mlsanityData to 7 Oct 2026

Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance

arXiv 1805.11897 ↗First posted 30 May 2018stat.ML cs.LGcited by 56

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Abstract (arXiv)

Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version that is less accurate but easy to differentiate. In this work we characterize the differential properties of the original Sinkhorn distance, proving that it enjoys the same smoothness as its regularized version and we explicitly provide an efficient algorithm to compute its gradient. We show that this result benefits both theory and applications: on one hand, high order smoothness confers statistical guarantees to learning with Wasserstein approximations. On the other hand, the gradient formula allows us to efficiently solve learning and optimization problems in practice. Promising preliminary experiments complement our analysis.

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 May 2018.

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Citing papers per year: 2021: 17; 2022: 10; 2023: 5; 2024: 13; 2025: 4; 2026: 7.

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  1. 2021Sinkformers: Transformers with Doubly Stochastic Attentioncited by 136
  2. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 96
  3. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  4. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  5. 2021Sinkhorn Distributionally Robust Optimizationcited by 38
  6. 2021Low Budget Active Learning via Wasserstein Distance: An Integer Programming Approachcited by 34
  7. 2022A Unified Framework for Implicit Sinkhorn Differentiationcited by 28
  8. 2022WaterNeRF: Neural Radiance Fields for Underwater Scenescited by 28
  9. 2023One-step differentiation of iterative algorithmscited by 28
  10. 2022Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenterscited by 22
  11. 2021Bi-level Feature Alignment for Versatile Image Translation and Manipulationcited by 20
  12. 2021ST-MTL: Spatio-Temporal Multitask Learning Model to Predict Scanpath While Tracking Instruments in Robotic Surgerycited by 20
38 more
  1. 2021Adaptive Hierarchical Graph Reasoning with Semantic Coherence for Video-and-Language Inferencecited by 18
  2. 2021Learning Generalized Gumbel-max Causal Mechanismscited by 16
  3. 2022Rethinking Initialization of the Sinkhorn Algorithmcited by 14
  4. 2022Alternating Implicit Projected SGD and Its Efficient Variants for Equality-constrained Bilevel Optimizationcited by 10
  5. 2022The derivatives of Sinkhorn-Knopp convergecited by 9
  6. 2024Accelerating Sinkhorn Algorithm with Sparse Newton Iterationscited by 9
  7. 2021Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samplescited by 8
  8. 2021An Exploration of Learnt Representations of W Jetscited by 8
  9. 2021KNOT: Knowledge Distillation using Optimal Transport for Solving NLP Taskscited by 8
  10. 2024Contrasting Multiple Representations with the Multi-Marginal Matching Gapcited by 8
  11. 2021FGOT: Graph Distances based on Filters and Optimal Transportcited by 7
  12. 2024VectorPainter: Advanced Stylized Vector Graphics Synthesis Using Stroke-Style Priorscited by 7
  13. 2024A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributionscited by 7
  14. 2022Exploiting Problem Structure in Deep Declarative Networks: Two Case Studiescited by 6
  15. 2021Learning Graphon Autoencoders for Generative Graph Modelingcited by 4
  16. 2021Optimal transport with f-divergence regularization and generalized Sinkhorn algorithmcited by 4
  17. 2024Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distancescited by 4
  18. 2021Bayesian Distributional Policy Gradientscited by 3
  19. 2022Machine-Learning Compression for Particle Physics Discoveriescited by 3
  20. 2024A Sinkhorn-type Algorithm for Constrained Optimal Transportcited by 3
  21. 2024OTCXR: Rethinking Self-supervised Alignment using Optimal Transport for Chest X-ray Analysiscited by 3
  22. 2024Consistency of Neural Causal Partial Identificationcited by 3
  23. 2024Exploring Optimal Transport-Based Multi-Grained Alignments for Text-Molecule Retrievalcited by 3
  24. 2021Domain-oriented Language Pre-training with Adaptive Hybrid Masking and Optimal Transport Alignmentcited by 2
  25. 2022StreamNet: A WAE for White Matter Streamline Analysiscited by 2
  26. 2024Trade-off Between Dependence and Complexity for Nonparametric Learning -- an Empirical Process Approachcited by 2
  27. 2025Agentic Design Review Systemcited by 2
  28. 2025Enforcing convex constraints in Graph Neural Networkscited by 2
  29. 2023Memory Efficient And Minimax Distribution Estimation Under Wasserstein Distance Using Bayesian Histogramscited by 1
  30. 2023Generalized Sum Pooling for Metric Learningcited by 1
  31. 2024Differentiable Cost-Parameterized Monge Map Estimatorscited by 1
  32. 2024AdapFair: Ensuring Adaptive Fairness for Machine Learning Operationscited by 1
  33. 2024Auditing and Enforcing Conditional Fairness via Optimal Transportcited by 1
  34. 2025Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modescited by 1
  35. 2021Efficient Discretizations of Optimal Transportcited by 0
  36. 2023Optimal Transport for Kernel Gaussian Mixture Modelscited by 0
  37. 2025Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transportcited by 0
  38. 2026Post-Training Neural Network Pruning using Graph Curvaturecited by 0

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