ScanObjectNN ShapeNetPart
Metrics: overall accuracy few-shot accuracy mIoU standard deviation over 10 runs
Baselines: Point-MAE Point-M2AE Point-BERT PointMamba PCM DGCNN PointNet++ I2P-MAE ACT Point-GPT-S
Builds on: Mamba Point-Mamba Point-MAE PCM normalized cuts
Closest papers by meaning
- Point Cloud Mamba: Point Cloud Learning via State Space Model (AAAI 2025 · similarity 0.91)
- PointMamba: A Simple State Space Model for Point Cloud Analysis (NeurIPS 2024 · similarity 0.91)
- Pamba: Enhancing Global Interaction in Point Clouds via State Space Model (AAAI 2025 · similarity 0.89)
- ZigzagPointMamba: Spatial-Semantic Mamba for Point Cloud Understanding (NeurIPS 2025 · similarity 0.89)
- LCM: Locally Constrained Compact Point Cloud Model for Masked Point Modeling (NeurIPS 2024 · similarity 0.87)
- PointRWKV: Efficient RWKV-Like Model for Hierarchical Point Cloud Learning (AAAI 2025 · similarity 0.87)
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