mlsanityData to 7 Oct 2026

A gradient descent perspective on Sinkhorn

arXiv 2002.03758 ↗First posted 10 Feb 2020math.OCcited by 24

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Abstract (arXiv)

We present a new perspective on the popular Sinkhorn algorithm, showing that it can be seen as a Bregman gradient descent (mirror descent) of a relative entropy (Kullback-Leibler divergence). This viewpoint implies a new sublinear convergence rate with a robust constant.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Feb 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 3; 2024: 4; 2025: 8; 2026: 4.

24 papers.

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  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  2. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  3. 2022Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EMcited by 33
  4. 2025Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuningcited by 15
  5. 2025Provable Maximum Entropy Manifold Exploration via Diffusion Modelscited by 12
  6. 2023Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithmcited by 10
  7. 2024Accelerating Sinkhorn Algorithm with Sparse Newton Iterationscited by 9
  8. 2025Momentum Multi-Marginal Schr"odinger Bridge Matchingcited by 9
  9. 2025Quantum Doubly Stochastic Transformerscited by 6
  10. 2022Mirror Sinkhorn: Fast Online Optimization on Transport Polytopescited by 5
  11. 2024Feedback Schr"odinger Bridge Matchingcited by 4
  12. 2024A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithmcited by 4
12 more
  1. 2024Inferring Dynamic Networks from Marginals with Iterative Proportional Fittingcited by 3
  2. 2025Variational Online Mirror Descent for Robust Learning in Schr"odinger Bridgecited by 2
  3. 2026A Unified Density Operator View of Flow Control and Mergingcited by 2
  4. 2023Information Geometry for the Working Information Theoristcited by 1
  5. 2023Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn Algorithmcited by 1
  6. 2026New Trends in the Stability of Sinkhorn Semigroupscited by 1
  7. 2026Robust Sublinear Convergence Rates for Iterative Bregman Projectionscited by 1
  8. 2026Generalized Schr"odinger Bridge on Graphscited by 1
  9. 2022Metric Distribution to Vector: Constructing Data Representation via Broad-Scale Discrepanciescited by 0
  10. 2025Linear Bandits beyond Inner Product Spaces, the case of Bandit Optimal Transportcited by 0
  11. 2025Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitycited by 0
  12. 2025Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspectivecited by 0