Verification of Sigmoidal Artificial Neural Networks using iSAT

This paper presents an approach for verifying the behaviour of nonlinear Artificial Neural Networks (ANNs) found in cyber-physical safety-critical systems. We implement a dedicated interval constraint propagator for the sigmoid function into the SMT solver iSAT and compare this approach with a compositional approach encoding the sigmoid function by basic arithmetic features available in iSAT and an approximating approach. Our experimental results show that the dedicated and the compositional approach clearly outperform the approximating approach. Throughout all our benchmarks, the dedicated approach showed an equal or better performance compared to the compositional approach. This work has received funding from the German Federal Ministry of Economic Affairs and Climate Action (BMWK) through the KI-Wissen project under grant agreement No. 19A20020M, and from the State of Lower Saxony within the framework “Zukunftslabor Mobilit ¨ at Niedersachsen” ( https://www.zdin.de/zukunftslabore/ ).