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Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transport

arXiv · AI, language, vision and robotics · article · Sep 4, 2026 · UTC

The purpose of this paper is to rigorously quantify the statistical and learning-theoretic properties of adversarial training models for classification. Equivalently, we establish the statistical properties of empirical optimal partial transport. Precisely, first we provide two types of central limit theorems (CLT): CLT centered at the expected empirical value, and CLT centered at the population one with smoothing. These results are based on the uniqueness of optimal potential for various equivalent optimal transport formulations, and the empirical process theory argument. For the binary setti

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