Luca Marzari

We present *P*robabilistically *T*ightened *Li*near *R*elaxation-based *P*erturbation *A*nalysis (PT-LiRPA), a novel framework that combines over-approximation techniques from LiRPA-based approaches with a sampling-based method to compute tight intermediate reachable sets. In detail, we show that with negligible computational overhead, PT-LiRPA exploiting the estimated reachable sets, significantly tightens the lower and upper linear bounds of a neural network’s output, reducing the computational cost of formal verification tools while providing probabilistic guarantees on verification soundness. Extensive experiments on standard formal verification benchmarks, including the International Verification of Neural Networks Competition, show that our PT-LiRPA-based verifier improves robustness certificates by up to 3.31X and 2.26X compared to related work. Importantly, our probabilistic approach results in a valuable solution for challenging competition entries where state-of-the-art formal verification methods fail, allowing us to provide answers with high confidence (i.e., at least 99%).

We study the problem of assessing the robustness of counterfactual explanations for deep learning models. We focus on plausible model shifts altering model parameters and propose a novel framework to reason about the robustness property in this setting. To motivate our solution, we begin by showing for the first time that computing the robustness of counterfactuals with respect to plausible model shifts is NP-complete. As this (practically) rules out the existence of scalable algorithms for exactly computing robustness, we propose a novel probabilistic approach which is able to provide tight estimates of robustness with strong guarantees while preserving scalability. Remarkably, and differently from existing solutions targeting plausible model shifts, our approach does not impose requirements on the network to be analyzed, thus enabling robustness analysis on a wider range of architectures. Experiments on four binary classification datasets indicate that our method improves the state of the art in generating robust explanations, outperforming existing methods on a range of metrics.

Identifying safe areas is a key point to guarantee trust for systems that are based on Deep Neural Networks (DNNs). To this end, we introduce the AllDNN-Verification problem: given a safety property and a DNN, enumerate the set of all the regions of the property input domain which are safe, i.e., where the property does hold. Due to the #P-hardness of the problem, we propose an efficient approximation method called ε-ProVe. Our approach exploits a controllable underestimation of the output reachable sets obtained via statistical prediction of tolerance limits, and can provide a tight (with provable probabilistic guarantees) lower estimate of the safe areas. Our empirical evaluation on different standard benchmarks shows the scalability and effectiveness of our method, offering valuable insights for this new type of verification of DNNs.

Deep Neural Networks are increasingly adopted in critical tasks that require a high level of safety, e.g., autonomous driving. While state-of-the-art verifiers can be employed to check whether a DNN is unsafe w.r.t. some given property (i.e., whether there is at least one unsafe input configuration), their yes/no output is not informative enough for other purposes, such as shielding, model selection, or training improvements. In this paper, we introduce the #DNN-Verification problem, which involves counting the number of input configurations of a DNN that result in a violation of a particular safety property. We analyze the complexity of this problem and propose a novel approach that returns the exact count of violations. Due to the #P-completeness of the problem, we also propose a randomized, approximate method that provides a provable probabilistic bound of the correct count while significantly reducing computational requirements. We present experimental results on a set of safety-critical benchmarks that demonstrate the effectiveness of our approximate method and evaluate the tightness of the bound.