MAG-SSM: Motion-Adaptive Geometric State-Space Modeling for 4D Point Cloud Video Understanding

4D point cloud videos naturally represent 3D geometry and temporal evolution, but their irregular and evolving structures challenge adaptive local modeling and coherent long-range propagation. Existing methods often rely on fixed local aggregation and predefined sequence organization, limiting their ability to jointly adapt receptive fields, token organization, and local geometric modeling to evolving 4D structures. Our core insight is that effective state-space modeling of dynamic point clouds requires geometric adaptation to be coordinated throughout the propagation pipeline, rather than confined to local feature extraction. To this end, we propose MAG-SSM, a Motion-Adaptive Geometric State-Space Model for 4D point cloud video understanding that coordinates geometric adaptation across local representation, sequence organization, and geometric recovery. Specifically, Motion-Adaptive Spatio-Temporal Sampling (MSTS) adapts cross-frame local representations through bounded anchor relocation. Motion-Adaptive Semantic Routing Scanning (MSR-Scanning) forms priority-aware sequences from motion-adaptive representations, while Offset-Guided Local Geometric Fusion (OGLF) restores local geometric relations with aligned offset priors. Experiments on MSR-Action3D, Synthia 4D, and HOI4D demonstrate consistent improvements in action recognition, 4D semantic segmentation, and action segmentation with favorable computational efficiency.