arXiv:2607. 16329v1 Announce Type: cross Abstract: Lipschitz continuity is a fundamental property of neural networks that characterizes their sensitivity to input perturbations.
By R\'ois\'in Luo, James McDermott, Colm O'Riordan
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
The paper introduces a method for constructing L-Lipschitz deep residual networks (ResNets) using a Linear Matrix Inequality (LMI) framework. By reformulating the ResNet architecture as a pseudo-tridiagonal LMI and applying the Gershgorin circle theorem, the authors derive closed‑form constraints on network parameters that guarantee Lipschitz continuity. The work also presents a compositional framework for handling recursive systems in hierarchical architectures, while noting that the Gershgorin-based approximations can over‑constrain the system, reducing expressive capacity.
By Marius F. R. Juston, William R. Norris, Dustin Nottage, Ahmet Soylemezoglu
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
arXiv:2607. 07745v1 Announce Type: new Abstract: While accuracy, robustness, and calibration are all essential for reliable neural networks, they are often studied separately; developing models that satisfy all three simultaneously remains a central challenge.
By Arthur Chiron (IRIT, EPE UT), Franck Mamalet (IRIT, DTIPG - SNCF, UT3), Thomas Massena (IRIT, DTIPG - SNCF, UT3), Thomas Deltort (IRIT), Mathieu Serrurier (IRIT, UT2J)
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