arXiv Machine Learning

Lipschitz Continuity in Deep Learning: A Systematic Review of Theoretical Foundations, Estimation Methods, Regularization Approaches, and Certifiable Robustness

arXiv:2607. 16329v1 Announce Type: cross Abstract: Lipschitz continuity is a fundamental property of neural networks that characterizes their sensitivity to input perturbations.

arXiv AI

Jul 13

Principles of Lipschitz continuity in neural networks

arXiv:2602. 04078v2 Announce Type: replace-cross Abstract: Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence.

By R\'ois\'in Luo

arXiv AI

Jun 16

Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability

arXiv:2606. 16883v1 Announce Type: cross Abstract: Generalization is a critical property of data-driven models, particularly deep learning models deployed in safety-critical applications.

By Abdul-Rauf Nuhu, Parham M. Kebria, Vahid Hemmati, Mahmoud N. Mahmoud, Edward Tunstel, Abdollah Homaifar

safety

arXiv Machine Learning

Aug 11

Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks

arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.

By Po Chen, Rujun Jiang, Peng Wang

arXiv Machine Learning

Aug 6

Robustness Emerges Early in Training Dynamics, but Is Not Preserved

arXiv:2608. 04442v1 Announce Type: new Abstract: Robustness to natural corruptions remains a fundamental challenge for deep neural networks.

By Jiangang Yang, Wenhui Shi, Lu Hu, Jing Xing, Jian Liu

computer-vision benchmarks

arXiv Machine Learning

Jun 19

Convex training of Lipschitz-regularized shallow neural networks

arXiv:2606. 19652v1 Announce Type: new Abstract: In this work, we introduce a training procedure for shallow neural networks that promotes robustness against adversarial attacks.

By Chao Yin, Antoine Lesage-Landry

safety

arXiv Machine Learning

Jul 30

Minimax-Optimal Generalization Bounds for Smooth Deep Neural Networks Trained by (Stochastic) Gradient Descent

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.

By Junyu Zhou, Puyu Wang, Dennis Wagner, Yunwen Lei, Marius Kloft, Yiming Ying

arXiv Machine Learning

Jun 5

Mitigating the Curse of Dimensionality in Uniform Convergence of Deep Neural Networks via Smooth Activations

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.

By Yizhe Ding, Runze Li, Jia Liu, Lingzhou Xue

arXiv Machine Learning

Jul 3

From Approximation to Emergence: A Theory of Deep Learning

arXiv:2607. 01311v1 Announce Type: new Abstract: Deep learning has outgrown any single mathematical explanation.

By Zhilin Zhao

llms safety

arXiv Machine Learning

Jul 23

A convergence result of a continuous model of deep learning via a \L{}ojasiewicz--Simon inequality

arXiv:2311. 15365v3 Announce Type: replace Abstract: We study an idealized training process for deep neural networks in a continuous-depth, mean-field model in which each layer is parameterized by a probability measure on a Euclidean parameter space.

By Noboru Isobe

arXiv Machine Learning

Aug 11

Generalized Convexity and Smoothness via Conjugate Duality: Optimization Theory for Deep Neural Networks

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.

By Binchuan Qi

safety

arXiv AI

Jun 8

Generalization in Deep Neural Networks: Minimax Rates for Gradient Methods

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.

By Junyu Zhou, Puyu Wang, Yunwen Lei, Marius Kloft, Yiming Ying

arXiv Machine Learning

Jun 15

Uncertainty Estimation and Generalization Bounds for Modern Deep Learning

arXiv:2606. 13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems.

By Luis A. Ortega

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