Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein

Fuente: arXiv
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Autori principali: Shahbazi, Ashkan, Liu, Xinran, He, Ping, Kolouri, Soheil
Natura: Preprint
Pubblicazione: 2026
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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