SinkSLOT: Sinkhorn via Sparse Lifted Optimal Transport

2026-08-28

AI Summary

本文提出SinkSLOT方法，通过稀疏提升的运输计划解决大规模数据集上熵最优传输计算效率低和独立耦合问题。

Abstract

Entropic optimal transport (EOT) has been shown to offer a computationally tractable approximation to exact optimal transport. However, the standard Sinkhorn-Knopp algorithm has two main limitations. First, given discrete measures with $N$ points, each iteration requires $O(N^2)$ operations, which restricts its use on large-scale datasets (e.g. $N\geq10^4$). Second, it uses the independent coupling as a reference measure for regularisation. This assigns mass to high-cost transport edges at moderate regularisation strengths. We propose SinkSLOT, which addresses both limitations by putting forth the expected sliced lifted transport plan as a natural way to sparsify the Gibbs kernel with a non-independent prior coupling. We prove that: 1) SinkSLOT converges; 2) with $L$ slices, each resulting sparse Sinkhorn iteration costs $O(LN)$; and 3) the resulting objective is a divergence requiring no debiasing. Experiments on synthetic benchmarks show that SinkSLOT delivers substantial speedups over state-of-the-art dense and sparse EOT methods. We also demonstrate the applicability of the proposed divergence in a gradient flow experiment. The code is publicly available at https://github.com/cai4cai/SinkSLOT.

Problem

• Entropic optimal transport
• Sinkhorn-Knopp algorithm
• large-scale datasets
• independent coupling
• sparse

Innovation

• SinkSLOT
• sparse lifted optimal transport
• expected sliced lifted transport plan
• Gibbs kernel sparsification
• computational efficiency