Geometry-Aware State Space Modeling for Point Cloud Length Extrapolation

Dense point clouds provide rich geometric details for 3D perception, but most point cloud models are trained with a fixed number of input points and struggle when test density changes. Downsampling high-density inputs to the training size may remove important structures, while retraining for each density is costly and impractical. In this paper, we study point cloud length extrapolation, where a model trained on short serialized point-token sequences is directly tested on much longer sequences with fixed parameters. We reframe point cloud density variation as token-length variation after serialization, without test-time raw-point downsampling or high-density retraining. This setting is challenging because dense 3D inputs contain redundant nearby tokens, geometry-critical regions, and token-channel interactions tied to spatial structure. To address these challenges, we propose PointLEX-Mamba, a geometry-aware state space modeling framework. It introduces Geometry-Aware Channel Routing to assign token-channel features to local and global branches, and Geo-Score Token Filtering to select critical global tokens using temporal response, geometric saliency, and spatial diversity. Experiments on ModelNet40 and ScanObjectNN show that PointLEX-Mamba reduces accuracy decay under point cloud length extrapolation relative to baseline and direct-transfer methods as input density and serialized length grow. Ablation studies further verify complementary contributions from both modules.