mlsanityData to 7 Oct 2026

Structured Optimal Transport

arXiv 1712.06199 ↗First posted 17 Dec 2017stat.ML cs.LGcited by 30

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Abstract (arXiv)

Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground metric" is limited. In this work, we develop a nonlinear generalization of (discrete) optimal transport that is able to reflect much additional structure. We demonstrate how to leverage the geometry of this new model for fast algorithms, and explore connections and properties. Illustrative experiments highlight the benefit of the induced structured couplings for tasks in domain adaptation and natural language processing.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Dec 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 4; 2023: 9; 2024: 6; 2025: 4; 2026: 2.

30 papers.

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  1. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  2. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  3. 2023CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labelscited by 17
  4. 2021Learning Generalized Gumbel-max Causal Mechanismscited by 16
  5. 2021Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solutioncited by 13
  6. 2021Re-evaluating Word Mover's Distancecited by 10
  7. 2021Hierarchical Optimal Transport for Unsupervised Domain Adaptationcited by 10
  8. 2022InfoOT: Information Maximizing Optimal Transportcited by 9
  9. 2024Accelerating Sinkhorn Algorithm with Sparse Newton Iterationscited by 9
  10. 2023Optimal Transport for Measures with Noisy Tree Metriccited by 7
  11. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  12. 2023Unbalanced Optimal Transport for Unbalanced Word Alignmentcited by 6
18 more
  1. 2022Mirror Sinkhorn: Fast Online Optimization on Transport Polytopescited by 5
  2. 2021Order Constraints in Optimal Transportcited by 4
  3. 2024Submodular Framework for Structured-Sparse Optimal Transportcited by 4
  4. 2025Distance-Based Tree-Sliced Wasserstein Distancecited by 4
  5. 2022Improving word mover's distance by leveraging self-attention matrixcited by 3
  6. 2024A Sinkhorn-type Algorithm for Constrained Optimal Transportcited by 3
  7. 2023OT-Net: A Reusable Neural Optimal Transport Solvercited by 2
  8. 2024What is the Right Notion of Distance between Predict-then-Optimize Tasks?cited by 2
  9. 2025Wasserstein Distances Made Explainable: Insights Into Dataset Shifts and Transport Phenomenacited by 2
  10. 2026An Improved Last-Iterate Convergence Rate for Anchored Gradient Descent Ascentcited by 2
  11. 2022Fully Probabilistic Design for Optimal Transportcited by 1
  12. 2024Optimal Transportation by Orthogonal Coupling Dynamicscited by 1
  13. 2023Safe Screening for Unbalanced Optimal Transportcited by 0
  14. 2023Robust Graph Matching Using An Unbalanced Hierarchical Optimal Transport Frameworkcited by 0
  15. 2023Geometry-Aware Normalizing Wasserstein Flows for Optimal Causal Inferencecited by 0
  16. 2025Many-to-Many Matching via Sparsity Controlled Optimal Transportcited by 0
  17. 2025Bispectral OT: Dataset Comparison using Symmetry-Aware Optimal Transportcited by 0
  18. 2026Optimal Transport under Group Fairness Constraintscited by 0