Abstract: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.
| Subjects: | Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV) |
| Cite as: | arXiv:2605.13753 [cs.LG] |
| (or arXiv:2605.13753v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13753 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ashkan Shahbazi Mr. [view email]
[v1]
Wed, 13 May 2026 16:33:10 UTC (8,578 KB)