{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T19:46:33Z","timestamp":1786131993311,"version":"build-2736575974"},"reference-count":39,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"funder":[{"name":"project of China National Petroleum Corporation, titled \u201cResearch on Key Technologies for Fracture Identification and Characterization of Carbonate Reservoirs\u201d","award":["2024ZG21"],"award-info":[{"award-number":["2024ZG21"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Access"],"published-print":{"date-parts":[[2026]]},"DOI":"10.1109\/access.2026.3718887","type":"journal-article","created":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T18:12:49Z","timestamp":1785521569000},"page":"117026-117045","source":"Crossref","is-referenced-by-count":0,"title":["Scalable Parallel Verification of Quantized Neural Networks via MIQCP Optimization Encoding"],"prefix":"10.1109","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-1929-7762","authenticated-orcid":false,"given":"Shifu","family":"Yang","sequence":"first","affiliation":[{"name":"Research Institute of Petroleum Exploration and Development-NorthWest (NWGI), PetroChina","place":["Lanzhou, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wuyang","family":"Yang","sequence":"additional","affiliation":[{"name":"Research Institute of Petroleum Exploration and Development-NorthWest (NWGI), PetroChina","place":["Lanzhou, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref1","article-title":"A white paper on neural network quantization","author":"Nagel","year":"2021","journal-title":"arXiv:2106.08295"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00286"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2024\/474"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2019.2962338"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2022.3144407"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.vehcom.2019.100184"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1145\/3453688.3461755"},{"key":"ref8","article-title":"Defensive quantization: When efficiency meets robustness","author":"Lin","year":"2019","journal-title":"arXiv:1904.08444"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-63387-9_5"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68167-2_19"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-63387-9_1"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1145\/3597926.3598034"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v32i1.12206"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1145\/3319535.3354245"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-45237-7_5"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68167-2_18"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s10601-018-9285-6"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-77935-5_9"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2022.3197697"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1145\/3551349.3556916"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v38i19.30108"},{"key":"ref22","article-title":"Evaluating robustness of neural networks with mixed integer programming","author":"Tjeng","year":"2017","journal-title":"arXiv:1711.07356"},{"key":"ref23","first-page":"5283","article-title":"Provable defenses against adversarial examples via the convex outer adversarial polytope","volume-title":"Proc. 35th Int. Conf. Mach. Learn. (ICML)","author":"Wong"},{"key":"ref24","first-page":"5273","article-title":"Towards fast computation of certified robustness for relu networks","volume-title":"Proc. 35th Int. Conf. Mach. Learn. (ICML)","volume":"80","author":"Weng"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/SP.2018.00058"},{"key":"ref26","first-page":"4944","article-title":"Efficient neural network robustness certification with general activation functions","volume-title":"Proc. Adv. Neural Inf. Process. Syst., Annu. Conf. Neural Inf. Process. Syst. (NeurIPS)","author":"Zhang"},{"key":"ref27","first-page":"10900","article-title":"Semidefinite relaxations for certifying robustness to adversarial examples","volume-title":"Proc. Adv. Neural Inf. Process. Syst., Annu. Conf. Neural Inf. Process. Syst. (NeurIPS)","author":"Raghunathan"},{"key":"ref28","first-page":"3575","article-title":"Differentiable abstract interpretation for provably robust neural networks","volume-title":"Proc. 35th Int. Conf. Mach. Learn. (ICML)","author":"Mirman"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1145\/3290354"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-25540-4_26"},{"key":"ref31","volume-title":"Quantization\u2014PyTorch Documentation. PyTorch Version 2.3 Documentation","year":"2024"},{"key":"ref32","volume-title":"Gurobi Optimizer Reference Manual","year":"2023"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/130915303"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580665"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.22.4.455"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8917-8"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-37703-7_20"},{"key":"ref38","volume-title":"The MNIST database of handwritten digits","author":"LeCun","year":"1998"},{"key":"ref39","article-title":"Fashion-MNIST: A novel image dataset for benchmarking machine learning algorithms","author":"Xiao","year":"2017","journal-title":"arXiv:1708.07747"}],"container-title":["IEEE Access"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/6287639\/11323511\/11635894.pdf?arnumber=11635894","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T19:04:46Z","timestamp":1786129486000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11635894\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":39,"URL":"https:\/\/doi.org\/10.1109\/access.2026.3718887","relation":{},"ISSN":["2169-3536"],"issn-type":[{"value":"2169-3536","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]}}}