The paper studies a variant of stochastic gradient descent called SGDIR, which incorporates initial regularization. It derives dimension‑free upper bounds on the expected excess risk for the squared loss, providing new rates for both averaged and non‑averaged SGDIR under various assumptions. The authors also establish matching lower bounds in certain regimes and compare SGDIR to ridge regression in noisy settings, showing comparable performance up to a polylogarithmic factor.
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.
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: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...
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.
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.
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...
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.
The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.
arXiv:2505.20817v3 Announce Type: replace-cross Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...
arXiv:2608.30382v1 Announce Type: new Abstract: Popular adaptive stochastic gradient descent (SGD) methods to train artificial intelligence (AI) systems include the RMSprop, the Adam, and the AdamW o...
arXiv:2602. 12471v2 Announce Type: replace Abstract: We consider the optimization problem of minimizing the logistic loss with gradient descent to train a linear model for binary classification with separable data.
arXiv:2604. 13130v2 Announce Type: replace Abstract: We study learning to learn through the lens of hyperparameter tuning.