{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T18:04:55Z","timestamp":1743012295366,"version":"3.40.3"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031067723"},{"type":"electronic","value":"9783031067730"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-06773-0_17","type":"book-chapter","created":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T11:24:44Z","timestamp":1652959484000},"page":"318-337","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Permutation Invariance of\u00a0Deep Neural Networks with\u00a0ReLUs"],"prefix":"10.1007","author":[{"given":"Diganta","family":"Mukhopadhyay","sequence":"first","affiliation":[]},{"given":"Kumar","family":"Madhukar","sequence":"additional","affiliation":[]},{"given":"Mandayam","family":"Srivas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,20]]},"reference":[{"key":"17_CR1","unstructured":"Akintunde, M., Lomuscio, A., Maganti, L., Pirovano, E.: Reachability analysis for neural agent-environment systems. In: Thielscher, M., Toni, F., Wolter, F., (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, Tempe, Arizona, 30 October - 2 November 2018, pp. 184\u2013193. AAAI Press (2018)"},{"key":"17_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1007\/978-3-030-59152-6_5","volume-title":"Automated Technology for Verification and Analysis","author":"P Ashok","year":"2020","unstructured":"Ashok, P., Hashemi, V., K\u0159et\u00ednsk\u00fd, J., Mohr, S.: DeepAbstract: neural network abstraction for accelerating verification. In: Hung, D.V., Sokolsky, O. (eds.) ATVA 2020. LNCS, vol. 12302, pp. 92\u2013107. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-59152-6_5"},{"key":"17_CR3","doi-asserted-by":"crossref","unstructured":"Botoeva, E., Kouvaros, P., Kronqvist, J., Lomuscio, A., Misener, R.: Efficient verification of relu-based neural networks via dependency analysis. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, no. 04, 3291\u20133299 (2020)","DOI":"10.1609\/aaai.v34i04.5729"},{"key":"17_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/978-3-540-78800-3_24","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"L de Moura","year":"2008","unstructured":"de Moura, L., Bj\u00f8rner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337\u2013340. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-78800-3_24"},{"key":"17_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/978-3-319-77935-5_9","volume-title":"NASA Formal Methods","author":"S Dutta","year":"2018","unstructured":"Dutta, S., Jha, S., Sankaranarayanan, S., Tiwari, A.: Output range analysis for deep feedforward neural networks. In: Dutle, A., Mu\u00f1oz, C., Narkawicz, A. (eds.) NFM 2018. LNCS, vol. 10811, pp. 121\u2013138. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-77935-5_9"},{"key":"17_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/978-3-319-68167-2_19","volume-title":"Automated Technology for Verification and Analysis","author":"R Ehlers","year":"2017","unstructured":"Ehlers, R.: Formal verification of piece-wise linear feed-forward neural networks. In: D\u2019Souza, D., Narayan Kumar, K. (eds.) ATVA 2017. LNCS, vol. 10482, pp. 269\u2013286. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-68167-2_19"},{"key":"17_CR7","series-title":"pp","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/978-3-030-53288-8_3","volume-title":"Computer Aided Verification","author":"YY Elboher","year":"2020","unstructured":"Elboher, Y.Y., Gottschlich, J., Katz, G.: An abstraction-based framework for neural network verification. In: Lahiri, S.K., Wang, C. (eds.) Computer Aided Verification. pp, pp. 43\u201365. Springer International Publishing, Cham (2020)"},{"key":"17_CR8","doi-asserted-by":"crossref","unstructured":"Eliyahu, T., Kazak, Y., Katz, G., Schapira, M.: Verifying learning-augmented systems. In: Kuipers, F.A., Caesar, M.C. (eds.), ACM SIGCOMM 2021 Conference, Virtual Event, USA, 23\u201327 August 2021, pp. 305\u2013318. ACM (2021)","DOI":"10.1145\/3452296.3472936"},{"key":"17_CR9","doi-asserted-by":"crossref","unstructured":"Gehr, T., Mirman, M., Drachsler-Cohen, D., Tsankov, P., Chaudhuri, S., Vechev, M.: Ai2: safety and robustness certification of neural networks with abstract interpretation. In: 2018 IEEE Symposium on Security and Privacy (SP), Los Alamitos, CA, USA, IEEE Computer Society, May 2018","DOI":"10.1109\/SP.2018.00058"},{"key":"17_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-319-63387-9_1","volume-title":"Computer Aided Verification","author":"X Huang","year":"2017","unstructured":"Huang, X., Kwiatkowska, M., Wang, S., Wu, M.: Safety verification of deep neural networks. In: Majumdar, R., Kun\u010dak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 3\u201329. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63387-9_1"},{"key":"17_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/978-3-030-59152-6_3","volume-title":"Automated Technology for Verification and Analysis","author":"Y Jacoby","year":"2020","unstructured":"Jacoby, Y., Barrett, C., Katz, G.: Verifying recurrent neural networks using invariant inference. In: Hung, D.V., Sokolsky, O. (eds.) ATVA 2020. LNCS, vol. 12302, pp. 57\u201374. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-59152-6_3"},{"key":"17_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/978-3-319-63387-9_5","volume-title":"Computer Aided Verification","author":"G Katz","year":"2017","unstructured":"Katz, G., Barrett, C., Dill, D.L., Julian, K., Kochenderfer, M.J.: Reluplex: an efficient SMT solver for verifying deep neural networks. In: Majumdar, R., Kun\u010dak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 97\u2013117. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63387-9_5"},{"key":"17_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/978-3-030-25540-4_26","volume-title":"Computer Aided Verification","author":"G Katz","year":"2019","unstructured":"Katz, G., et al.: The marabou framework for verification and analysis of deep neural networks. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 443\u2013452. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-25540-4_26"},{"key":"17_CR14","doi-asserted-by":"crossref","unstructured":"Kazak, Y., Barrett, C.W., Katz, G., Schapira, M.: Verifying deep-rl-driven systems. In: Proceedings of the 2019 Workshop on Network Meets AI & ML, NetAI@SIGCOMM 2019, Beijing, China, 23 August 2019, pp. 83\u201389. ACM (2019)","DOI":"10.1145\/3341216.3342218"},{"key":"17_CR15","unstructured":"Prabhakar, P., Afzal, Z.R.: Abstraction based output range analysis for neural networks. In: Wallach, H.M., Larochelle, H., Beygelzimer, A., d\u2019Alch\u00e9-Buc, F., Fox, E.B., Garnett, R. (eds.), Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, 8\u201314 December 2019, Vancouver, BC, Canada, pp. 15762\u201315772 (2019)"},{"key":"17_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/978-3-642-14295-6_24","volume-title":"Computer Aided Verification","author":"L Pulina","year":"2010","unstructured":"Pulina, L., Tacchella, A.: An abstraction-refinement approach to verification of artificial neural networks. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 243\u2013257. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-14295-6_24"},{"key":"17_CR17","unstructured":"Singh, G., Gehr, T., Mirman, M., P\u00fcschel, M., Vechev, M.T.: Fast and effective robustness certification. In: Bengio, S., Wallach, H.M., Larochelle, H., Grauman, K., Cesa-Bianchi, N., Garnett, R. (eds.), Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3\u20138, 2018, Montr\u00e9al, Canada, pp. 10825\u201310836 (2018)"},{"key":"17_CR18","doi-asserted-by":"crossref","unstructured":"Singh, G., Gehr, T., P\u00fcschel, M., Vechev, M.T.: An abstract domain for certifying neural networks. Proc. ACM Program. Lang. 3(POPL), 41:1\u201341:30 (2019)","DOI":"10.1145\/3290354"},{"key":"17_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/978-3-030-72013-1_15","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"M Sotoudeh","year":"2021","unstructured":"Sotoudeh, M., Thakur, A.V.: SyReNN: a tool for analyzing deep neural networks. In: TACAS 2021. LNCS, vol. 12652, pp. 281\u2013302. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-72013-1_15"},{"key":"17_CR20","unstructured":"Tjeng, V., Xiao, K.Y., Tedrake, R.: Evaluating robustness of neural networks with mixed integer programming. In: ICLR (2019)"},{"key":"17_CR21","doi-asserted-by":"crossref","unstructured":"Wicker, M., Huang, X., Kwiatkowska, M.: Feature-guided black-box safety testing of deep neural networks. In: Beyer, D., Huisman, M. (eds.), Tools and Algorithms for the Construction and Analysis of Systems - 24th International Conference, TACAS 2018, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018, Thessaloniki, Greece, 14\u201320 April 2018, Proceedings, Part I, volume 10805 of LNCS, pp. 408\u2013426. Springer (2018)","DOI":"10.1007\/978-3-319-89960-2_22"},{"key":"17_CR22","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/j.tcs.2019.05.046","volume":"807","author":"M Wu","year":"2020","unstructured":"Wu, M., Wicker, M., Ruan, W., Huang, X., Kwiatkowska, M.: A game-based approximate verification of deep neural networks with provable guarantees. Theor. Comput. Sci. 807, 298\u2013329 (2020)","journal-title":"Theor. Comput. Sci."},{"issue":"11","key":"17_CR23","doi-asserted-by":"publisher","first-page":"5777","DOI":"10.1109\/TNNLS.2018.2808470","volume":"29","author":"W Xiang","year":"2018","unstructured":"Xiang, W., Tran, H., Johnson, T.T.: Output reachable set estimation and verification for multilayer neural networks. IEEE Trans. Neural Netw. Learn. Syst. 29(11), 5777\u20135783 (2018)","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"17_CR24","unstructured":"Zhang, H., Shinn, M., Gupta, A., Gurfinkel, A., Le, N., Narodytska, N.: Verification of recurrent neural networks for cognitive tasks via reachability analysis. In: Giacomo, G.D. (eds.) et al., ECAI 2020\u201324th European Conference on Artificial Intelligence, 29 August-8 September 2020, Santiago de Compostela, Spain, August 29 - September 8, 2020 - Including 10th Conference on Prestigious Applications of Artificial Intelligence (PAIS 2020), volume 325 of Frontiers in Artificial Intelligence and Applications, pp. 1690\u20131697. IOS Press (2020)"}],"container-title":["Lecture Notes in Computer Science","NASA Formal Methods"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-06773-0_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T11:11:09Z","timestamp":1659352269000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-06773-0_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031067723","9783031067730"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-06773-0_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"20 May 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"NFM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"NASA Formal Methods Symposium","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Pasadena, CA","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 May 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 May 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"nfm2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/shemesh.larc.nasa.gov\/nfm2022\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"118","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"33","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"6","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"28% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"6.3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}