L-Lipschitz Gershgorin ResNet Network

תקציר מקורי באנגליתarXiv:2502.21279v2 Announce Type: replace Abstract: Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz bound in neural networks has emerged as an essential area of research for enhancing adversarial robustness and network certifiability. This paper uses a rigorous approach to design $\mathcal{L}$-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. The ResNet architecture was reformulated as a pseudo-tri-diagonal LMI with off-diagonal elements and derived closed-form constraints on network parameters to ensure $\mathcal{L}$-Lipschitz continuity. To address the lack of explicit eigenvalue compu