This article addresses the problem of verifying the safety of autonomous systems with neural network (NN) controllers. We focus on NNs with sigmoid/tanh activations and use the fact that the sigmoid/tanh is the solution to a quadratic differential equation. This allows us to convert the NN into an equivalent hybrid system and cast the problem as a hybrid system verification problem, which can be solved by existing tools. Furthermore, we improve the scalability of the proposed method by approximating the sigmoid with a Taylor series with worst-case error bounds. Finally, we provide an evaluation over four benchmarks, including comparisons with alternative approaches based on mixed integer linear programming as well as on star sets.

This paper presents Verisig 2.0, a verification tool for closed-loop systems with neural network (NN) controllers. We focus on NNs with tanh/sigmoid activations and develop a Taylor-model-based reachability algorithm through Taylor model preconditioning and shrink wrapping. Furthermore, we provide a parallelized implementation that allows Verisig 2.0 to efficiently handle larger NNs than existing tools can. We provide an extensive evaluation over 10 benchmarks and compare Verisig 2.0 against three state-of-the-art verification tools. We show that Verisig 2.0 is both more accurate and faster, achieving speed-ups of up to 21x and 268x against different tools, respectively.

This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with artificial intelligence (AI) components. Specifically, machine learning (ML) components in cyber-physical systems (CPS), such as feedforward neural networks used as feedback controllers in closed-loop systems are considered, which is a class of systems classically known as intelligent control systems, or in more modern and specific terms, neural network control systems (NNCS). We more broadly refer to this category as AI and NNCS (AINNCS). The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2021. In the third edition of this AINNCS category at ARCH-COMP, three tools have been applied to solve seven different benchmark problems, (in alphabetical order): JuliaReach, NNV, and Verisig. JuliaReach is a new participant in this category, Verisig participated previously in 2019 and NNV has participated in all previous competitions. This report is a snapshot of the current landscape of tools and the types of benchmarks for which these tools are suited. Due to the diversity of problems, lack of a shared hardware platform, and the early stage of the competition, we are not ranking tools in terms of performance, yet the presented results combined with 2020 results probably provide the most complete assessment of current tools for safety verification of NNCS.

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