arXiv:2606. 00442v1 Announce Type: new Abstract: Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks.
arXiv:2607. 09967v1 Announce Type: cross Abstract: Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps.
arXiv:2610.02182v1 Announce Type: cross Abstract: Quasi-Newton (QN) methods have long been among the most effective methods for large-scale unconstrained convex optimization. Two obstacles have limit...
arXiv:2510. 18784v3 Announce Type: replace Abstract: Despite significant work on low-bit quantization-aware training (QAT), there is still an accuracy gap between such techniques and native training.
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.
arXiv:2605. 09075v2 Announce Type: replace-cross Abstract: Although the Laplace approximation offers a simple route to uncertainty quantification in deep neural networks, its reliance on inverting large Hessian matrices has motivated a range of computationally feasible low-dimensional or sparse approximations.
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).
arXiv:2606. 04662v1 Announce Type: cross Abstract: Muon improves training efficiency over Adam in large language-model training by about two times, but the local geometric source of this advantage remains unclear.
arXiv:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.
arXiv:2602. 00329v4 Announce Type: replace-cross Abstract: Reliable data attribution is essential for mitigating bias and reducing computational waste in modern machine learning, with the Shapley value serving as the theoretical gold standard.
The paper presents an exact, information‑theoretic analysis of stochastic gradient descent (SGD) and its variants, showing that a preconditioned SGD step corresponds to a posterior‑mean update in a Gaussian Bayes model. It decomposes one‑step regret into an intrinsic‑time cost and a change in comparator information, extending this split to an identity for the objective itself. The framework links convex convergence, saddle‑point escape, flatness‑generalization trade‑offs, learning‑rate schedules, adaptive optimizers, and various SGD variants, and it is validated on synthetic and real training runs, revealing how different optimizers achieve the same training loss through distinct step characteristics.
arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.
arXiv:2606. 06772v1 Announce Type: cross Abstract: Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory.