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: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. 24616v4 Announce Type: replace-cross Abstract: For four decades statistical physics has been providing a framework to analyse neural networks.
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. 05599v1 Announce Type: new Abstract: This paper establishes a theoretical framework for the uniform convergence of smoothly activated deep neural network (DNN) estimators.
arXiv:2606. 04409v1 Announce Type: cross Abstract: Modern deep neural networks usually have large parameter scales and nonlinear hierarchical structures, and they have achieved strong performance in computer vision.
arXiv:2606. 21497v2 Announce Type: replace-cross Abstract: Modern deep neural networks are trained using error backpropagation, which requires sequential forward and backward computations across network layers.
arXiv:2607. 23397v1 Announce Type: new Abstract: Hierarchical neural networks are widely used in artificial intelligence, yet their mathematical properties remain incompletely understood.
arXiv:2106. 06998v5 Announce Type: replace Abstract: Training convolutional neural networks at scale demands substantial memory, largely because intermediate activations must be stored for backpropagation.
arXiv:2606. 09658v1 Announce Type: cross Abstract: Muon has recently emerged as a state-of-the-art optimizer for pretraining Large Language Models (LLMs) and vision classifiers.
arXiv:2602. 06245v2 Announce Type: replace-cross Abstract: Neural-network techniques are often transferred across architecture families by analogy, but such transfer is valid only when the assumptions required by a technique are preserved.
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.