发表机构
Sorbonne Université; King’s College London（索邦大学; 伦敦国王学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出SinkSLOT算法，通过引入非独立先验耦合的期望切片提升传输计划稀疏化Gibbs核，解决标准Sinkhorn-Knopp算法的局限，实验显示其在合成基准上加速效果显著，且所得散度可应用于梯度流实验。
AI 中文摘要
熵最优传输（EOT）已被证明能为精确最优传输提供计算上可处理的近似方法。然而，标准Sinkhorn-Knopp算法存在两个主要局限：其一，给定含N个点的离散测度时，每次迭代需要O(N²)次运算，这限制了其在大规模数据集（如N≥10⁴）上的应用；其二，该算法采用独立耦合作为正则化的参考测度，在中等正则化强度下会将质量分配给高成本传输边。我们提出SinkSLOT，通过将期望切片提升传输计划作为引入非独立先验耦合来稀疏化Gibbs核的自然方式，解决上述两个局限。我们证明：1）SinkSLOT具有收敛性；2）使用L个切片时，每次生成的稀疏Sinkhorn迭代成本为O(LN)；3）所得目标是无需去偏的散度。在合成基准上的实验表明，SinkSLOT相较于最先进的密集和稀疏EOT方法实现了显著加速，我们还在梯度流实验中验证了该散度的适用性。代码已公开于此https URL。
英文摘要
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.
