mlsanityData to 14 Oct 2026

Sliced Gromov-Wasserstein

arXiv 1905.10124 ↗First posted 24 May 2019stat.ML cs.LGcited by 66

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Abstract (arXiv)

Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance requires solving a complex non convex quadratic program which is most of the time very costly both in time and memory. Contrary to GW, the Wasserstein distance (W) enjoys several properties (e.g. duality) that permit large scale optimization. Among those, the solution of W on the real line, that only requires sorting discrete samples in 1D, allows defining the Sliced Wasserstein (SW) distance. This paper proposes a new divergence based on GW akin to SW. We first derive a closed form for GW when dealing with 1D distributions, based on a new result for the related quadratic assignment problem. We then define a novel OT discrepancy that can deal with large scale distributions via a slicing approach and we show how it relates to the GW distance while being O(nlog(n)) to compute. We illustrate the behavior of this so called Sliced Gromov-Wasserstein (SGW) discrepancy in experiments where we demonstrate its ability to tackle similar problems as GW while being several order of magnitudes faster to compute.

Key facts. Cited by 66 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 May 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 16; 2022: 12; 2023: 10; 2024: 7; 2025: 8; 2026: 13.

66 papers.

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  1. 2021Minibatch optimal transport distances; analysis and applicationscited by 65
  2. 2022The Schr"odinger Bridge between Gaussian Measures has a Closed Formcited by 63
  3. 2021Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costscited by 61
  4. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 46
  5. 2021Accurate Point Cloud Registration with Robust Optimal Transportcited by 38
  6. 2021The Right to Talk: An Audio-Visual Transformer Approachcited by 33
  7. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  8. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  9. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  10. 2021Quantized Gromov-Wassersteincited by 19
  11. 2023Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transportcited by 15
  12. 2021Entropy Partial Transport with Tree Metrics: Theory and Practicecited by 13
38 more
  1. 2022OTAdapt: Optimal Transport-based Approach For Unsupervised Domain Adaptationcited by 12
  2. 2022Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsificationcited by 11
  3. 2023A Convergent Single-Loop Algorithm for Relaxation of Gromov-Wasserstein in Graph Datacited by 11
  4. 2021Reversible Gromov-Monge Sampler for Simulation-Based Inferencecited by 10
  5. 2023Semidefinite Relaxations of the Gromov-Wasserstein Distancecited by 10
  6. 2021Robust W-GAN-Based Estimation Under Wasserstein Contaminationcited by 9
  7. 2022Auto-regressive Image Synthesis with Integrated Quantizationcited by 9
  8. 2025A Novel Sliced Fused Gromov-Wasserstein Distancecited by 9
  9. 2023Lidar Upsampling with Sliced Wasserstein Distancecited by 8
  10. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  11. 2025Geometry-Preserving Encoder/Decoder in Latent Generative Modelscited by 6
  12. 2021Sliced Multi-Marginal Optimal Transportcited by 5
  13. 2021Cycle Consistent Probability Divergences Across Different Spacescited by 5
  14. 2022Unsupervised Manifold Alignment with Joint Multidimensional Scalingcited by 5
  15. 2024On Probabilistic Embeddings in Optimal Dimension Reductioncited by 5
  16. 2026Structure-Centric Graph Foundation Model via Geometric Basescited by 5
  17. 2021Subspace Detours Meet Gromov-Wassersteincited by 4
  18. 2023Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Spacecited by 4
  19. 2022MoReL: Multi-omics Relational Learningcited by 3
  20. 2022Orthogonal Gromov-Wasserstein Discrepancy with Efficient Lower Boundcited by 3
  21. 2023Discriminative Radial Domain Adaptationcited by 3
  22. 2023CROVIA: Seeing Drone Scenes from Car Perspective via Cross-View Adaptationcited by 3
  23. 2023Monotone Generative Modeling via a Gromov-Monge Embeddingcited by 3
  24. 2024Relative Translation Invariant Wasserstein Distancecited by 3
  25. 2021Sketching Merge Trees for Scientific Data Visualizationcited by 2
  26. 2021Alignment and Comparison of Directed Networks via Transition Couplings of Random Walkscited by 2
  27. 2024Fast Gradient Computation for Gromov-Wasserstein Distancecited by 2
  28. 2024Improving Hyperbolic Representations via Gromov-Wasserstein Regularizationcited by 2
  29. 2024Privacy without Noisy Gradients: Slicing Mechanism for Generative Model Trainingcited by 2
  30. 2025An in depth look at the Procrustes-Wasserstein distance: properties and barycenterscited by 2
  31. 2021Heterogeneous Wasserstein Discrepancy for Incomparable Distributionscited by 1
  32. 2021A Regularized Wasserstein Framework for Graph Kernelscited by 1
  33. 2022Fast and Provably Convergent Algorithms for Gromov-Wasserstein in Graph Datacited by 1
  34. 2024LaCoOT: Layer Collapse through Optimal Transportcited by 1
  35. 2025Transfer Learning on Edge Connecting Probability Estimation under Graphon Modelcited by 1
  36. 2026Sliced Inner Product Gromov-Wasserstein Distancescited by 1
  37. 2021Incentive Compatible Pareto Alignment for Multi-Source Large Graphscited by 0
  38. 2022k-Sliced Mutual Information: A Quantitative Study of Scalability with Dimensioncited by 0

50 most cited of 66 All 66 (JSON)