# SM3D: Mitigating Spectral Bias and Semantic Dilution in Point Cloud State Space Models

arXiv: https://arxiv.org/abs/2505.11099 · HTML: https://mlsanity.com/paper/2505.11099/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 54 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 30 of 41)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Masked Autoencoders for Point Cloud Self-supervised Learning](https://mlsanity.com/paper/2203.06604/) (2022)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [Embracing Single Stride 3D Object Detector with Sparse Transformer](https://mlsanity.com/paper/2112.06375/) (2021)
- [Unsupervised Point Cloud Pre-Training via Occlusion Completion](https://mlsanity.com/paper/2010.01089/) (2020)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [Masked Discrimination for Self-Supervised Learning on Point Clouds](https://mlsanity.com/paper/2203.11183/) (2022)
- [Autoencoders as Cross-Modal Teachers: Can Pretrained 2D Image Transformers Help 3D Representation Learning?](https://mlsanity.com/paper/2212.08320/) (2022)
- [PointGPT: Auto-regressively Generative Pre-training from Point Clouds](https://mlsanity.com/paper/2305.11487/) (2023)
- [Swin3D: A Pretrained Transformer Backbone for 3D Indoor Scene Understanding](https://mlsanity.com/paper/2304.06906/) (2023)
- [CenterFormer: Center-based Transformer for 3D Object Detection](https://mlsanity.com/paper/2209.05588/) (2022)
- [FlatFormer: Flattened Window Attention for Efficient Point Cloud Transformer](https://mlsanity.com/paper/2301.08739/) (2023)
- [Point Cloud Mamba: Point Cloud Learning via State Space Model](https://mlsanity.com/paper/2403.00762/) (2024)
- [Mamba3D: Enhancing Local Features for 3D Point Cloud Analysis via State Space Model](https://mlsanity.com/paper/2404.14966/) (2024)
- [PatchFormer: An Efficient Point Transformer with Patch Attention](https://mlsanity.com/paper/2111.00207/) (2021)
- [Parameter-Efficient Fine-Tuning in Spectral Domain for Point Cloud Learning](https://mlsanity.com/paper/2410.08114/) (2024)
- [Towards Compact 3D Representations via Point Feature Enhancement Masked Autoencoders](https://mlsanity.com/paper/2312.10726/) (2023)

## Abstract (arXiv)

Point clouds are a fundamental 3D data representation that underpins various computer vision tasks. Recently, Mamba has demonstrated strong potential for 3D point cloud understanding. However, existing approaches primarily focus on point serialization, overlooking a more fundamental limitation: State Space Models (SSMs) inherently exhibit a spectral low-pass bias arising from their recursive formulation. In serialized point clouds, this bias is particularly detrimental, as it suppresses high-frequency geometric structures and progressively dilutes semantic discriminability across deep layers. To address these limitations, we propose SM3D, a spectral-aware framework designed to jointly preserve geometric fidelity and semantic consistency. First, a Geometric Spectral Compensator (GSC) is introduced to counteract the low-pass bias by explicitly injecting graph-guided high-frequency components through local Laplacian analysis, thereby restoring structural sensitivity. Second, we design a Semantic Coherence Refiner (SCR) to rectify semantic drift through frequency-aware channel recalibration. To balance theoretical precision and computational efficiency, SCR is instantiated via two pathways: an exact Laplacian eigendecomposition (SCR-L) and a linear-complexity Chebyshev polynomial approximation (SCR-C). Extensive experiments demonstrate that SM3D achieves state-of-the-art performance, including 96.0% accuracy on ModelNet40 and 86.5% mIoU on ShapeNetPart, validating its effectiveness in mitigating spectral low-pass bias and semantic dilution (Code: https://github.com/L1277471578/SM3D).