GAPS: Group-wise Affine-Perturbed Serialization for efficient 3D semantic segmentation

Abstract. Space-filling curves (SFCs) have enabled transformers to process massive 3D point clouds with linear complexity by mapping them into 1D sequences. However, standard SFCs rely on fixed, axis-aligned traversal orders, which introduce systematic axial anisotropy and frequently sever the connectivity of oblique geometric structures – a phenomenon we term “locality breaches”. While existing methods attempt to mitigate this by sequentially stacking multiple patterns, they incur a prohibitive linear increase in latency. To resolve this efficiency–accuracy dilemma, we propose GAPS (Group-wise Affine-Perturbed Serialization). Mathematically, we derive a flexible mechanism to generate diverse, bijective scanning paths via affine transformations over the Galois field 𝔽2. This allows for the synthesis of “sheared” and “rotated” traversals that effectively establish neighborhood connectivity along non-axial geometries. Architecturally, GAPS employs a group-wise parallel design that splits feature channels to aggregate multiple-perspective contexts simultaneously, thereby circumventing the computational penalty of serial execution. Extensive experiments on the ScanNet200 benchmark demonstrate that GAPS achieves 36.8 % mean Intersection over Union (mIoU), outperforming the strong baseline, Point Transformer V3 (PTv3), by 1.6 %. Remarkably, GAPS delivers this significant gain with zero parameter overhead and minimal latency overhead, establishing a new state-of-the-art performance among standard train-from-scratch 3D backbones.