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.

翻译：我们提出最小广义切片格罗莫夫-瓦瑟斯坦距离（min-GSGW），这是一种利用表达性广义切片器对格罗莫夫-瓦瑟斯坦（GW）问题进行切片化处理的新方法。其核心思想是学习耦合的非线性切片器，为两个输入测度分配相容的推前值，从而使得投影域中的单调耦合能够提升为对原始空间中GW目标函数进行评估的传输计划。由此产生的计划诱导出一个GW目标值，而min-GSGW直接在原始空间中最小化该成本。我们进一步证明min-GSGW具有刚体运动不变性，这是几何匹配与形状分析任务中的关键性质。我们的贡献包括三个方面：1）将广义切片器引入切片化GW框架；2）构建基于切片的高效GW传输计划；3）开发一种摊销变体，用学习的切片器替代针对未见输入对的逐实例优化。我们在动物网格匹配、马网格插值和ShapeNet部件迁移上开展实验。结果表明，与现有GW求解器相比，min-GSGW在显著更低的计算成本下即可产生有意义的几何对应关系和GW目标值。