arXiv:2509. 17251v2 Announce Type: replace-cross Abstract: Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regression and online stochastic gradient descent (SGD) are polynomially suboptimal for certain categories of such problems.
By Jingfeng Wu, Peter L. Bartlett, Sham M. Kakade, Jason D. Lee, Bin Yu
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:2610.28561v1 Announce Type: new
Abstract: Stochastic gradient descent (SGD) is the cornerstone of modern deep learning, yet its theoretical convergence properties remain poorly understood in no...
By Gabin Maxime Nguegnang, Bubacarr Bah, Holger Rauhut, Ulrich Terstiege
arXiv:2610. 23337v1 Announce Type: new Abstract: Pretrained models are often reused across downstream tasks, motivating the question of whether this transfer learning procedure can provide a substantial performance improvement, namely, in terms of the scaling law.
By Yalda Shabanzadeh, Diyuan Wu, Marco Mondelli
The paper presents a nonasymptotic generalization theory for multilayer fully connected neural networks trained with path regularization, covering both underparameterized and overparameterized regimes without assuming bounded loss, sparsity, or width/depth limits. It explicitly models approximation error, resolves an open problem on approximation rates in generalized Barron spaces, and establishes matching upper and lower bounds that show the error curve is non‑monotone—descending, rising, then descending again—as width increases. The analysis reveals that the rise is due to shrinkage imposed by regularization rather than overfitting, and this effect cannot be eliminated by width‑independent regularization.
By Hao Yu
arXiv:2508.04860v2 Announce Type: replace-cross
Abstract: Stochastic Gradient Descent (SGD) is a cornerstone of large-scale optimization, yet its theoretical behavior under heavy-tailed noise -- comm...
By Ilyas Fatkhullin, Florian H\"ubler, Guanghui Lan