arXiv:2510. 24616v4 Announce Type: replace-cross Abstract: For four decades statistical physics has been providing a framework to analyse neural networks.
arXiv:2505. 24849v2 Announce Type: replace-cross Abstract: For three decades statistical mechanics has been providing a framework to analyse neural networks.
Over the past decade, deep neural networks (DNNs) have achieved remarkable success on complex machine-learning tasks, yet the theoretical foundations of their performance remain incomplete. From a statistical viewpoint, a natural question is: can DNNs attain feature-learning and prediction consistency comparable to that of classical models?
arXiv:2501. 18530v3 Announce Type: replace-cross Abstract: We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional.
arXiv:2311. 02960v5 Announce Type: replace Abstract: Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data.
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.
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:2503. 07325v2 Announce Type: replace Abstract: Understanding and certifying the behavior of modern deep neural networks remains a fundamental challenge in reliable machine learning.
arXiv:2510. 02779v4 Announce Type: replace Abstract: Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks.
arXiv:2606. 05599v1 Announce Type: new Abstract: This paper establishes a theoretical framework for the uniform convergence of smoothly activated deep neural network (DNN) estimators.
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
arXiv:2607. 16720v1 Announce Type: new Abstract: Understanding deep neural networks remains a central challenge in machine learning.
arXiv:2606. 04583v1 Announce Type: new Abstract: Many researchers investigated neural networks with some of their weights fixed to values randomly drawn from a given distribution, e.