Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916010157670400 |
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| author | Shahbazi, Ashkan Liu, Xinran He, Ping Kolouri, Soheil |
| author_facet | Shahbazi, Ashkan Liu, Xinran He, Ping Kolouri, Soheil |
| contents | We propose min Generalized Sliced Gromov--Wasserstein (min-GSGW), a sliced formulation for the Gromov--Wasserstein (GW) problem using expressive generalized slicers. The key idea is to learn coupled nonlinear slicers that assign compatible push-forward values to both input measures, so that monotone coupling in the projected domain lifts to a transport plan evaluated against the GW objective in the original spaces. The resulting plan induces a GW objective value, and min-GSGW minimizes this cost directly in the original spaces. We further show that min-GSGW is rigid-motion invariant, a crucial property for geometric matching and shape analysis tasks. Our contributions are threefold: 1) we introduce generalized slicers into the sliced GW framework, 2) we construct a slicing-based efficient GW transport plan; and 3) we develop an amortized variant that replaces per-instance optimization with a learned slicer for unseen input pairs. We perform experiments on animal mesh matching, horse mesh interpolation, and ShapeNet part transfer. Results show that min-GSGW produces meaningful geometric correspondences and GW objective values at substantially lower computational cost than existing GW solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein Shahbazi, Ashkan Liu, Xinran He, Ping Kolouri, Soheil Machine Learning Computer Vision and Pattern Recognition We propose min Generalized Sliced Gromov--Wasserstein (min-GSGW), a sliced formulation for the Gromov--Wasserstein (GW) problem using expressive generalized slicers. The key idea is to learn coupled nonlinear slicers that assign compatible push-forward values to both input measures, so that monotone coupling in the projected domain lifts to a transport plan evaluated against the GW objective in the original spaces. The resulting plan induces a GW objective value, and min-GSGW minimizes this cost directly in the original spaces. We further show that min-GSGW is rigid-motion invariant, a crucial property for geometric matching and shape analysis tasks. Our contributions are threefold: 1) we introduce generalized slicers into the sliced GW framework, 2) we construct a slicing-based efficient GW transport plan; and 3) we develop an amortized variant that replaces per-instance optimization with a learned slicer for unseen input pairs. We perform experiments on animal mesh matching, horse mesh interpolation, and ShapeNet part transfer. Results show that min-GSGW produces meaningful geometric correspondences and GW objective values at substantially lower computational cost than existing GW solvers. |
| title | Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2605.13753 |