Geometry-Guided Conservative Soft Ordering for Point Cloud Understanding

3D point clouds are inherently unordered, whereas state space models (SSMs) process ordered sequences, making token ordering critical for point cloud understanding. Existing methods derive fixed hard orders from geometry that cannot be optimized by the task loss, forcing SSMs to accommodate suboptimal ordering and potentially weakening the learned representations. To address this limitation, we propose Geometry-guided Conservative Soft Ordering (GCSO), which replaces one-to-one hard assignment with trainable conservative soft ordering based on geometry prior. Specifically, GCSO uses current token features and coordinates to predict a local offset for each scan position in a geometric base order. Then the offset centers the weights over neighboring tokens, whose weighted feature mixture forms the soft ordering. Since the weights vary continuously, the task loss can optimize the offset and the resulting feature-adaptive soft ordering end to end. Moreover, GCSO organizes the weights into a nonnegative doubly stochastic routing matrix, ensuring that each scan position receives one unit of assignment while each source token contributes one unit of participation. Experiments on shape classification and part segmentation support the effectiveness of GCSO for point cloud understanding.