The paper analyzes Gradient Descent (GD) on a minimal binary classification problem with a two‑neuron ReLU network trained on two instances. It proves that GD converges to an optimal robustness margin—maximizing the distance between the decision boundary and training points—but does so at a very slow rate, specifically θ(1/ln(t)). Empirical simulations confirm this slow convergence across various initializations, and the authors provide a rigorous analysis of GD trajectories across different activation patterns to establish the first explicit lower bound on robustness convergence in a non‑linear model.
By Guy Smorodinsky, Sveta Gimpleson, Itay Safran
arXiv:2607. 00207v1 Announce Type: cross Abstract: We develop a framework for analyzing the learning dynamics of $\ell_2$-adversarial training of single-index models on Gaussian mixtures in the high-dimensional limit under streaming stochastic gradient descent (SGD).
By Fabrizzio Sabelli
arXiv:2602.10971v3 Announce Type: replace
Abstract: We consider heteroskedastic generalized linear bandits (GLBs) with adversarial corruptions and propose \texttt{HCW-GLB-OMD}, a simple algorithm tha...
By Sanghwa Kim, Junghyun Lee, Se-Young Yun
arXiv:2606. 27685v1 Announce Type: cross Abstract: Pervasive data contamination -- stemming from measurement errors, outliers, or adversarial corruption -- has motivated the development of robust statistical methods.
By Shixiang Liu, Hanming Yang
arXiv:2605. 28335v2 Announce Type: replace Abstract: Federated Learning (FL) enables multiple clients to collaboratively train models without sharing raw data, but it is highly vulnerable to Byzantine attacks.
By Shiyuan Zuo, Jiashuo Li, Rongfei Fan, Han Hu, Jie Xu
arXiv:2607. 03075v1 Announce Type: new Abstract: Safety-critical applications require classifiers that are both robust and reliable.
By Nicolas Sournac, Ahmed Baha Ben Jmaa, Bertrand Braeckeveldt
The paper introduces MS‑WDRO, a multi‑source Wasserstein distributionally robust optimization framework for reconstructing complex network topologies from scarce target‑domain data and abundant heterogeneous source data. It fuses sources via a weighted Wasserstein barycenter, builds an ambiguity set around it, and solves a regularized Laplacian estimator using a provably convergent ADMM scheme. The authors provide finite‑sample guarantees, demonstrate that naive aggregation is suboptimal, and show through experiments on synthetic data and the ABIDE I neuroimaging dataset that MS‑WDRO outperforms seven baselines in graph recovery, sample efficiency, and diagnostic utility, especially when target samples are limited.
By Chuansen Peng, Yifan Xia, Jinshan Zhong, Xiaojing Shen
arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
By Raziyeh Takbiri
arXiv:2606. 04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function.
By Berk Tinaz, Changzhi Xie, Mahdi Soltanolkotabi
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
The paper introduces a federated minimax framework where the minimization variable is shared across clients while each client retains a personalized maximization variable. It proposes a projected ascent method for the personalized variables and shows that in nonconvex-concave settings it achieves a sublinear convergence rate, but in nonconvex-PL settings it suffers from a noise floor. To overcome this, the authors develop VR-SGDA, a variance‑reduced algorithm that eliminates the noise floor through a two‑timescale update scheme, and demonstrate its effectiveness on subpopulation‑robustness and NLP adversarial training tasks.
By M Yashwanth, Sharannya Ghosh, Saikiran Bulusu, Anirban Chakraborty
arXiv:2610. 23007v1 Announce Type: new Abstract: Gradient descent (GD) with large learning rates can successfully optimize neural networks even though classical smoothness-based learning rate conditions are violated.
By Quan Nguyen, Robin Yadav, Param Mody, Mark Schmidt