{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T05:52:35Z","timestamp":1745560355022,"version":"3.37.3"},"reference-count":46,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"3","license":[{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61836005","61972260","61772347"],"award-info":[{"award-number":["61836005","61972260","61772347"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100021171","name":"Basic and Applied Basic Research Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2019A1515011577"],"award-info":[{"award-number":["2019A1515011577"]}],"id":[{"id":"10.13039\/501100021171","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Stable Support Programs of Shenzhen City","award":["20200810150421002"],"award-info":[{"award-number":["20200810150421002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Rel."],"published-print":{"date-parts":[[2023,9]]},"DOI":"10.1109\/tr.2022.3209081","type":"journal-article","created":{"date-parts":[[2022,10,4]],"date-time":"2022-10-04T19:43:24Z","timestamp":1664912604000},"page":"1191-1205","source":"Crossref","is-referenced-by-count":1,"title":["Output Range Analysis for Feed-Forward Deep Neural Networks via Linear Programming"],"prefix":"10.1109","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6727-440X","authenticated-orcid":false,"given":"Zhiwu","family":"Xu","sequence":"first","affiliation":[{"name":"College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China"}]},{"given":"Yazheng","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3028-8191","authenticated-orcid":false,"given":"Shengchao","family":"Qin","sequence":"additional","affiliation":[{"name":"College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9310-3460","authenticated-orcid":false,"given":"Zhong","family":"Ming","sequence":"additional","affiliation":[{"name":"College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China"}]}],"member":"263","reference":[{"article-title":"Adversarial examples-a complete characterisation of the phenomenon","year":"2018","author":"Serban","key":"ref1"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1145\/3178115"},{"key":"ref3","first-page":"3104","article-title":"Sequence to sequence learning with neural networks","volume-title":"Proc. 27th Conf. Neural Inf. Process. Syst.","author":"Sutskever","year":"2014"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-5225-8407-0.ch007"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2019.2948775"},{"article-title":"The threat of adversarial attacks on machine learning in network securityA survey","year":"2019","author":"Ibitoye","key":"ref6"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1186\/s40537-014-0007-7"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2015.2509024"},{"key":"ref9","article-title":"Intriguing properties of neural networks","volume-title":"Proc. 2nd Int. Conf. Learn. Representations","author":"Szegedy","year":"2014"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.2514\/1.G003724"},{"key":"ref11","first-page":"5273","article-title":"Towards fast computation of certified robustness for relu networks","volume-title":"Proc. 35th Int. Conf. Mach. Learn.","author":"Weng","year":"2018"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1561\/2400000035"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-63387-9_5"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68167-2_19"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-77935-5_9"},{"key":"ref16","first-page":"1599","article-title":"Formal security analysis of neural networks using symbolic intervals","volume-title":"Proc. 27th USENIX Secur. Symp.","author":"Wang","year":"2018"},{"key":"ref17","article-title":"Evaluating robustness of neural networks with mixed integer programming","volume-title":"Proc. 7th Int. Conf. Learn. Representations","author":"Tjeng","year":"2019"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2018\/368"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2018.2808470"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2019.01168"},{"key":"ref21","first-page":"4944","article-title":"Efficient neural network robustness certification with general activation functions","volume-title":"Proc. 32nd Int. Conf. Neural Inf. Process. Syst.","author":"Zhang","year":"2018"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v33i01.33013240"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v35i13.17388"},{"key":"ref24","first-page":"2513","article-title":"Efficient neural network verification via adaptive refinement and adversarial search","volume-title":"Proc. 24th Eur. Conf. Artif. Intell.","author":"Henriksen","year":"2020"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v34i04.5944"},{"key":"ref26","first-page":"9832","article-title":"A convex relaxation barrier to tight robustness verification of neural networks","volume-title":"Proc. 32nd Conf. Neural Inf. Process. Syst.","author":"Salman","year":"2019"},{"key":"ref27","first-page":"2613","article-title":"Measuring neural net robustness with constraints","volume-title":"Proc. 29th Conf. Neural Inf. Process. Syst.","author":"Bastani","year":"2016"},{"article-title":"An approach to reachability analysis for feed-forward relu neural networks","year":"2017","author":"Lomuscio","key":"ref28"},{"key":"ref29","article-title":"Fast and accurate deep network learning by exponential linear units (ELUs","volume-title":"Proc. 2nd Int. Conf. Learn. Representations","author":"Clevert","year":"2016"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-63387-9_1"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.23919\/ACC.2018.8431048"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1137\/15M1020575"},{"article-title":"The MNIST database of handwritten digits","year":"1998","author":"LeCun","key":"ref33"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2018.08.026"},{"key":"ref35","first-page":"6369","article-title":"Efficient formal safety analysis of neural networks","volume-title":"Proc. 31st Conf. Neural Inf. Process. Syst.","author":"Wang","year":"2018"},{"key":"ref36","first-page":"4795","article-title":"A unified view of piecewise linear neural network verification","volume-title":"Proc. 31st Conf. Neural Inf. Process. Syst.","author":"Bunel","year":"2018"},{"key":"ref37","first-page":"5283","article-title":"Provable defenses against adversarial examples via the convex outer adversarial polytope","volume-title":"Proc. 35th Int. Conf. Mach. Learn.","author":"Wong","year":"2018"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/SP.2018.00058"},{"key":"ref39","first-page":"15762","article-title":"Abstraction based output range analysis for neural networks","volume-title":"Proc. 32nd Conf. Neural Inf. Process. Syst.","author":"Prabhakar","year":"2019"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14295-6_24"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1145\/3302504.3311806"},{"article-title":"A reachability method for verifying dynamical systems with deep neural network controllers","year":"2019","author":"Julian","key":"ref42"},{"key":"ref43","first-page":"10825","article-title":"Fast and effective robustness certification","volume-title":"Proc. 31st Conf. Neural Inf. Process. Syst.","author":"Singh","year":"2018"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1145\/3290354"},{"key":"ref45","first-page":"550","article-title":"A dual approach to scalable verification of deep networks","volume-title":"Proc. 34th Conf. Uncertainty Artif. Intell.","author":"Dvijotham","year":"2018"},{"key":"ref46","article-title":"Certified defenses against adversarial examples","volume-title":"Proc. 6th Int. Conf. Learn. Representations","author":"Raghunathan","year":"2018"}],"container-title":["IEEE Transactions on Reliability"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/24\/10236915\/09910600.pdf?arnumber=9910600","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T23:10:20Z","timestamp":1705965020000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9910600\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9]]},"references-count":46,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.1109\/tr.2022.3209081","relation":{},"ISSN":["0018-9529","1558-1721"],"issn-type":[{"type":"print","value":"0018-9529"},{"type":"electronic","value":"1558-1721"}],"subject":[],"published":{"date-parts":[[2023,9]]}}}