# Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modes

arXiv: https://arxiv.org/abs/2506.14780 · HTML: https://mlsanity.com/paper/2506.14780/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 18 of 18)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://mlsanity.com/paper/1610.06519/) (2016)
- [Faster Wasserstein Distance Estimation with the Sinkhorn Divergence](https://mlsanity.com/paper/2006.08172/) (2020)
- [Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance](https://mlsanity.com/paper/1805.11897/) (2018)
- [Massively scalable Sinkhorn distances via the Nystr"om method](https://mlsanity.com/paper/1812.05189/) (2018)
- [On the Efficiency of Entropic Regularized Algorithms for Optimal Transport](https://mlsanity.com/paper/1906.01437/) (2019)
- [Semi-dual Regularized Optimal Transport](https://mlsanity.com/paper/1811.05527/) (2018)
- [Screening Sinkhorn Algorithm for Regularized Optimal Transport](https://mlsanity.com/paper/1906.08540/) (2019)
- [Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport](https://mlsanity.com/paper/1711.01851/) (2017)
- [Rethinking Initialization of the Sinkhorn Algorithm](https://mlsanity.com/paper/2206.07630/) (2022)
- [Accelerating Sinkhorn Algorithm with Sparse Newton Iterations](https://mlsanity.com/paper/2401.12253/) (2024)
- [Greedy stochastic algorithms for entropy-regularized optimal transport problems](https://mlsanity.com/paper/1803.01347/) (2018)
- [The derivatives of Sinkhorn-Knopp converge](https://mlsanity.com/paper/2207.12717/) (2022)
- [Annealed Sinkhorn for Optimal Transport: convergence, regularization path and debiasing](https://mlsanity.com/paper/2408.11620/) (2024)

## Built on by (most cited first, 1 of 1)

- [Accelerating Birkhoff Projection for Manifold-Constrained Hyper-Connections](https://mlsanity.com/paper/2606.07574/) (2026)

## Abstract (arXiv)

In this paper, we propose an accelerated version for the Sinkhorn algorithm, which is the reference method for computing the solution to Entropic Optimal Transport. Its main draw-back is the exponential slow-down of convergence as the regularization weakens varepsilon rightarrow 0. Thanks to spectral insights on the behavior of the Hessian, we propose to mitigate the problem via an original spectral warm-start strategy. This leads to faster convergence compared to the reference method, as also demonstrated in our numerical experiments.