{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/gotube-scalable-stochastic-verification-of","title":"GoTube: Scalable Stochastic Verification of Continuous-Depth Models","arxiv_id":"2107.08467","date":"2021-07-18","proceeding":null,"authors":["Sophie Gruenbacher","Mathias Lechner","Ramin Hasani","Daniela Rus","Thomas A. Henzinger","Scott Smolka","Radu Grosu"],"abstract":"We introduce a new stochastic 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.","url_abs":"https://arxiv.org/abs/2107.08467v2","url_pdf":"https://arxiv.org/pdf/2107.08467v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"gotube-scalable-stochastic-verification-of","repo_url":"https://github.com/DatenVorsprung/GoTube","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"global-optimization","task_name":"global-optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2107.08467","atlas_url":"https://app.syntology.ai/?focus=2107.08467","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}