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

TL;DR

SM3D introduces a spectral-aware framework for point cloud understanding that mitigates spectral bias and semantic dilution in State Space Models, improving geometric and semantic fidelity in 3D tasks.

Contribution

The paper proposes SM3D, a novel spectral-aware framework with GSC and SCR modules to counteract spectral bias and semantic drift in point cloud models, with two efficient implementations.

Findings

Achieves 96.0% accuracy on ModelNet40

Attains 86.5% mIoU on ShapeNetPart

Outperforms previous methods in spectral bias mitigation

Abstract

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).