Enumerating Safe Regions in Deep Neural Networks with Provable Probabilistic Guarantees

TL;DR

This paper introduces a probabilistic method called epsilon-ProVe for efficiently approximating and enumerating all safe input regions of deep neural networks, providing guarantees despite the problem's computational hardness.

Contribution

It presents a novel probabilistic approximation technique for the AllDNN-Verification problem, enabling scalable safe region enumeration with provable guarantees.

Findings

Method scales well on standard benchmarks

Provides tight probabilistic lower bounds

Effective in identifying safe input regions

Abstract

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 epsilon-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.