mlsanityData to 7 Oct 2026

Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances

arXiv 1306.0895 ↗First posted 4 Jun 2013stat.MLcited by 2,277

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Cited by 106 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the histograms' dimension exceeds a few hundreds. We propose in this work a new family of optimal transportation distances that look at transportation problems from a maximum-entropy perspective. We smooth the classical optimal transportation problem with an entropic regularization term, and show that the resulting optimum is also a distance which can be computed through Sinkhorn-Knopp's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transportation solvers. We also report improved performance over classical optimal transportation distances on the MNIST benchmark problem.

Key facts. Cited by 2,277 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Jun 2013.

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Citing papers per year: 2019: 1; 2020: 3; 2021: 271; 2022: 332; 2023: 406; 2024: 366; 2025: 430; 2026: 468.

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