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.
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: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:2602. 05600v2 Announce Type: replace Abstract: Stochastic Gradient Descent (SGD) introduces anisotropic noise that is correlated with the local curvature of the loss landscape, thereby biasing optimization toward flat minima.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
arXiv:2608. 04382v1 Announce Type: new Abstract: Gradient descent has been of particular interest in modern machine learning beyond sole focus on optimization.
arXiv:2602. 02431v2 Announce Type: replace-cross Abstract: It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning.
arXiv:2606. 20469v1 Announce Type: new Abstract: A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative.
arXiv:2606. 04031v1 Announce Type: new Abstract: Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training.
arXiv:2604. 03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs.
arXiv:2602. 02877v2 Announce Type: replace Abstract: This paper studies optimization for a family of problems termed $\textbf{compositional entropic risk minimization}$, in which each data's loss is formulated as a Log-Expectation-Exponential (Log-E-Exp) function.
arXiv:2608. 07224v1 Announce Type: new Abstract: Motivated by LLMs, which generate outputs by iteratively sampling from next-token distributions, we introduce a PAC-learning model for binary stochastic autoregressive learning.
arXiv:2607. 12360v1 Announce Type: new Abstract: The cooldown phase of a warmup-stable-decay (WSD) learning-rate schedule, now a default in large-model pretraining, lowers the final training loss in some settings and does nothing in others.