Deep neural networks are widely used for nonlinear function approximation, with
applications ranging from computer vision to control. Although these networks involve the …

Historically, scalability has been a major challenge for the successful application of
semidefinite programming in fields such as machine learning, control, and robotics. In this …

It is common practice in deep learning to use overparameterized networks and train for as
long as possible; there are numerous studies that show, both theoretically and empirically …

Bound propagation based incomplete neural network verifiers such as CROWN are very
efficient and can significantly accelerate branch-and-bound (BaB) based complete …

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 …

Great advances in deep neural networks (DNNs) have led to state-of-the-art performance on
a wide range of tasks. However, recent studies have shown that DNNs are vulnerable to …

We introduce an efficient method for the verification of ReLU-based feed-forward neural
networks. We derive an automated procedure that exploits dependency relations between …

A method is presented to analyze the stability of feedback systems with neural network
controllers. Two stability theorems are given to prove asymptotic stability and to compute an …

Important research efforts have focused on the design and training of neural networks with a
controlled Lipschitz constant. The goal is to increase and sometimes guarantee the …

Convex relaxations have emerged as a promising approach for verifying properties of neural
networks, but widely used using Linear Programming (LP) relaxations only provide …