{"acknowledgement":"This research was supported in part by the Austrian Science Fund (FWF) under grant Z211-N23 (Wittgenstein\r\nAward), ERC CoG 863818 (FoRM-SMArt), and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.\r\n","related_material":{"record":[{"status":"public","id":"11362","relation":"dissertation_contains"}]},"main_file_link":[{"open_access":"1","url":"https://ojs.aaai.org/index.php/AAAI/article/view/16496"}],"ec_funded":1,"date_updated":"2023-06-23T07:01:11Z","intvolume":"        35","abstract":[{"text":"Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an idealized model of the actual network which works over real arithmetic and ignores rounding imprecisions. This idealization is in stark contrast to network quantization, which is a technique that trades numerical precision for computational efficiency and is, therefore, often applied in practice. Neglecting rounding errors of such low-bit quantized neural networks has been shown to lead to wrong conclusions about the network’s correctness. Thus, the desired approach for verifying quantized neural networks would be one that takes these rounding errors\r\ninto account. In this paper, we show that verifying the bitexact implementation of quantized neural networks with bitvector specifications is PSPACE-hard, even though verifying idealized real-valued networks and satisfiability of bit-vector specifications alone are each in NP. Furthermore, we explore several practical heuristics toward closing the complexity gap between idealized and bit-exact verification. In particular, we propose three techniques for making SMT-based verification of quantized neural networks more scalable. Our experiments demonstrate that our proposed methods allow a speedup of up to three orders of magnitude over existing approaches.","lang":"eng"}],"status":"public","day":"28","quality_controlled":"1","has_accepted_license":"1","external_id":{"arxiv":["2012.08185"]},"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020","grant_number":"665385"},{"call_identifier":"FWF","grant_number":"Z211","name":"The Wittgenstein Prize","_id":"25F42A32-B435-11E9-9278-68D0E5697425"},{"grant_number":"863818","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"}],"volume":35,"language":[{"iso":"eng"}],"file_date_updated":"2022-01-26T07:41:16Z","author":[{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","first_name":"Thomas A","orcid":"0000-0002-2985-7724","full_name":"Henzinger, Thomas A"},{"full_name":"Lechner, Mathias","first_name":"Mathias","last_name":"Lechner","id":"3DC22916-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Zikelic, Dorde","first_name":"Dorde","last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87"}],"page":"3787-3795","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"GradSch"},{"_id":"ToHe"}],"alternative_title":["Technical Tracks"],"publication":"Proceedings of the AAAI Conference on Artificial Intelligence","date_created":"2022-01-25T15:15:02Z","file":[{"date_updated":"2022-01-26T07:41:16Z","content_type":"application/pdf","file_size":137235,"file_name":"16496-Article Text-19990-1-2-20210518 (1).pdf","date_created":"2022-01-26T07:41:16Z","relation":"main_file","file_id":"10684","access_level":"open_access","success":1,"checksum":"2bc8155b2526a70fba5b7301bc89dbd1","creator":"mlechner"}],"year":"2021","ddc":["000"],"date_published":"2021-05-28T00:00:00Z","article_processing_charge":"No","publication_identifier":{"isbn":["978-1-57735-866-4"],"issn":["2159-5399"],"eissn":["2374-3468"]},"_id":"10665","month":"05","issue":"5A","title":"Scalable verification of quantized neural networks","oa_version":"Published Version","citation":{"ieee":"T. A. Henzinger, M. Lechner, and D. Zikelic, “Scalable verification of quantized neural networks,” in <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, Virtual, 2021, vol. 35, no. 5A, pp. 3787–3795.","chicago":"Henzinger, Thomas A, Mathias Lechner, and Dorde Zikelic. “Scalable Verification of Quantized Neural Networks.” In <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, 35:3787–95. AAAI Press, 2021.","mla":"Henzinger, Thomas A., et al. “Scalable Verification of Quantized Neural Networks.” <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, vol. 35, no. 5A, AAAI Press, 2021, pp. 3787–95.","ama":"Henzinger TA, Lechner M, Zikelic D. Scalable verification of quantized neural networks. In: <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>. Vol 35. AAAI Press; 2021:3787-3795.","ista":"Henzinger TA, Lechner M, Zikelic D. 2021. Scalable verification of quantized neural networks. Proceedings of the AAAI Conference on Artificial Intelligence. AAAI: Association for the Advancement of Artificial Intelligence, Technical Tracks, vol. 35, 3787–3795.","apa":"Henzinger, T. A., Lechner, M., &#38; Zikelic, D. (2021). Scalable verification of quantized neural networks. In <i>Proceedings of the AAAI Conference on Artificial Intelligence</i> (Vol. 35, pp. 3787–3795). Virtual: AAAI Press.","short":"T.A. Henzinger, M. Lechner, D. Zikelic, in:, Proceedings of the AAAI Conference on Artificial Intelligence, AAAI Press, 2021, pp. 3787–3795."},"type":"conference","scopus_import":"1","oa":1,"publisher":"AAAI Press","publication_status":"published","conference":{"name":"AAAI: Association for the Advancement of Artificial Intelligence","location":"Virtual","start_date":"2021-02-02","end_date":"2021-02-09"}}