# Federated Sinkhorn

arXiv: https://arxiv.org/abs/2502.07021 · HTML: https://mlsanity.com/paper/2502.07021/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2025.

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

- [Field Codes for Distributed Coupling Samplers and Certified Empirical Transport](https://mlsanity.com/paper/2607.27078/) (2026)

## Abstract (arXiv)

We study distributed Sinkhorn iterations for entropy-regularized optimal transport when the Gibbs kernel operator is row-partitioned across c workers and cannot be centralized. We present Federated Sinkhorn, two exact synchronous protocols that exchange only scaling-vector slices: (i) an All-to-All scheme implemented by Allgather, and (ii) a Star (parameter-server) scheme implemented by client to server sends and server to client broadcasts. For both, we derive closed-form per-iteration compute, communication, and memory costs under an alpha-beta latency--bandwidth model, and show that the distributed iterates match centralized Sinkhorn under standard positivity assumptions. Multi-node CPU/GPU experiments validate the model and show that repeated global scaling exchange quickly becomes the dominant bottleneck as c increases. We also report an optional bounded-delay asynchronous schedule and an optional privacy measurement layer for communicated log-scalings.