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该论文提出带误差证书的Sliced Wasserstein草图方法，通过一维最优加权MM-原子量化并扩展到高维切片，将平方距离误差精确分解为残差与分区不匹配项，从而为任意质心草图提供可计算的误差保证，在文档、点云和流式细胞术基准上以更少存储保持了原始切片距离的分类性能。
该论文提出垂直切片Wasserstein距离(VSW)，一种用于比较meta-measures（分布的分布）的可扩展度量，证明其为有效度量并具有维度无关的统计收敛保证，在效率和精度上优于现有方法。
Introduces TopoTuner, a topology-guided fine-tuning framework that selectively freezes attention projection matrices by measuring topological drift via Wasserstein distances between persistence diagrams. It achieves competitive performance to full fine-tuning while training only 1-2% of parameters and outperforms LoRA in most settings.
Proposes learned predictive ambiguity sets (LPAS) for distributionally robust optimization, where a deep contextual model outputs a nominal scenario distribution, state-dependent Wasserstein radius, and ground metric, trained with decision loss and calibration. Applied to portfolio optimization on S&P 500 data, the method achieves higher returns and Sharpe ratio with reduced conservatism compared to fixed-radius baselines.