2025/12/17 by Sasan Sharifipour, Constantino Álvarez Casado, Sharifipour, Sasan +5
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Artificial Intelligence (cs.AI) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2512.19743
openalex publication_date 2025/12/17 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28
Loss functions are fundamental to learning accurate 3D point cloud models, yet common choices trade geometric fidelity for computational cost. Chamfer Distance is efficient but permits many-to-one correspondences, while Earth Mover Distance better reflects one-to-one transport at high computational cost. APML approximates transport with differentiable Sinkhorn iterations and an analytically derived temperature, but its dense formulation scales quadratically in memory. We present CUDA-APML, a sparse GPU implementation that thresholds negligible assignments and runs adaptive softmax, bidirectional symmetrization, and Sinkhorn normalization directly in COO form. This yields near-linear memory scaling and preserves gradients on the stored support, while pairwise distance evaluation remains quadratic in the current implementation. On ShapeNet and MM-Fi, CUDA-APML matches dense APML within a small tolerance while reducing peak GPU memory by 99.9%. Code available at: https://github.com/Multimodal-Sensing-Lab/apml