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A Polyak-Ruppert Central Limit Theorem for SA-Adam with Momentum and Non-Convergent Adaptive Preconditioning
Sunyoung An, Xiaoming Huo
Adaptive optimizers combining preconditioning, momentum, and weight decay (Adam and AdamW) are, under Polyak-Ruppert averaging, candidate engines for one-pass inference. Does the a…
When Does Dynamic Preconditioning Preserve the Polyak-Ruppert CLT? A Stabilization Threshold
Sunyoung An, Xiaoming Huo
Polyak-Ruppert averaging yields an asymptotically normal estimator with sandwich covariance , the foundation of online inference. When the gradient step is precondit…
High-dimensional (Group) Adversarial Training in Linear Regression
Yiling Xie, Xiaoming Huo
Adversarial training can achieve robustness against adversarial perturbations and has been widely used in machine learning models. This paper delivers a non-asymptotic consistency…
Asymptotic Behavior of Adversarial Training Estimator under -Perturbation
Yiling Xie, Xiaoming Huo
Adversarial training has been proposed to protect machine learning models against adversarial attacks. This paper focuses on adversarial training under -perturbation,…