mlsanityData to 14 Oct 2026

Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms

arXiv 2608.11016 ↗First posted 11 Aug 2026math.OC cs.CG cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

Clustering is a fundamental class of data analysis techniques with the most important representatives being centroid-based methods like k-means. Such methods are strongly connected to quantization problems, which aim to approximate general probability measures with discrete ones. For example, k-means corresponds to quantization with respect to the Wasserstein distance. While Wasserstein quantization clusters points within a fixed space, this paper studies Gromov-Wasserstein (GW) quantization, which additionally aims at clustering the ambient geometry of the space. We show existence of solutions to the GW quantization problem and give a characterization that justifies an analogue to the k-means algorithm (Lloyd's algorithm) to approximate them numerically. We further calculate the quantization rate for usual Euclidean geometries that are used in the GW context, and relate it to standard Wasserstein quantization rates. Finally, numerical experiments show that GW quantization opens up many modeling possibilities beyond normal clustering methods (e.g., for geodesic distances of 3D shapes or structured pruning of neural networks) and that the introduced algorithm leads to useful numerical solutions with approximation quality often in line with theoretically optimal rates.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 37 of its 78 references that are in the map. First posted on arXiv 11 Aug 2026.

Builds on

37 of 78 references.

References · 37

  1. 2021Convex optimizationcited by 2,515
  2. 2016Pruning Filters for Efficient ConvNetscited by 1,143
  3. 2023A Simple and Effective Pruning Approach for Large Language Modelscited by 800
  4. 2021Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networkscited by 527
  5. 2019Model Fusion via Optimal Transportcited by 219
  6. 2013Fast Computation of Wasserstein Barycenterscited by 216
  7. 2019Gromov-Wasserstein Learning for Graph Matching and Node Embeddingcited by 126
  8. 2018Gromov-Wasserstein Alignment of Word Embedding Spacescited by 122
  9. 2019Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matchingcited by 103
  10. 2018Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical propertiescited by 93
  11. 2019Sliced Gromov-Wassersteincited by 66
  12. 2021Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costscited by 61
25 more
  1. 2020The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxationcited by 56
  2. 2020Generalized Spectral Clustering via Gromov-Wasserstein Learningcited by 38
  3. 2021Online Graph Dictionary Learningcited by 37
  4. 2019A Unifying Framework for Spectrum-Preserving Graph Sparsification and Coarseningcited by 31
  5. 2019Gromov-Wasserstein Factorization Models for Graph Clusteringcited by 25
  6. 2021Quantized Gromov-Wassersteincited by 19
  7. 2021On a linear Gromov-Wasserstein distancecited by 17
  8. 2022On the existence of Monge maps for the Gromov-Wasserstein problemcited by 16
  9. 2023A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarseningcited by 15
  10. 2025Neural Pruning for 3D Scene Reconstruction: Efficient NeRF Accelerationcited by 10
  11. 2019Gromov-Wasserstein Averaging in a Riemannian Frameworkcited by 9
  12. 2022Multi-Marginal Gromov-Wasserstein Transport and Barycenterscited by 9
  13. 2025A Novel Sliced Fused Gromov-Wasserstein Distancecited by 9
  14. 2022On Assignment Problems Related to Gromov-Wasserstein Distances on the Real Linecited by 8
  15. 2020From Optimal Transport to Discrepancycited by 7
  16. 2023Globally solving the Gromov-Wasserstein problem for point clouds in low dimensional Euclidean spacescited by 7
  17. 2018Sketching and Clustering Metric Measure Spacescited by 5
  18. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  19. 2019Curve Based Approximation of Measures on Manifolds by Discrepancy Minimizationcited by 4
  20. 2026Gromov-Wasserstein at Scale, Beyond Squared Normscited by 4
  21. 2024Tangential Fixpoint Iterations for Gromov-Wasserstein Barycenterscited by 3
  22. 2024On the sequential convergence of Lloyd's algorithmscited by 3
  23. 2025Gromov-Wasserstein Graph Coarseningcited by 2
  24. 2025Asymptotics of the quantization problem on metric measure spacescited by 1
  25. 2026Partial Fusion of Neural Networks: Efficient Tradeoffs Between Ensembles and Weight Aggregationcited by 1

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2025Slicing the Gaussian Mixture Wasserstein Distance
  2. 2024Robust Clustering on High-Dimensional Data with Stochastic Quantization
  3. 2025Quantization-based Bounds on the Wasserstein Metric
  4. 2026Multi-Domain Clustering via Measure Quantization
  5. 2025Weighted quantization using MMD: From mean field to mean shift via gradient flows
  6. 2025Kernel k-Medoids as General Vector Quantization
  7. 2023Soft Quantization using Entropic Regularization
  8. 2026Distributionally Robust K-Means Clustering