mlsanityData to 14 Oct 2026

Sliced Inner Product Gromov-Wasserstein Distances

arXiv 2605.08546 ↗First posted 8 May 2026stat.ML cs.LG math.OCcited by 1

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Abstract (arXiv)

The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing techniques offer an appealing route to scalability, but, unlike Wasserstein distances, GW problems do not generally admit closed-form solutions in one-dimension. We resolve this problem for the GW problem with inner product cost (IGW), propose a sliced IGW distance that enjoys a natural rotational invariance property, and comprehensively study its structural and computational properties. Numerical experiments validating our theory are presented, followed by applications to heterogeneous clustering of text data and language model representation comparison.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 45 of its 89 references that are in the map. First posted on arXiv 8 May 2026.

Builds on

45 of 89 references.

References · 45

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  2. 2019Similarity of Neural Network Representations Revisitedcited by 1,755
  3. 2022MTEB: Massive Text Embedding Benchmarkcited by 640
  4. 2021Datasets: A Community Library for Natural Language Processingcited by 530
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  8. 2019Max-Sliced Wasserstein Distance and its use for GANscited by 119
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33 more
  1. 2020The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxationcited by 56
  2. 2019Asymptotic Guarantees for Learning Generative Models with the Sliced-Wasserstein Distancecited by 43
  3. 2022Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distancescited by 41
  4. 2021A gradient sampling method with complexity guarantees for Lipschitz functions in high and low dimensionscited by 39
  5. 2020On Projection Robust Optimal Transport: Sample Complexity and Model Misspecificationcited by 34
  6. 2021Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projectionscited by 33
  7. 2024Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifoldscited by 28
  8. 2019Minimax Confidence Intervals for the Sliced Wasserstein Distancecited by 24
  9. 2019Approximate Bayesian Computation with the Sliced-Wasserstein Distancecited by 22
  10. 2021Semi-relaxed Gromov-Wasserstein divergence with applications on graphscited by 21
  11. 2024Expected Sliced Transport Planscited by 19
  12. 2022Amortized Projection Optimization for Sliced Wasserstein Generative Modelscited by 17
  13. 2022On the existence of Monge maps for the Gromov-Wasserstein problemcited by 16
  14. 2020A contribution to Optimal Transport on incomparable spacescited by 15
  15. 2021Entropic Gromov-Wasserstein between Gaussian Distributionscited by 12
  16. 2022Dissolving Constraints for Riemannian Optimizationcited by 12
  17. 2023Markovian Sliced Wasserstein Distances: Beyond Independent Projectionscited by 11
  18. 2023Semidefinite Relaxations of the Gromov-Wasserstein Distancecited by 10
  19. 2024Sharp bounds for max-sliced Wasserstein distancescited by 10
  20. 2025ESPFormer: Doubly-Stochastic Attention with Expected Sliced Transport Planscited by 10
  21. 2021SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddingscited by 9
  22. 2022The cost of nonconvexity in deterministic nonsmooth optimizationcited by 9
  23. 2022On Assignment Problems Related to Gromov-Wasserstein Distances on the Real Linecited by 8
  24. 2022A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifoldcited by 7
  25. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  26. 2021Cycle Consistent Probability Divergences Across Different Spacescited by 5
  27. 2025Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distancescited by 5
  28. 2025Efficient Transferable Optimal Transport via Min-Sliced Transport Planscited by 4
  29. 2025Approximation Analysis of the Entropic Penalty in Quadratic Programmingcited by 3
  30. 2024Gradient Flows and Riemannian Structure in the Gromov-Wasserstein Geometrycited by 2
  31. 2025Constrained Sliced Wasserstein Embeddingcited by 2
  32. 2025S2WTM: Spherical Sliced-Wasserstein Autoencoder for Topic Modelingcited by 1
  33. 2025Optimal Transportation and Alignment Between Gaussian Measurescited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Averaged Mirror Descent and Dual Gradient Methods: Convergent Algorithms for Entropic Gromov-Wasserstein Problemscited by 0