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S. Grünbacher, M. Lechner, R. Hasani, D. Rus, T. Henzinger, S. Smolka, R. Grosu:
"GoTube: Scalable Statistical Verification of Continuous-Depth Models";
accepted as talk for: 36th AAAI Conference on Artificial Intelligence (AAAI-22), Vancouver; 2022-02-22 - 2022-03-01; in: "Proceedings of the 36th AAAI Conference on Artificial Intelligence", IEEE (ed.); Vol. 36 (2022).

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.