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arXiv · 2512.19743

From Theory to Throughput: CUDA-Optimized APML for Large-Batch 3D Learning

Sasan Sharifipour·Constantino Álvarez Casado·Manuel Lage Cañellas·Miguel Bordallo López
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Abstract

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

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Sasan Sharifipour, Constantino Álvarez Casado, Manuel Lage Cañellas, Miguel Bordallo López. 2025-12-17. From Theory to Throughput: CUDA-Optimized APML for Large-Batch 3D Learning. https://arxiv.org/abs/2512.19743

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