This paper introduces a novel approach to evaluate the reliability of Neural Networks (NNs) by integrating adversarial attacks with Importance Sampling (IS), enhancing the assessment’s precision and efficiency. Leveraging adversarial attacks to guide IS, our method efficiently identifies vulnerable input regions, offering a more directed alternative to traditional Monte Carlo methods. While comparing our approach with classical reliability techniques like FORM and SORM, and with classical rare event simulation methods such as Cross-Entropy IS, we acknowledge its reliance on the effectiveness of adversarial attacks and its inability to handle very high-dimensional data such as ImageNet. Despite these challenges, our comprehensive empirical validations on the datasets the MNIST and CIFAR10 demonstrate the method’s capability to accurately estimate NN reliability for a variety of models. Our research not only presents an innovative strategy for reliability assessment in NNs but also sets the stage for further work exploiting the connection between adversarial robustness and the field of statistical reliability engineering.

Deep neural networks are robust against random corruptions of the inputs to some extent. This global sense of safety is not sufficient in critical applications where probabilities of failure must be assessed with accuracy. Some previous works applied known statistical methods from the field of rare event analysis to classification. Yet, they use classifiers as black-box models without taking into account gradient information, readily available for deep learning models via auto-differentiation. We propose a new and highly efficient estimator of probabilities of failure dedicated to neural networks as it leverages the fast computation of gradients of the model through back-propagation.

We quantify the robustness of a trained network to input uncertainties with a stochastic simulation inspired by the field of Statistical Reliability Engineering. The robustness assessment is cast as a statistical hypothesis test: the network is deemed as locally robust if the estimated probability of failure is lower than a critical level.The procedure is based on an Importance Splitting simulation generating samples of rare events. We derive theoretical guarantees that are non-asymptotic w.r.t. sample size. Experiments tackling large scale networks outline the efficiency of our method making a low number of calls to the network function.