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

2026-05-13

AI Summary

This work addresses the high computational complexity and limited scalability of traditional Gromov–Wasserstein (GW) distance in large-scale geometric matching by proposing min-GSGW, a novel approach that introduces learnable nonlinear generalized slicers into the sliced GW framework for the first time. By constructing monotone couplings in the projected space and lifting them to transport plans in the original space, min-GSGW directly optimizes the GW objective while preserving invariance under rigid transformations. An amortized variant further enables efficient inference on unseen data pairs. Evaluated on tasks including animal mesh registration, horse shape interpolation, and ShapeNet part transfer, min-GSGW achieves accurate GW approximations and semantically meaningful geometric correspondences at substantially lower computational cost.

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.

Problem

• Gromov-Wasserstein
• scalability
• computational cost
• geometric matching
• sliced formulation

Innovation

• Gromov-Wasserstein
• sliced optimal transport
• generalized slicers
• amortized optimization
• geometric matching