{"date_created":"2022-01-25T15:47:20Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"oa_version":"Published Version","publisher":"AAAI Press","status":"public","title":"On the verification of neural ODEs with stochastic guarantees","quality_controlled":"1","alternative_title":["Technical Tracks"],"day":"28","file":[{"file_id":"10680","success":1,"date_created":"2022-01-26T07:38:08Z","file_size":286906,"date_updated":"2022-01-26T07:38:08Z","content_type":"application/pdf","file_name":"17372-Article Text-20866-1-2-20210518.pdf","creator":"mlechner","access_level":"open_access","relation":"main_file","checksum":"468d07041e282a1d46ffdae92f709630"}],"type":"conference","date_updated":"2022-05-24T06:33:14Z","month":"05","article_processing_charge":"No","issue":"13","date_published":"2021-05-28T00:00:00Z","publication_status":"published","abstract":[{"lang":"eng","text":"We show that Neural ODEs, an emerging class of timecontinuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an\r\nabstraction-based technique for constructing a tight Reachtube (an over-approximation of the set of reachable states\r\nover a given time-horizon), and provide stochastic guarantees in the form of confidence intervals for the Reachtube bounds. SLR inherently avoids the infamous wrapping effect (accumulation of over-approximation errors) by performing local optimization steps to expand safe regions instead of repeatedly forward-propagating them as is done by deterministic reachability methods. To enable fast local optimizations, we introduce a novel forward-mode adjoint sensitivity method to compute gradients without the need for backpropagation. Finally, we establish asymptotic and non-asymptotic convergence rates for SLR."}],"main_file_link":[{"url":"https://ojs.aaai.org/index.php/AAAI/article/view/17372","open_access":"1"}],"department":[{"_id":"GradSch"},{"_id":"ToHe"}],"volume":35,"intvolume":"        35","year":"2021","file_date_updated":"2022-01-26T07:38:08Z","acknowledgement":"The authors would like to thank the reviewers for their insightful comments. RH and RG were partially supported by\r\nHorizon-2020 ECSEL Project grant No. 783163 (iDev40). RH was partially supported by Boeing. ML was supported\r\nin part by the Austrian Science Fund (FWF) under grant Z211-N23 (Wittgenstein Award). SG was funded by FWF\r\nproject W1255-N23. JC was partially supported by NAWA Polish Returns grant PPN/PPO/2018/1/00029. SS was supported by NSF awards DCL-2040599, CCF-1918225, and CPS-1446832.\r\n","ddc":["000"],"project":[{"grant_number":"Z211","name":"The Wittgenstein Prize","_id":"25F42A32-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"page":"11525-11535","author":[{"full_name":"Grunbacher, Sophie","first_name":"Sophie","last_name":"Grunbacher"},{"full_name":"Hasani, Ramin","first_name":"Ramin","last_name":"Hasani"},{"id":"3DC22916-F248-11E8-B48F-1D18A9856A87","full_name":"Lechner, Mathias","first_name":"Mathias","last_name":"Lechner"},{"full_name":"Cyranka, Jacek","first_name":"Jacek","last_name":"Cyranka"},{"full_name":"Smolka, Scott A","first_name":"Scott A","last_name":"Smolka"},{"last_name":"Grosu","first_name":"Radu","full_name":"Grosu, Radu"}],"has_accepted_license":"1","publication":"Proceedings of the AAAI Conference on Artificial Intelligence","publication_identifier":{"isbn":["978-1-57735-866-4"],"eissn":["2374-3468"],"issn":["2159-5399"]},"external_id":{"arxiv":["2012.08863"]},"citation":{"ieee":"S. Grunbacher, R. Hasani, M. Lechner, J. Cyranka, S. A. Smolka, and R. Grosu, “On the verification of neural ODEs with stochastic guarantees,” in <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, Virtual, 2021, vol. 35, no. 13, pp. 11525–11535.","mla":"Grunbacher, Sophie, et al. “On the Verification of Neural ODEs with Stochastic Guarantees.” <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, vol. 35, no. 13, AAAI Press, 2021, pp. 11525–35.","short":"S. Grunbacher, R. Hasani, M. Lechner, J. Cyranka, S.A. Smolka, R. Grosu, in:, Proceedings of the AAAI Conference on Artificial Intelligence, AAAI Press, 2021, pp. 11525–11535.","chicago":"Grunbacher, Sophie, Ramin Hasani, Mathias Lechner, Jacek Cyranka, Scott A Smolka, and Radu Grosu. “On the Verification of Neural ODEs with Stochastic Guarantees.” In <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, 35:11525–35. AAAI Press, 2021.","ista":"Grunbacher S, Hasani R, Lechner M, Cyranka J, Smolka SA, Grosu R. 2021. On the verification of neural ODEs with stochastic guarantees. Proceedings of the AAAI Conference on Artificial Intelligence. AAAI: Association for the Advancement of Artificial Intelligence, Technical Tracks, vol. 35, 11525–11535.","apa":"Grunbacher, S., Hasani, R., Lechner, M., Cyranka, J., Smolka, S. A., &#38; Grosu, R. (2021). On the verification of neural ODEs with stochastic guarantees. In <i>Proceedings of the AAAI Conference on Artificial Intelligence</i> (Vol. 35, pp. 11525–11535). Virtual: AAAI Press.","ama":"Grunbacher S, Hasani R, Lechner M, Cyranka J, Smolka SA, Grosu R. On the verification of neural ODEs with stochastic guarantees. In: <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>. Vol 35. AAAI Press; 2021:11525-11535."},"conference":{"name":"AAAI: Association for the Advancement of Artificial Intelligence","start_date":"2021-02-02","end_date":"2021-02-09","location":"Virtual"},"language":[{"iso":"eng"}],"_id":"10669"}