arXiv AI
Sep 15

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.

By Marius F. R. Juston, William R. Norris, Dustin Nottage, Ahmet Soylemezoglu