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

Sasan Sharifipour, Constantino Álvarez Casado, Manuel Lage Cañellas, Miguel Bordallo López

TL;DR

<3-5 sentence high-level summary>

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

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

TL;DR

<3-5 sentence high-level summary>

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
Paper Structure (17 sections, 5 equations, 2 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 5 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Proposed Methodology
  4. Background: dense APML
  5. Sparsity of the APML initialization
  6. Sparse COO adaptive softmax and Sinkhorn on GPU
  7. Loss, gradients, and stability
  8. Complexity, memory, and implementation details
  9. Evaluation Methodology
  10. Datasets, models, and baselines
  11. Metrics and protocol
  12. Implementation details and measurement
  13. Experimental Results
  14. Quantitative results on ShapeNet and MM-Fi
  15. Efficiency and scaling behavior
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Qualitative comparison on an MM-Fi sample. From left to right: ground truth and predictions obtained with CD, InfoCD, HyperCD, APML, and CUDA-APML.
  • Figure 2: Scaling measurements for CUDA-APML on synthetic point sets. Left: number of nonzero COO entries after symmetrization as a function of point count (500 trials per $N$). Right: peak memory per sample for dense APML and CUDA-APML in the same setup.