Related papers: Probabilistic Verification and Reachability Analys…

Semidefinite programming is an important optimization task, often used in time-sensitive applications. Though they are solvable in polynomial time, in practice they can be too slow to be used in online, i.e. real-time applications. Here we…

Inverse problems exist in a wide variety of physical domains from aerospace engineering to medical imaging. The goal is to infer the underlying state from a set of observations. When the forward model that produced the observations is…

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…

As AI systems are becoming more and more popular and used in various critical domains (health, transport, energy, ...), the need to provide guarantees and trust of their safety is undeniable. To this end, we present PyRAT, a tool based on…

Techniques for understanding the functioning of complex machine learning models are becoming increasingly popular, not only to improve the validation process, but also to extract new insights about the data via exploratory analysis. Though…

We present $\textbf{P}$robabilistically $\textbf{T}$ightened $\textbf{Li}$near $\textbf{R}$elaxation-based $\textbf{P}$erturbation $\textbf{A}$nalysis ($\texttt{PT-LiRPA}$), a novel framework that combines over-approximation techniques from…

Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for…

Neural networks are now extensively used in perception, prediction and control of autonomous systems. Their deployment in safety-critical systems brings forth the need for verification techniques for such networks. As an alternative to…

Formal verification provides critical security assurances for neural networks, yet its practical application suffers from the long verification time. This work introduces a novel method for training verification-friendly neural networks,…

Designing neural networks with bounded Lipschitz constant is a promising way to obtain certifiably robust classifiers against adversarial examples. However, the relevant progress for the important $\ell_\infty$ perturbation setting is…

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

Quantification is well known to be a major obstacle in the construction of a probabilistic network, especially when relying on human experts for this purpose. The construction of a qualitative probabilistic network has been proposed as an…

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

In the last decade, a large body of work has emerged on robustness of neural networks, i.e., checking if the decision remains unchanged when the input is slightly perturbed. However, most of these approaches ignore the confidence of a…

Deep neural networks (DNNs) are increasingly being deployed to perform safety-critical tasks. The opacity of DNNs, which prevents humans from reasoning about them, presents new safety and security challenges. To address these challenges,…

We present a novel framework for specifying and verifying correctness globally for neural networks on perception tasks. Most previous works on neural network verification for perception tasks focus on robustness verification. Unlike…

Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects…

Ensuring the safety of neural networks under input uncertainty is a fundamental challenge in safety-critical applications. This paper builds on and expands Fazlyab's quadratic-constraint (QC) and semidefinite-programming (SDP) framework for…

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 concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…