arXiv:2607. 27995v2 Announce Type: replace-cross Abstract: Adversarial training can improve the robustness of predictive models to bounded perturbations, often at the cost of statistical efficiency.
By Yiling Xie, Xiaoming Huo
arXiv:2605. 29497v2 Announce Type: replace Abstract: We study the problem of robustly learning Gaussian Single Index Models (SIMs) in the presence of heavy-tailed noise and a constant fraction of adversarially corrupted covariates and responses.
By Santanu Das, Sagnik Chatterjee, Jatin Batra
arXiv:2607. 27995v1 Announce Type: cross Abstract: Adversarial training has emerged as a powerful approach for protecting models against adversarial attacks in a broad range of real-world applications.
By Yiling Xie, Xiaoming Huo
arXiv:2609.23688v1 Announce Type: new
Abstract: We study norm-constrained linear classification under Eu clidean adversarial perturbations in a Gaussian model with a low-dimen sional informative subs...
By Kunyu Wang, Dehan Wang, Wenjun Chen
The paper revisits median‑of‑means estimation from a deterministic optimization perspective, introducing a family of block‑Lp estimators (for 0 < p ≤ 1) that achieve robust learning with heavy‑tailed and adversarially corrupted data. It shows that any convex block M‑estimator cannot attain the trimmed‑block oracle constant, while the nonconvex block‑Lp family provides finite‑sample robustness bounds that approach this oracle constant as p decreases. The authors also prove that the block‑Lp objectives have a benign landscape—every local minimum is close to the true parameter—and combine these results with block‑level concentration to obtain sub‑Gaussian deviation bounds under finite 2+δ moments, extending to high‑dimensional robust mean estimation and sparse regression.
By Angshul Majumdar
arXiv:2609. 39449v1 Announce Type: new Abstract: Distributionally robust optimization (DRO) studies parameter estimation under uncertainty in the underlying probability distribution and has emerged as a principled framework for analyzing robustness and generalization.
By Elis Stefansson, David V\"avinggren, Ant\^onio H. Ribeiro