Probabilistic Verification and Reachability Analysis of Neural Networks via Semidefinite Programming

Understand

Quantifying the robustness of neural networks or verifying their safety properties against input uncertainties or adversarial attacks have become an important research area in learning-enabled systems.

• Most results concentrate around the worst-case scenario where the input of the neural network is perturbed within a norm-bounded uncertainty set.
• In this paper, we consider a probabilistic setting in which the uncertainty is random with known first two moments.
• In this context, we discuss two relevant problems: (i) probabilistic safety verification, in which the goal is to find an upper bound on the probability of violating a safety specification; and (ii) confidence ellipsoid estimation, in which given a confidence ellipsoid for the input of the neural network, our goal is to compute a confidence ellipsoid for the output.