从统计学习角度分析对抗式最优传输方法的泛化误差，为神经网络生成模型提供理论支持。
A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers
- 基于统计学习理论，推导出对抗式二次最优传输解的泛化误差上界。
- 上界仅依赖于神经网络的常规统计与数学性质，不依赖特定数据分布。
- 适用于图像超分辨率、领域迁移等生成任务，适合研究生成模型理论的学者。
基于神经网络的最优传输（OT）是生成建模领域的新兴且富有成效的方向，已应用于领域转换、图像超分辨率、计算生物学等多个领域。其中，基于半对偶形式的对抗极小极大求解器备受关注。尽管前景广阔，这类方法在统计学习视角下的理论分析仍属空白。本文填补了这一空白，建立了由极小极大二次OT求解器恢复的近似OT映射的泛化误差上界。重要的是，所得到的上界仅依赖于所考虑函数类（神经网络）的标准统计与数学性质。虽然我们的分析聚焦于二次OT，但认为类似上界也可推广至一般OT情形，为未来研究开辟了有前景的方向。实验结果见GitHub：https://github.com/milenagazdieva/StatOT。
原文摘要 · Abstract (English)
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing OT approaches, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural nets). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for general OT case, paving the promising direction for future research. Our experimental illustrations are available online https://github.com/milenagazdieva/StatOT.
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