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

arXiv: https://arxiv.org/abs/2605.13753 · HTML: https://mlsanity.com/paper/2605.13753/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 15 of 15)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Sliced Gromov-Wasserstein](https://mlsanity.com/paper/1905.10124/) (2019)
- [Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs](https://mlsanity.com/paper/2106.01128/) (2021)
- [Orthogonal Estimation of Wasserstein Distances](https://mlsanity.com/paper/1903.03784/) (2019)
- [Quantized Gromov-Wasserstein](https://mlsanity.com/paper/2104.02013/) (2021)
- [Expected Sliced Transport Plans](https://mlsanity.com/paper/2410.12176/) (2024)
- [On the existence of Monge maps for the Gromov-Wasserstein problem](https://mlsanity.com/paper/2210.11945/) (2022)
- [LapSum -- One Method to Differentiate Them All: Ranking, Sorting and Top-k Selection](https://mlsanity.com/paper/2503.06242/) (2025)
- [Semidefinite Relaxations of the Gromov-Wasserstein Distance](https://mlsanity.com/paper/2312.14572/) (2023)
- [On Assignment Problems Related to Gromov-Wasserstein Distances on the Real Line](https://mlsanity.com/paper/2205.09006/) (2022)
- [Differentiable Generalized Sliced Wasserstein Plans](https://mlsanity.com/paper/2505.22049/) (2025)
- [Efficient Transferable Optimal Transport via Min-Sliced Transport Plans](https://mlsanity.com/paper/2511.19741/) (2025)

## Abstract (arXiv)

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.