Optimal Transport (OT) offers a powerful framework for finding correspondences between distributions and addressing matching and alignment problems in various areas of computer vision, including shape analysis, image generation, and multimodal tasks. The computation cost of OT, however, hinders its scalability. Slice-based transport plans have recently shown promise for reducing the computational cost by leveraging the closed-form solutions of 1D OT problems. These methods optimize a one-dimensional projection (slice) to obtain a conditional transport plan that minimizes the transport cost in the ambient space. While efficient, these methods leave open the question of whether learned optimal slicers can transfer to new distribution pairs under distributional shift. Understanding this transferability is crucial in settings with evolving data or repeated OT computations across closely related distributions. In this paper, we study the min-Sliced Transport Plan (min-STP) framework and investigate the transferability of optimized slicers: can a slicer trained on one distribution pair yield effective transport plans for new, unseen pairs? Theoretically, we show that optimized slicers remain close under slight perturbations of the data distributions, enabling efficient transfer across related tasks. To further improve scalability, we introduce a minibatch formulation of min-STP and provide statistical guarantees on its accuracy. Empirically, we demonstrate that the transferable min-STP achieves strong one-shot matching performance and facilitates amortized training for point cloud alignment and flow-based generative modeling.

翻译：最优传输（Optimal Transport，OT）为寻找分布间的对应关系以及解决计算机视觉中形状分析、图像生成和多模态任务等领域的匹配与对齐问题提供了一个强大的框架。然而，OT的计算成本限制了其可扩展性。基于切片的传输计划最近通过利用一维OT问题的闭式解，在降低计算成本方面显示出潜力。这些方法通过优化一维投影（切片）来获得条件传输计划，从而最小化环境空间中的传输成本。尽管高效，但这些方法尚未解决在分布偏移下，学习到的最优切片器能否迁移到新分布对的问题。理解这种可迁移性在数据不断演化或需要在密切相关的分布间重复进行OT计算的场景中至关重要。本文研究了最小切片传输计划（min-Sliced Transport Plan，min-STP）框架，并探讨了优化切片器的可迁移性：在一个分布对上训练的切片器能否为新的、未见过的分布对产生有效的传输计划？理论上，我们证明在数据分布轻微扰动下，优化的切片器保持接近，从而能够在相关任务间实现高效迁移。为进一步提升可扩展性，我们引入了min-STP的小批量公式，并提供了其准确性的统计保证。实证结果表明，可迁移的min-STP在点云对齐和基于流的生成建模中实现了强大的一次性匹配性能，并促进了摊销训练。