The paper introduces a method for adversarial training that avoids computing input gradients by using a low‑rank Householder expansion (LRHE) to directly generate small‑norm adversarial examples from a network’s parameters. This approach requires only forward passes and standard back‑propagation, eliminating the inner maximization loop and reducing computational cost to roughly 2.8 PGD steps per epoch. The resulting models achieve comparable robustness to multi‑step PGD training for small relative ε budgets, demonstrating the feasibility of gradient‑free adversarial training.
arXiv:2505. 22578v2 Announce Type: replace Abstract: The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint.
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).
arXiv:2601. 16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks.
arXiv:2607. 28959v1 Announce Type: cross Abstract: Adversarial training is one of the most effective defenses against adversarial attacks, yet the computational cost remains prohibitive at modern scales, especially for large language models (LLMs).
arXiv:2609.06430v1 Announce Type: new Abstract: We study the identity straight-through estimator (STE) for training a two-layer binary-activation network with hinge loss from the perspective of Stati...
arXiv:2608. 03197v1 Announce Type: new Abstract: Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear.
arXiv:2607. 04145v1 Announce Type: new Abstract: Adversarial attacks guide and provide additional training and test data for both adversarial training and adversarial robustness validation, and expose the 'piecewise linearity' of deep learning based models.
arXiv:2607. 16720v1 Announce Type: new Abstract: Understanding deep neural networks remains a central challenge in machine learning.
arXiv:2510. 18989v2 Announce Type: replace Abstract: Neural operators are commonly utilized as fast surrogates for numerical solvers in PDE problems, mapping input functions to solution functions.
arXiv:2211. 14966v2 Announce Type: replace Abstract: Deep neural networks (DNNs) are highly vulnerable to adversarial attacks.
Sharpness-Aware Minimization (SAM) improves generalization by seeking parameters whose loss is robust to local adversarial perturbations, but the quantitative mechanism underlying its implicit bias toward flat minima remains unclear. In particular, the perturbation radius $ρ$ is typically treated as an isolated tuning parameter, despite defining the neighborhood in which SAM measures sharpness.
arXiv:2604. 07328v3 Announce Type: replace Abstract: How does the choice of training data influence an AI model?