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

arXiv: https://arxiv.org/abs/2512.19743 · HTML: https://mlsanity.com/paper/2512.19743/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 27 of 27)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Large-scale Point Cloud Semantic Segmentation with Superpoint Graphs](https://mlsanity.com/paper/1711.09869/) (2017)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [Semantic3D.net: A new Large-scale Point Cloud Classification Benchmark](https://mlsanity.com/paper/1704.03847/) (2017)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [MM-Fi: Multi-Modal Non-Intrusive 4D Human Dataset for Versatile Wireless Sensing](https://mlsanity.com/paper/2305.10345/) (2023)
- [TorchSparse: Efficient Point Cloud Inference Engine](https://mlsanity.com/paper/2204.10319/) (2022)
- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [Accelerating Sinkhorn Algorithm with Sparse Newton Iterations](https://mlsanity.com/paper/2401.12253/) (2024)
- [Importance Sparsification for Sinkhorn Algorithm](https://mlsanity.com/paper/2306.06581/) (2023)
- [TUM2TWIN: Introducing the Large-Scale Multimodal Urban Digital Twin Benchmark Dataset](https://mlsanity.com/paper/2505.07396/) (2025)
- [APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction](https://mlsanity.com/paper/2509.08104/) (2025)
- [Spatio-Temporal 3D Point Clouds from WiFi-CSI Data via Transformer Networks](https://mlsanity.com/paper/2410.16303/) (2024)

## Abstract (arXiv)

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