# Fast Log-Domain Sinkhorn Optimal Transport with Warp-Level GPU Reductions

arXiv: https://arxiv.org/abs/2605.00837 · HTML: https://mlsanity.com/paper/2605.00837/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 4 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://mlsanity.com/paper/1610.06519/) (2016)
- [Low-Rank Sinkhorn Factorization](https://mlsanity.com/paper/2103.04737/) (2021)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [Multiscale Strategies for Computing Optimal Transport](https://mlsanity.com/paper/1708.02469/) (2017)

## Abstract (arXiv)

Entropic regularized optimal transport (OT) via the Sinkhorn algorithm has become a fundamental tool in machine learning, yet existing implementations either suffer from numerical instability for small regularization parameters or incur significant overhead from deep learning frameworks. We present FastSinkhorn, a lightweight, native CUDA implementation of the log-domain Sinkhorn algorithm that combines warp-level shuffle reductions with shared-memory tiling to achieve high GPU utilization without sacrificing numerical stability. Our solver operates entirely in the log-domain, enabling robust computation for regularization parameters as small as epsilon = 10^{-4} where standard-domain methods fail. On dense OT problems with n = m = 8192, our implementation achieves 12x speedup over the widely-used POT library and 5.9x speedup over GPU-accelerated PyTorch baselines, while consuming only 256 MB of GPU memory. We validate our solver on image color transfer, 3D point cloud matching, and convergence analysis, demonstrating that native CUDA kernels with careful numerical treatment provide a practical and efficient foundation for large-scale optimal transport computation.