mlsanityData to 13 Oct 2026

The derivatives of Sinkhorn-Knopp converge

arXiv 2207.12717 ↗First posted 26 Jul 2022math.OC stat.MLcited by 9

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Abstract (arXiv)

We show that the derivatives of the Sinkhorn-Knopp algorithm, or iterative proportional fitting procedure, converge towards the derivatives of the entropic regularization of the optimal transport problem with a locally uniform linear convergence rate.

Key facts. Cited by 9 papers in the map (data through 13 Oct 2026). Builds on 13 of its 35 references that are in the map. First posted on arXiv 26 Jul 2022.

Builds on

13 of 35 references.

References · 13

  1. 2020Unsupervised Learning of Visual Features by Contrasting Cluster Assignmentscited by 2,850
  2. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,295
  3. 2018Computational Optimal Transportcited by 772
  4. 2017Learning Generative Models with Sinkhorn Divergencescited by 311
  5. 2019Optimizing Millions of Hyperparameters by Implicit Differentiationcited by 303
  6. 2019Differentiable Ranks and Sorting using Optimal Transportcited by 113
  7. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 98
  8. 2018Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distancecited by 56
  9. 2022A Unified Framework for Implicit Sinkhorn Differentiationcited by 28
  10. 2022Automatic differentiation of nonsmooth iterative algorithmscited by 25
  11. 2019Automatic Differentiation of Some First-Order Methods in Parametric Optimizationcited by 18
  12. 2022Rethinking Initialization of the Sinkhorn Algorithmcited by 14
1 more
  1. 2020Supervised Quantile Normalization for Low-rank Matrix Approximationcited by 3

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 1; 2026: 5.

9 papers.

  1. 2023One-step differentiation of iterative algorithmscited by 28
  2. 2023Neural Schr"odinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assemblycited by 10
  3. 2024Automatic Differentiation of Optimization Algorithms with Time-Varying Updatescited by 1
  4. 2025Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modescited by 1
  5. 2026Optimal Transport under Group Fairness Constraintscited by 0
  6. 2026Understanding the Curse of Unrollingcited by 0
  7. 2026Block-Wise Differentiable Sinkhorn Attention: Tail-Refinement Gradients with a Gap-Aware Dustbin Bridgecited by 0
  8. 2026Convergence of empirical subgradients for optimal transport-based objectivescited by 0
  9. 2026Support Topology and Gradient Mixing in Sinkhorn Layerscited by 0