We review state-of-the-art formal methods applied to the emerging field of the verification of
machine learning systems. Formal methods can provide rigorous correctness guarantees on …

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 …

Deep learning has transformed the way we think of software and what it can do. But deep
neural networks are fragile and their behaviors are often surprising. In many settings, we …

This book provides an introduction to the mathematical analysis of deep learning. It covers
fundamental results in approximation theory, optimization theory, and statistical learning …

As robustness verification methods are becoming more precise, training certifiably robust
neural networks is becoming ever more relevant. To this end, certified training methods …

Convex relaxations are a key component of training and certifying provably safe neural
networks. However, despite substantial progress, a wide and poorly understood accuracy …

This paper proposes a tentative and original survey of meeting points between Knowledge
Representation and Reasoning (KRR) and Machine Learning (ML), two areas which have …

To verify safety and robustness of neural networks, researchers have successfully applied
abstract interpretation, primarily using the interval abstract domain. In this paper, we study …

Certified defenses based on convex relaxations are an established technique for training
provably robust models. The key component is the choice of relaxation, varying from simple …

Interval Bound Propagation (IBP) is so far the base of state-of-the-art methods for training
neural networks with certifiable robustness guarantees when potential adversarial …