GoTube: Scalable statistical verification of continuous-depth models
Gruenbacher SA, Lechner M, Hasani R, Rus D, Henzinger TA, Smolka SA, Grosu R. 2022. GoTube: Scalable statistical verification of continuous-depth models. Proceedings of the AAAI Conference on Artificial Intelligence. 36(6), 6755–6764.
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https://arxiv.org/abs/2107.08467
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Journal Article
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Author
Gruenbacher, Sophie A.;
Lechner, MathiasISTA;
Hasani, Ramin;
Rus, Daniela;
Henzinger, Thomas AISTA ;
Smolka, Scott A.;
Grosu, Radu
Department
Abstract
We introduce a new statistical verification algorithm that formally quantifies the behavioral robustness of any time-continuous process formulated as a continuous-depth model. Our algorithm solves a set of global optimization (Go) problems over a given time horizon to construct a tight enclosure (Tube) of the set of all process executions starting from a ball of initial states. We call our algorithm GoTube. Through its construction, GoTube ensures that the bounding tube is conservative up to a desired probability and up to a desired tightness.
GoTube is implemented in JAX and optimized to scale to complex continuous-depth neural network models. Compared to advanced reachability analysis tools for time-continuous neural networks, GoTube does not accumulate overapproximation errors between time steps and avoids the infamous wrapping effect inherent in symbolic techniques. We show that GoTube substantially outperforms state-of-the-art verification tools in terms of the size of the initial ball, speed, time-horizon, task completion, and scalability on a large set of experiments.
GoTube is stable and sets the state-of-the-art in terms of its ability to scale to time horizons well beyond what has been previously possible.
Keywords
Publishing Year
Date Published
2022-06-28
Journal Title
Proceedings of the AAAI Conference on Artificial Intelligence
Publisher
Association for the Advancement of Artificial Intelligence
Acknowledgement
SG is funded by the Austrian Science Fund (FWF) project number W1255-N23. ML and TH are supported in part by FWF under grant Z211-N23 (Wittgenstein Award) and the ERC-2020-AdG 101020093. SS is supported by NSF awards DCL-2040599, CCF-1918225, and CPS-1446832. RH and DR are partially supported by Boeing. RG is partially supported by Horizon-2020 ECSEL Project grant No. 783163 (iDev40).
Volume
36
Issue
6
Page
6755-6764
ISBN
ISSN
eISSN
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Cite this
Gruenbacher SA, Lechner M, Hasani R, et al. GoTube: Scalable statistical verification of continuous-depth models. Proceedings of the AAAI Conference on Artificial Intelligence. 2022;36(6):6755-6764. doi:10.1609/aaai.v36i6.20631
Gruenbacher, S. A., Lechner, M., Hasani, R., Rus, D., Henzinger, T. A., Smolka, S. A., & Grosu, R. (2022). GoTube: Scalable statistical verification of continuous-depth models. Proceedings of the AAAI Conference on Artificial Intelligence. Association for the Advancement of Artificial Intelligence. https://doi.org/10.1609/aaai.v36i6.20631
Gruenbacher, Sophie A., Mathias Lechner, Ramin Hasani, Daniela Rus, Thomas A Henzinger, Scott A. Smolka, and Radu Grosu. “GoTube: Scalable Statistical Verification of Continuous-Depth Models.” Proceedings of the AAAI Conference on Artificial Intelligence. Association for the Advancement of Artificial Intelligence, 2022. https://doi.org/10.1609/aaai.v36i6.20631.
S. A. Gruenbacher et al., “GoTube: Scalable statistical verification of continuous-depth models,” Proceedings of the AAAI Conference on Artificial Intelligence, vol. 36, no. 6. Association for the Advancement of Artificial Intelligence, pp. 6755–6764, 2022.
Gruenbacher SA, Lechner M, Hasani R, Rus D, Henzinger TA, Smolka SA, Grosu R. 2022. GoTube: Scalable statistical verification of continuous-depth models. Proceedings of the AAAI Conference on Artificial Intelligence. 36(6), 6755–6764.
Gruenbacher, Sophie A., et al. “GoTube: Scalable Statistical Verification of Continuous-Depth Models.” Proceedings of the AAAI Conference on Artificial Intelligence, vol. 36, no. 6, Association for the Advancement of Artificial Intelligence, 2022, pp. 6755–64, doi:10.1609/aaai.v36i6.20631.
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arXiv 2107.08467