{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T04:58:37Z","timestamp":1777957117031,"version":"3.51.4"},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p>Deep Neural Networks are increasingly adopted in critical tasks that require a high level of safety, e.g., autonomous driving.\n\nWhile state-of-the-art verifiers can be employed to check whether a DNN is unsafe w.r.t. some given property (i.e., whether there is at least one unsafe input configuration), their yes\/no output is not informative enough for other purposes, such as shielding, model selection, or training improvements.\n\nIn this paper, we introduce the #DNN-Verification problem, which involves counting the number of input configurations of a DNN that result in a violation of a particular safety property. We analyze the complexity of this problem and propose a novel approach that returns the exact count of violations. Due to the #P-completeness of the problem, we also propose a randomized, approximate method that provides a provable probabilistic bound of the correct count while significantly reducing computational requirements.\n\nWe present experimental results on a set of safety-critical benchmarks that demonstrate the effectiveness of our approximate method and evaluate the tightness of the bound.<\/jats:p>","DOI":"10.24963\/ijcai.2023\/25","type":"proceedings-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:31:30Z","timestamp":1691742690000},"page":"217-224","source":"Crossref","is-referenced-by-count":4,"title":["The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networks"],"prefix":"10.24963","author":[{"given":"Luca","family":"Marzari","sequence":"first","affiliation":[{"name":"University of Verona"}]},{"given":"Davide","family":"Corsi","sequence":"additional","affiliation":[{"name":"University of Verona"}]},{"given":"Ferdinando","family":"Cicalese","sequence":"additional","affiliation":[{"name":"University of Verona"}]},{"given":"Alessandro","family":"Farinelli","sequence":"additional","affiliation":[{"name":"University of Verona, Italy"}]}],"member":"10584","event":{"name":"Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}","theme":"Artificial Intelligence","location":"Macau, SAR China","acronym":"IJCAI-2023","number":"32","sponsor":["International Joint Conferences on Artificial Intelligence Organization (IJCAI)"],"start":{"date-parts":[[2023,8,19]]},"end":{"date-parts":[[2023,8,25]]}},"container-title":["Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence"],"original-title":[],"deposited":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:32:34Z","timestamp":1691742754000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ijcai.org\/proceedings\/2023\/25"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2023,8]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/ijcai.2023\/25","relation":{},"subject":[],"published":{"date-parts":[[2023,8]]}}}