arXiv Machine Learning

Homogenization of $\ell_2$-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent

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 Machine Learning
Jul 7

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).

By Steffen Dereich, Arnulf Jentzen, Adrian Riekert
arXiv Machine Learning
Jul 14

Exact Dynamics of Multi-class Stochastic Gradient Descent

arXiv:2510. 14074v2 Announce Type: replace-cross Abstract: We develop a framework for analyzing the learning dynamics of high-dimensional problems trained using one-pass stochastic gradient descent (SGD) with data from multiple anisotropic classes.

By Elizabeth Collins-Woodfin, Inbar Seroussi
arXiv Machine Learning
Jul 30

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent

arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.

By Junyu Zhou, Puyu Wang, Dennis Wagner, Yunwen Lei, Marius Kloft, Yiming Ying
arXiv Machine Learning
Jun 3

Data- and Variance-dependent Regret Bounds for Online Tabular MDPs

arXiv:2602. 01903v2 Announce Type: replace Abstract: This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime.

By Mingyi Li, Taira Tsuchiya, Kenji Yamanishi
arXiv AI
Jul 7

Machine Unlearning via Information Theoretic Regularization

arXiv:2502. 05684v5 Announce Type: replace-cross Abstract: How can we effectively remove or ``unlearn'' undesirable information, such as specific features or the influence of individual data points, from a learning outcome while minimizing utility loss and ensuring rigorous guarantees?

By Shizhou Xu, Thomas Strohmer