Efficient Transferable Optimal Transport via Min-Sliced Transport Plans

Optimal Transport (OT) plans provide correspondences between distributions supporting alignment tasks in various domains. Sliced transport plans have been recently proposed as a computationally efficient alternative to OT plans. These methods optimize a one-dimensional projection (slice) to obtain a conditional transport plan that minimizes the transport cost in the ambient space. Despite their efficiency, it remains unclear whether learned slicers transfer to new distribution pairs under shift, an issue central to evolving data and repeated OT computations over related distributions. We study the min-Sliced Transport Plan (min-STP) framework and examine slicer transferability: can a slicer learned on one distribution pair produce effective transport plans for 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 and image analysis. Our code is available at https://anonymous.4open.science/r/Min-STP-CF74.