相关论文: Efficiently Computing Local Lipschitz Constants of…

The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…

The Jacobian matrix (or the gradient for single-output networks) is directly related to many important properties of neural networks, such as the function landscape, stationary points, (local) Lipschitz constants and robustness to…

The local Lipschitz constant of a neural network is a useful metric with applications in robustness, generalization, and fairness evaluation. We provide novel analytic results relating the local Lipschitz constant of nonsmooth vector-valued…

The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…

The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers. Obtaining…

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…

The Lipschitz constant is a key measure for certifying the robustness of neural networks to input perturbations. However, computing the exact constant is NP-hard, and standard approaches to estimate the Lipschitz constant involve solving a…

Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…

Due to their susceptibility to adversarial perturbations, neural networks (NNs) are hardly used in safety-critical applications. One measure of robustness to such perturbations in the input is the Lipschitz constant of the input-output map…

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…

Deriving sharp and computable upper bounds of the Lipschitz constant of deep neural networks is crucial to formally guarantee the robustness of neural-network based models. We analyse three existing upper bounds written for the $l^2$ norm.…

Lipschitz Bound Estimation is an effective method of regularizing deep neural networks to make them robust against adversarial attacks. This is useful in a variety of applications ranging from reinforcement learning to autonomous systems.…

Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…

We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain…

Ensuring neural network robustness is essential for the safe and reliable operation of robotic learning systems, especially in perception and decision-making tasks within real-world environments. This paper investigates the robustness of…

This paper is concerned with the computation of the local Lipschitz constant of feedforward neural networks (FNNs) with activation functions being rectified linear units (ReLUs). The local Lipschitz constant of an FNN for a target input is…

Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…

It has been shown that a neural network's Lipschitz constant can be leveraged to derive robustness guarantees, to improve generalizability via regularization or even to construct invertible networks. Therefore, a number of methods varying…

High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior…