提出新方法，高效求解几何匹配中的广义Wasserstein问题。
Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein
- 用可学习的非线性投影器构造切片，提升匹配精度。
- 计算成本远低于现有方法，且保持几何不变性。
- 适合需要快速、精准形状匹配的研究者使用。
我们提出min广义切片Gromov-Wasserstein（min-GSGW），一种基于表达性强广义切片器的GW问题切片形式。核心思想是学习耦合的非线性切片器，使输入测度在投影域中具有相容的前向值，从而保证投影域中的单调耦合能提升为原空间中的运输方案，并直接在原始空间中评估GW目标函数。该方案诱导出一个GW目标值，min-GSGW即直接最小化此代价。我们进一步证明min-GSGW具备刚体运动不变性，这对几何匹配与形状分析任务至关重要。贡献包括：1）将广义切片器引入切片GW框架；2）构建基于切片的高效GW运输方案；3）设计一种摊销变体，以学习到的切片器替代每次实例优化。在动物网格匹配、马匹网格插值和ShapeNet部件迁移任务上实验表明，min-GSGW以显著更低的计算成本生成有意义的几何对应关系及准确的GW目标值。
原文摘要 · Abstract (English)
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.
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