arXiv AI September 15, 2026 By Marius F. R. Juston, William R. Norris, Dustin Nottage, Ahmet Soylemezoglu

L-Lipschitz Gershgorin ResNet Network

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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 Machine Learning

Aug 18

LiD-GLM: Lipschitz-constrained Deep Generalized Linear Models

arXiv:2608. 16340v1 Announce Type: cross Abstract: The combination of traditional statistical models and neural network (NN) components into semi-structured hybrid models is an intriguing approach to construct models that, ideally, combine traditional interpretability with the unprecedented flexibility of NNs.

By Tom Splittgerber, Niklas Koenen, Marvin N. Wright, Werner Brannath

safety

arXiv Machine Learning

Jun 2

Multigrade Neural Network Approximation

arXiv:2601. 16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks.

By Shijun Zhang, Zuowei Shen, Yuesheng Xu

arXiv Machine Learning

Jun 4

Measuring Model Robustness via Fisher Information: Spectral Bounds, Theoretical Guarantees, and Practical Algorithms

arXiv:2606. 04767v1 Announce Type: new Abstract: The robustness of deep neural networks is crucial for safety-critical deployments, yet existing evaluation methods are often attack-dependent and lack interpretability.

By Chong Zhang, Xiang Li, Jia Wang, Qiufeng Wang, Xiaobo Jin

llms safety

arXiv Machine Learning

Aug 26

$(\text{DNN})^2$: Doubly Non-Negative Relaxations for Deep Neural Networks

arXiv:2608.24743v1 Announce Type: new Abstract: Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-...

By Hanna Jiamei Zhang, Alan Papalia, Michael Everett, David M. Rosen

agents safety

arXiv Machine Learning

Jul 21

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.

By R\'ois\'in Luo, James McDermott, Colm O'Riordan

One email a morning, machine-written

Related stories

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

LiD-GLM: Lipschitz-constrained Deep Generalized Linear Models

Multigrade Neural Network Approximation

Measuring Model Robustness via Fisher Information: Spectral Bounds, Theoretical Guarantees, and Practical Algorithms

$(\text{DNN})^2$: Doubly Non-Negative Relaxations for Deep Neural Networks

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