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

TL;DR

This paper introduces min-GSGW, a scalable sliced approach to Gromov--Wasserstein that learns nonlinear slicers for efficient geometric matching and shape analysis.

Contribution

It integrates generalized slicers into the GW framework, enabling efficient transport plan computation and an amortized variant for unseen data.

Findings

Produces meaningful geometric correspondences

Achieves lower computational cost than existing GW solvers

Effective in shape matching and transfer tasks

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.