Abstract
Functional architectures of cyber-physical systems increasingly comprise components that are generated by training and machine learning rather than by more traditional engineering approaches, as necessary in safety-critical application domains, poses various unsolved challenges. Commonly used computational structures underlying machine learning, like deep neural networks, still lack scalable automatic verification support. Due to size, non-linearity, and non-convexity, neural network verification is a challenge to state-of-art Mixed Integer linear programming (MILP) solvers and satisfiability modulo theories (SMT) solvers [2], [3]. In this research, we focus on artificial neural network with activation functions beyond the Rectified Linear Unit (ReLU). We are thus leaving the area of piecewise linear function supported by the majority of SMT solvers and specialized solvers for Artificial Neural Networks (ANNs), the successful like Reluplex solver [1]. A major part of this research is using the SMT solver iSAT [4] which aims at solving complex Boolean combinations of linear and non-linear constraint formulas (including transcendental functions), and therefore is suitable to verify the safety properties of a specific kind of neural network known as Multi-Layer Perceptron (MLP) which contain non-linear activation functions.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: DFG-GRK 1765/2
Funding statement: This work is supported by the German Research Foundation through the Research Training Group “SCARE: System Correctness under Adverse Conditions” (DFG-GRK 1765/2), https://www.uni-oldenburg.de/en/scare.
About the authors
Farzaneh Moradkhani received the M.Sc. degree in Computer engineering from Islamic Azad University, Zanjan, Iran, in 2013. For 8 years, she was working as a research assistant in the Industrial Intelligence Research Group, Academic Centre Education Culture & Research (ACECR), Zanjan, Iran. She is currently a Ph.D. student and working on verification of neural works project in the Department of Computer Science, Hybrid Systems group at the University of Oldenburg, Germany. Her research interests include verification and machine learning.
Prof. Dr. Martin Fränzle has been Professor for Hybrid Systems within the Department of Computing Science at the University of Oldenburg since 2004 and the university’s Vice President for Research, Transfer, and Digitalization since 2020. He holds a diploma and a doctoral degree in Computer Science from the University of Kiel and was an associate professor and later a Velux visiting professor at the Technical University of Denmark. Further visiting professorships and extended research stays led him to Freiburg and Saarbrücken (both Germany), Copenhagen (Denmark), Tallinn (Estonia), Grenoble (France), Oxford (UK), and the Chinese Academy of Sciences. Fränzle’s research focuses on the mathematical modelling as well as the verification and synthesis of secure and reliable cyber-physical systems, i. e., the merging of physical objects with information technology into “smart” infrastructures such as autonomous vehicles, production facilities, or supply networks. His research interests thereby span from theoretical foundations to applications and industrial transfer, the latter often pursued within the associated research institute OFFIS e. V., where he is long-standing member of the executive board of the R&D division Transportation.
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