@article{10.1145/3419742,
    Abstract = {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.},
    Address = {New York, NY, USA},
    Author = {Ivanov, Radoslav and Carpenter, Taylor J. and Weimer, James and Alur, Rajeev and Pappas, George J. and Lee, Insup},
    ISSN = {1539-9087},
    Journal = {ACM Trans. Embed. Comput. Syst.},
    Keywords = {hybrid systems with neural network controllers, Neural network verification, safe autonomy},
    Month = {December},
    Number = {1},
    Publisher = {Association for Computing Machinery},
    Title = {Verifying the Safety of Autonomous Systems with Neural Network Controllers},
    URL = {https://doi.org/10.1145/3419742},
    Volume = {20},
    Year = {2020},
    articleno = {7},
    bdsk-url-1 = {https://doi.org/10.1145/3419742},
    date-added = {2020-12-14 09:13:18 +0100},
    date-modified = {2020-12-14 09:13:18 +0100},
    issue_date = {December 2020},
    numpages = {26},
    doi = {10.1145/3419742}
}

@article{10.1145/3419742, Abstract = {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.}, Address = {New York, NY, USA}, Author = {Ivanov, Radoslav and Carpenter, Taylor J. and Weimer, James and Alur, Rajeev and Pappas, George J. and Lee, Insup}, ISSN = {1539-9087}, Journal = {ACM Trans. Embed. Comput. Syst.}, Keywords = {hybrid systems with neural network controllers, Neural network verification, safe autonomy}, Month = {December}, Number = {1}, Publisher = {Association for Computing Machinery}, Title = {Verifying the Safety of Autonomous Systems with Neural Network Controllers}, URL = {https://doi.org/10.1145/3419742}, Volume = {20}, Year = {2020}, articleno = {7}, bdsk-url-1 = {https://doi.org/10.1145/3419742}, date-added = {2020-12-14 09:13:18 +0100}, date-modified = {2020-12-14 09:13:18 +0100}, issue_date = {December 2020}, numpages = {26}, doi = {10.1145/3419742} }