{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T14:53:57Z","timestamp":1763564037361,"version":"3.41.0"},"publisher-location":"New York, NY, USA","reference-count":57,"publisher":"ACM","license":[{"start":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T00:00:00Z","timestamp":1559952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2019,6,8]]},"DOI":"10.1145\/3314221.3314614","type":"proceedings-article","created":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T21:02:18Z","timestamp":1559941338000},"page":"731-744","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":60,"title":["Optimization and abstraction: a synergistic approach for analyzing neural network robustness"],"prefix":"10.1145","author":[{"given":"Greg","family":"Anderson","sequence":"first","affiliation":[{"name":"University of Texas at Austin, USA"}]},{"given":"Shankara","family":"Pailoor","sequence":"additional","affiliation":[{"name":"University of Texas at Austin, USA"}]},{"given":"Isil","family":"Dillig","sequence":"additional","affiliation":[{"name":"University of Texas at Austin, USA"}]},{"given":"Swarat","family":"Chaudhuri","sequence":"additional","affiliation":[{"name":"Rice University, USA"}]}],"member":"320","published-online":{"date-parts":[[2019,6,8]]},"reference":[{"volume-title":"d.]","key":"e_1_3_2_2_1_1","unstructured":"[n. d.] . ELINA : ETH Library for Numerical Analysis . http:\/\/elina.ethz.ch. [n. d.]. ELINA: ETH Library for Numerical Analysis. http:\/\/elina.ethz.ch."},{"key":"e_1_3_2_2_2_1","unstructured":"[n. d.]. Google Cloud Platform (GCP). https:\/\/cloud.google.com\/. Accessed: 2018-11-14.  [n. d.]. Google Cloud Platform (GCP). https:\/\/cloud.google.com\/. Accessed: 2018-11-14."},{"key":"e_1_3_2_2_3_1","unstructured":"ApolloAuto. 2017. apollo. https:\/\/github.com\/ApolloAuto\/apollo.  ApolloAuto. 2017. apollo. https:\/\/github.com\/ApolloAuto\/apollo."},{"key":"e_1_3_2_2_4_1","volume-title":"Measuring Neural Net Robustness with Constraints. In Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016","author":"Bastani Osbert","year":"2016","unstructured":"Osbert Bastani , Yani Ioannou , Leonidas Lampropoulos , Dimitrios Vytiniotis , Aditya V. Nori , and Antonio Criminisi . 2016 . Measuring Neural Net Robustness with Constraints. In Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016 , December 5-10, 2016, Barcelona, Spain. 2613-2621. Osbert Bastani, Yani Ioannou, Leonidas Lampropoulos, Dimitrios Vytiniotis, Aditya V. Nori, and Antonio Criminisi. 2016. Measuring Neural Net Robustness with Constraints. In Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10, 2016, Barcelona, Spain. 2613-2621."},{"key":"e_1_3_2_2_5_1","volume-title":"Davide Del Testa","author":"Bojarski Mariusz","year":"2016","unstructured":"Mariusz Bojarski , Davide Del Testa , Daniel Dworakowski, Bernhard Firner , Beat Flepp, Prasoon Goyal, Lawrence D. Jackel, Mathew Monfort, Urs Muller, Jiakai Zhang, Xin Zhang, Jake Zhao, and Karol Zieba. 2016 . End to End Learning for Self-Driving Cars. CoRR abs\/1604.07316 (2016). http:\/\/arxiv.org\/abs\/1604.07316. Mariusz Bojarski, Davide Del Testa, Daniel Dworakowski, Bernhard Firner, Beat Flepp, Prasoon Goyal, Lawrence D. Jackel, Mathew Monfort, Urs Muller, Jiakai Zhang, Xin Zhang, Jake Zhao, and Karol Zieba. 2016. End to End Learning for Self-Driving Cars. CoRR abs\/1604.07316 (2016). http:\/\/arxiv.org\/abs\/1604.07316."},{"key":"e_1_3_2_2_6_1","volume-title":"A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning. abs\/1012.2599 (12","author":"Brochu Eric","year":"2010","unstructured":"Eric Brochu , Vlad M. Cora , and Nando De Freitas . 2010. A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning. abs\/1012.2599 (12 2010 ). Eric Brochu, Vlad M. Cora, and Nando De Freitas. 2010. A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning. abs\/1012.2599 (12 2010)."},{"key":"e_1_3_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/512950.512973"},{"key":"e_1_3_2_2_8_1","volume-title":"Output Range Analysis for Deep Neural Networks. CoRR abs\/1709.09130","author":"Dutta Souradeep","year":"2017","unstructured":"Souradeep Dutta , Susmit Jha , Sriram Sankaranarayanan , and Ashish Tiwari . 2017. Output Range Analysis for Deep Neural Networks. CoRR abs\/1709.09130 ( 2017 ). arXiv:1709.09130 http:\/\/arxiv.org\/abs\/1709.09130. Souradeep Dutta, Susmit Jha, Sriram Sankaranarayanan, and Ashish Tiwari. 2017. Output Range Analysis for Deep Neural Networks. CoRR abs\/1709.09130 (2017). arXiv:1709.09130 http:\/\/arxiv.org\/abs\/1709.09130."},{"key":"e_1_3_2_2_9_1","volume-title":"Dermatologist-level classification of skin cancer with deep neural networks. Nature 542 (01","author":"Esteva Andre","year":"2017","unstructured":"Andre Esteva , Brett Kuprel , Roberto A. Novoa , Justin Ko , Susan M. Swetter , Helen M. Blau , and Sebastian Thrun . 2017. Dermatologist-level classification of skin cancer with deep neural networks. Nature 542 (01 2017 ), 115-118. Andre Esteva, Brett Kuprel, Roberto A. Novoa, Justin Ko, Susan M. Swetter, Helen M. Blau, and Sebastian Thrun. 2017. Dermatologist-level classification of skin cancer with deep neural networks. Nature 542 (01 2017), 115-118."},{"key":"e_1_3_2_2_10_1","volume-title":"Robust Physical-World Attacks on Machine Learning Models. CoRR abs\/1707.08945","author":"Evtimov Ivan","year":"2017","unstructured":"Ivan Evtimov , Kevin Eykholt , Earlence Fernandes , Tadayoshi Kohno , Bo Li , Atul Prakash , Amir Rahmati , and Dawn Song . 2017. Robust Physical-World Attacks on Machine Learning Models. CoRR abs\/1707.08945 ( 2017 ). arXiv:1707.08945 http:\/\/arxiv.org\/abs\/1707.08945. Ivan Evtimov, Kevin Eykholt, Earlence Fernandes, Tadayoshi Kohno, Bo Li, Atul Prakash, Amir Rahmati, and Dawn Song. 2017. Robust Physical-World Attacks on Machine Learning Models. CoRR abs\/1707.08945 (2017). arXiv:1707.08945 http:\/\/arxiv.org\/abs\/1707.08945."},{"key":"e_1_3_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.5555\/898758"},{"key":"e_1_3_2_2_12_1","first-page":"286","volume-title":"Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12)","author":"Gao Sicun","unstructured":"Sicun Gao , Jeremy Avigad , and Edmund M. Clarke . 2012. ?-complete Decision Procedures for Satisfiability over the Reals . In Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12) . Springer-Verlag, Berlin, Heidelberg , 286 - 300 . Sicun Gao, Jeremy Avigad, and Edmund M. Clarke. 2012. ?-complete Decision Procedures for Satisfiability over the Reals. In Proceedings of the 6th International Joint Conference on Automated Reasoning (IJCAR'12). Springer-Verlag, Berlin, Heidelberg, 286-300."},{"key":"e_1_3_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-08867-9_5"},{"key":"e_1_3_2_2_14_1","first-page":"3","volume-title":"2018 IEEE Symposium on Security and Privacy (SP). IEEE","author":"Gehr Timon","unstructured":"Timon Gehr , Matthew Mirman , Dana Drachsler-Cohen , Petar Tsankov , Swarat Chaudhuri , and M. Vechev . 2018. AI2: Safety and Robustness Certification of Neural Networks with Abstract Interpretation . In 2018 IEEE Symposium on Security and Privacy (SP). IEEE , San Francisco, CA, USA , 3 - 18 . Timon Gehr, Matthew Mirman, Dana Drachsler-Cohen, Petar Tsankov, Swarat Chaudhuri, and M. Vechev. 2018. AI2: Safety and Robustness Certification of Neural Networks with Abstract Interpretation. In 2018 IEEE Symposium on Security and Privacy (SP). IEEE, San Francisco, CA, USA, 3-18."},{"key":"e_1_3_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02658-4_47"},{"key":"e_1_3_2_2_16_1","volume-title":"An Overview of Vulnerabilities of Voice Controlled Systems. arXiv preprint arXiv:1803.09156","author":"Gong Yuan","year":"2018","unstructured":"Yuan Gong and Christian Poellabauer . 2018. An Overview of Vulnerabilities of Voice Controlled Systems. arXiv preprint arXiv:1803.09156 ( 2018 ). Yuan Gong and Christian Poellabauer. 2018. An Overview of Vulnerabilities of Voice Controlled Systems. arXiv preprint arXiv:1803.09156 (2018)."},{"key":"e_1_3_2_2_17_1","volume-title":"Explaining and Harnessing Adversarial Examples. In International Conference on Learning Representations.","author":"Goodfellow Ian J.","year":"2015","unstructured":"Ian J. Goodfellow , Jonathon Shlens , and Christian Szegedy . 2015 . Explaining and Harnessing Adversarial Examples. In International Conference on Learning Representations. Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy. 2015. Explaining and Harnessing Adversarial Examples. In International Conference on Learning Representations."},{"key":"e_1_3_2_2_18_1","volume-title":"Deepsafe: A data-driven approach for checking adversarial robustness in neural networks. arXiv preprint arXiv:1710.00486","author":"Gopinath Divya","year":"2017","unstructured":"Divya Gopinath , Guy Katz , Corina S Pasareanu , and Clark Barrett . 2017 . Deepsafe: A data-driven approach for checking adversarial robustness in neural networks. arXiv preprint arXiv:1710.00486 (2017). Divya Gopinath, Guy Katz, Corina S Pasareanu, and Clark Barrett. 2017. Deepsafe: A data-driven approach for checking adversarial robustness in neural networks. arXiv preprint arXiv:1710.00486 (2017)."},{"key":"e_1_3_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-66399-9_4"},{"key":"e_1_3_2_2_20_1","volume-title":"McDaniel","author":"Grosse Kathrin","year":"2016","unstructured":"Kathrin Grosse , Nicolas Papernot , Praveen Manoharan , Michael Backes , and Patrick D . McDaniel . 2016 . Adversarial Perturbations Against Deep Neural Networks for Malware Classification. CoRR abs\/1606.04435 (2016). http:\/\/arxiv.org\/abs\/1606.04435. Kathrin Grosse, Nicolas Papernot, Praveen Manoharan, Michael Backes, and Patrick D. McDaniel. 2016. Adversarial Perturbations Against Deep Neural Networks for Malware Classification. CoRR abs\/1606.04435 (2016). http:\/\/arxiv.org\/abs\/1606.04435."},{"key":"e_1_3_2_2_21_1","volume-title":"Deep Residual Learning for Image Recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 770-778","author":"He Kaiming","year":"2016","unstructured":"Kaiming He , Xiangyu Zhang , Shaoqing Ren , and Jian Sun . 2016 . Deep Residual Learning for Image Recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 770-778 . Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. 2016. Deep Residual Learning for Image Recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). 770-778."},{"key":"e_1_3_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-53413-7_12"},{"key":"e_1_3_2_2_23_1","volume-title":"Safety Verification of Deep Neural Networks. CoRR abs\/1610.06940","author":"Huang Xiaowei","year":"2016","unstructured":"Xiaowei Huang , Marta Kwiatkowska , Sen Wang , and Min Wu. 2016. Safety Verification of Deep Neural Networks. CoRR abs\/1610.06940 ( 2016 ). Xiaowei Huang, Marta Kwiatkowska, Sen Wang, and Min Wu. 2016. Safety Verification of Deep Neural Networks. CoRR abs\/1610.06940 (2016)."},{"volume-title":"2016 IEEE\/AIAA 35th Digital Avionics Systems Conference (DASC). 1-10","author":"Julian Kyle D.","key":"e_1_3_2_2_24_1","unstructured":"Kyle D. Julian , Jessica Lopez , Jeffrey S. Brush , Michael P. Owen , and Mykel J. Kochenderfer . 2016. Policy compression for aircraft collision avoidance systems . In 2016 IEEE\/AIAA 35th Digital Avionics Systems Conference (DASC). 1-10 . Kyle D. Julian, Jessica Lopez, Jeffrey S. Brush, Michael P. Owen, and Mykel J. Kochenderfer. 2016. Policy compression for aircraft collision avoidance systems. In 2016 IEEE\/AIAA 35th Digital Avionics Systems Conference (DASC). 1-10."},{"volume-title":"Proceedings of the 29th International Conference On Computer Aided Verification.","author":"Katz Guy","key":"e_1_3_2_2_25_1","unstructured":"Guy Katz , Clark Barrett , David L. Dill , Kyle Julian , and Mykel J. Kochenderfer . 2017. Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks . In Proceedings of the 29th International Conference On Computer Aided Verification. Guy Katz, Clark Barrett, David L. Dill, Kyle Julian, and Mykel J. Kochenderfer. 2017. Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks. In Proceedings of the 29th International Conference On Computer Aided Verification."},{"key":"e_1_3_2_2_26_1","volume-title":"Kochenderfer","author":"Katz Guy","year":"2017","unstructured":"Guy Katz , Clark W. Barrett , David L. Dill , Kyle Julian , and Mykel J . Kochenderfer . 2017 . Reluplex : An Efficient SMT Solver for Verifying Deep Neural Networks. CoRR abs\/1702.01135 (2017). Guy Katz, Clark W. Barrett, David L. Dill, Kyle Julian, and Mykel J. Kochenderfer. 2017. Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks. CoRR abs\/1702.01135 (2017)."},{"volume-title":"Advances in Neural Information Processing Systems 25","author":"Krizhevsky Alex","key":"e_1_3_2_2_28_1","unstructured":"Alex Krizhevsky , Ilya Sutskever , and Geoffrey E Hinton . 2012. ImageNet Classification with Deep Convolutional Neural Networks . In Advances in Neural Information Processing Systems 25 , F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger (Eds.). Curran Associates, Inc. , 1097-1105. http:\/\/papers.nips.cc\/paper\/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf. Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. 2012. ImageNet Classification with Deep Convolutional Neural Networks. In Advances in Neural Information Processing Systems 25, F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger (Eds.). Curran Associates, Inc., 1097-1105. http:\/\/papers.nips.cc\/paper\/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf."},{"key":"e_1_3_2_2_29_1","volume-title":"Adversarial Machine Learning at Scale. CoRR abs\/1611.01236","author":"Kurakin Alexey","year":"2016","unstructured":"Alexey Kurakin , Ian J. Goodfellow , and Samy Bengio . 2016. Adversarial Machine Learning at Scale. CoRR abs\/1611.01236 ( 2016 ). arXiv:1611.01236 http:\/\/arxiv.org\/abs\/1611.01236. Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio. 2016. Adversarial Machine Learning at Scale. CoRR abs\/1611.01236 (2016). arXiv:1611.01236 http:\/\/arxiv.org\/abs\/1611.01236."},{"key":"e_1_3_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/5.726791"},{"key":"e_1_3_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/1926385.1926391"},{"key":"e_1_3_2_2_32_1","volume-title":"An approach to reachability analysis for feed-forward ReLU neural networks. CoRR abs\/1706.07351","author":"Lomuscio Alessio","year":"2017","unstructured":"Alessio Lomuscio and Lalit Maganti . 2017. An approach to reachability analysis for feed-forward ReLU neural networks. CoRR abs\/1706.07351 ( 2017 ). arXiv:1706.07351 http:\/\/arxiv.org\/abs\/1706.07351. Alessio Lomuscio and Lalit Maganti. 2017. An approach to reachability analysis for feed-forward ReLU neural networks. CoRR abs\/1706.07351 (2017). arXiv:1706.07351 http:\/\/arxiv.org\/abs\/1706.07351."},{"key":"e_1_3_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2015.84"},{"key":"e_1_3_2_2_34_1","unstructured":"Aleksander Madry Aleksandar Makelov Ludwig Schmidt Dimitris Tsipras and Adrian Vladu. 2018. Towards deep learning models resistant to adversarial attacks.  Aleksander Madry Aleksandar Makelov Ludwig Schmidt Dimitris Tsipras and Adrian Vladu. 2018. Towards deep learning models resistant to adversarial attacks."},{"key":"e_1_3_2_2_35_1","first-page":"3915","article-title":"BayesOpt: A Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits","volume":"15","author":"Martinez-Cantin Ruben","year":"2014","unstructured":"Ruben Martinez-Cantin . 2014 . BayesOpt: A Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits . Journal of Machine Learning Research 15 (2014), 3915 - 3919 . http:\/\/jmlr.org\/papers\/v15\/martinezcantin14a.html. Ruben Martinez-Cantin. 2014. BayesOpt: A Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits. Journal of Machine Learning Research 15 (2014), 3915-3919. http:\/\/jmlr.org\/papers\/v15\/martinezcantin14a.html.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCVW.2017.94"},{"volume-title":"Visualization, Software, and Applications","author":"Mockus Jonas","key":"e_1_3_2_2_37_1","unstructured":"Jonas Mockus . 2010. Bayesian Heuristic Approach to Discrete and Global Optimization: Algorithms , Visualization, Software, and Applications . Springer-Verlag , Berlin, Heidelberg . Jonas Mockus. 2010. Bayesian Heuristic Approach to Discrete and Global Optimization: Algorithms, Visualization, Software, and Applications. Springer-Verlag, Berlin, Heidelberg."},{"key":"e_1_3_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2015.7298640"},{"key":"e_1_3_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/2814270.2814309"},{"key":"e_1_3_2_2_40_1","volume-title":"Goodfellow","author":"Papernot Nicolas","year":"2016","unstructured":"Nicolas Papernot , Patrick D. McDaniel , and Ian J . Goodfellow . 2016 . Transferability in Machine Learning: from Phenomena to Black-Box Attacks using Adversarial Samples. CoRR abs\/1605.07277 (2016). arXiv:1605.07277 http:\/\/arxiv.org\/abs\/1605.07277. Nicolas Papernot, Patrick D. McDaniel, and Ian J. Goodfellow. 2016. Transferability in Machine Learning: from Phenomena to Black-Box Attacks using Adversarial Samples. CoRR abs\/1605.07277 (2016). arXiv:1605.07277 http:\/\/arxiv.org\/abs\/1605.07277."},{"key":"e_1_3_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/3132747.3132785"},{"key":"e_1_3_2_2_42_1","volume-title":"Towards Practical Verification of Machine Learning: The Case of Computer Vision Systems. CoRR abs\/1712.01785","author":"Pei Kexin","year":"2017","unstructured":"Kexin Pei , Yinzhi Cao , Junfeng Yang , and Suman Jana . 2017. Towards Practical Verification of Machine Learning: The Case of Computer Vision Systems. CoRR abs\/1712.01785 ( 2017 ). arXiv:1712.01785 http:\/\/arxiv.org\/abs\/1712.01785. Kexin Pei, Yinzhi Cao, Junfeng Yang, and Suman Jana. 2017. Towards Practical Verification of Machine Learning: The Case of Computer Vision Systems. CoRR abs\/1712.01785 (2017). arXiv:1712.01785 http:\/\/arxiv.org\/abs\/1712.01785."},{"key":"e_1_3_2_2_43_1","volume-title":"22nd International Conference, CAV 2010, Edinburgh, UK, July 15-19, 2010. Proceedings. 243-257","author":"Pulina Luca","year":"2010","unstructured":"Luca Pulina and Armando Tacchella . 2010 . An Abstraction-Refinement Approach to Verification of Artificial Neural Networks. In Computer Aided Verification , 22nd International Conference, CAV 2010, Edinburgh, UK, July 15-19, 2010. Proceedings. 243-257 . Luca Pulina and Armando Tacchella. 2010. An Abstraction-Refinement Approach to Verification of Artificial Neural Networks. In Computer Aided Verification, 22nd International Conference, CAV 2010, Edinburgh, UK, July 15-19, 2010. Proceedings. 243-257."},{"key":"e_1_3_2_2_44_1","volume-title":"Williams","author":"Rasmussen Carl Edward","year":"2006","unstructured":"Carl Edward Rasmussen and Christopher K. I . Williams . 2006 . Gaussian Processes for Machine Learning. The MIT Press . Carl Edward Rasmussen and Christopher K. I. Williams. 2006. Gaussian Processes for Machine Learning. The MIT Press."},{"key":"e_1_3_2_2_45_1","volume-title":"Fleet","author":"Sabour Sara","year":"2015","unstructured":"Sara Sabour , Yanshuai Cao , Fartash Faghri , and David J . Fleet . 2015 . Adversarial Manipulation of Deep Representations. CoRR abs\/1511.05122 (2015). Sara Sabour, Yanshuai Cao, Fartash Faghri, and David J. Fleet. 2015. Adversarial Manipulation of Deep Representations. CoRR abs\/1511.05122 (2015)."},{"key":"e_1_3_2_2_46_1","first-page":"30","volume-title":"MBMV 2015","author":"Scheibler Karsten","year":"2015","unstructured":"Karsten Scheibler , Leonore Winterer , Ralf Wimmer , and Bernd Becker . 2015 . Towards Verification of Artificial Neural Networks. In Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen , MBMV 2015 , Chemnitz, Germany , March 3-4, 2015. 30 - 40 . Karsten Scheibler, Leonore Winterer, Ralf Wimmer, and Bernd Becker. 2015. Towards Verification of Artificial Neural Networks. In Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen, MBMV 2015, Chemnitz, Germany, March 3-4, 2015. 30-40."},{"key":"e_1_3_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-38856-9_21"},{"key":"e_1_3_2_2_48_1","volume-title":"Proceedings of the Thirty-second Conference on Neural Information Processing Systems.","author":"Si Xujie","year":"2018","unstructured":"Xujie Si , Hanjun Dai , Mukund Raghothaman , Mayur Naik , and Le Song . 2018 . Learning loop invariants for program verification . In Proceedings of the Thirty-second Conference on Neural Information Processing Systems. Xujie Si, Hanjun Dai, Mukund Raghothaman, Mayur Naik, and Le Song. 2018. Learning loop invariants for program verification. In Proceedings of the Thirty-second Conference on Neural Information Processing Systems."},{"key":"e_1_3_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/3009837.3009885"},{"key":"e_1_3_2_2_50_1","volume-title":"Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199","author":"Szegedy Christian","year":"2013","unstructured":"Christian Szegedy , Wojciech Zaremba , Ilya Sutskever , Joan Bruna , Dumitru Erhan , Ian Goodfellow , and Rob Fergus . 2013. Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199 ( 2013 ). Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus. 2013. Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199 (2013)."},{"key":"e_1_3_2_2_51_1","volume-title":"Intriguing properties of neural networks. CoRR abs\/1312.6199","author":"Szegedy Christian","year":"2013","unstructured":"Christian Szegedy , Wojciech Zaremba , Ilya Sutskever , Joan Bruna , Dumitru Erhan , Ian J. Goodfellow , and Rob Fergus . 2013. Intriguing properties of neural networks. CoRR abs\/1312.6199 ( 2013 ). Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian J. Goodfellow, and Rob Fergus. 2013. Intriguing properties of neural networks. CoRR abs\/1312.6199 (2013)."},{"key":"e_1_3_2_2_52_1","doi-asserted-by":"publisher","DOI":"10.1109\/IJCNN.2016.7727230"},{"key":"e_1_3_2_2_53_1","volume-title":"Verifying Neural Networks with Mixed Integer Programming. CoRR abs\/1711.07356","author":"Tjeng Vincent","year":"2017","unstructured":"Vincent Tjeng and Russ Tedrake . 2017. Verifying Neural Networks with Mixed Integer Programming. CoRR abs\/1711.07356 ( 2017 ). arXiv:1711.07356 http:\/\/arxiv.org\/abs\/1711.07356. Vincent Tjeng and Russ Tedrake. 2017. Verifying Neural Networks with Mixed Integer Programming. CoRR abs\/1711.07356 (2017). arXiv:1711.07356 http:\/\/arxiv.org\/abs\/1711.07356."},{"key":"e_1_3_2_2_54_1","first-page":"1599","volume-title":"27th USENIX Security Symposium (USENIX Security 18)","author":"Wang Shiqi","year":"2018","unstructured":"Shiqi Wang , Kexin Pei , Justin Whitehouse , Junfeng Yang , and Suman Jana . 2018 . Formal Security Analysis of Neural Networks using Symbolic Intervals . In 27th USENIX Security Symposium (USENIX Security 18) . USENIX Association, Baltimore, MD , 1599 - 1614 . https:\/\/www.usenix.org\/conference\/usenixsecurity18\/presentation\/wang-shiqi. Shiqi Wang, Kexin Pei, Justin Whitehouse, Junfeng Yang, and Suman Jana. 2018. Formal Security Analysis of Neural Networks using Symbolic Intervals. In 27th USENIX Security Symposium (USENIX Security 18). USENIX Association, Baltimore, MD, 1599-1614. https:\/\/www.usenix.org\/conference\/usenixsecurity18\/presentation\/wang-shiqi."},{"key":"e_1_3_2_2_55_1","volume-title":"Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation. CoRR abs\/1609.08144","author":"Wu Yonghui","year":"2016","unstructured":"Yonghui Wu , Mike Schuster , Zhifeng Chen , Quoc V. Le , Mohammad Norouzi , Wolfgang Macherey , Maxim Krikun , Yuan Cao , Qin Gao , Klaus Macherey , Jeff Klingner , Apurva Shah , Melvin Johnson , Xiaobing Liu , Lukasz Kaiser , Stephan Gouws , Yoshikiyo Kato , Taku Kudo , Hideto Kazawa , Keith Stevens , George Kurian , Nishant Patil , Wei Wang , Cliff Young , Jason Smith , Jason Riesa , Alex Rudnick , Oriol Vinyals , Greg Corrado , Macduff Hughes , and Jeffrey Dean . 2016. Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation. CoRR abs\/1609.08144 ( 2016 ). http:\/\/arxiv.org\/abs\/1609.08144. Yonghui Wu, Mike Schuster, Zhifeng Chen, Quoc V. Le, Mohammad Norouzi, Wolfgang Macherey, Maxim Krikun, Yuan Cao, Qin Gao, Klaus Macherey, Jeff Klingner, Apurva Shah, Melvin Johnson, Xiaobing Liu, Lukasz Kaiser, Stephan Gouws, Yoshikiyo Kato, Taku Kudo, Hideto Kazawa, Keith Stevens, George Kurian, Nishant Patil, Wei Wang, Cliff Young, Jason Smith, Jason Riesa, Alex Rudnick, Oriol Vinyals, Greg Corrado, Macduff Hughes, and Jeffrey Dean. 2016. Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation. CoRR abs\/1609.08144 (2016). http:\/\/arxiv.org\/abs\/1609.08144."},{"key":"e_1_3_2_2_56_1","volume-title":"Rajendra Rana Bhat, and Xiaolin Li","author":"Yuan Xiaoyong","year":"2017","unstructured":"Xiaoyong Yuan , Pan He , Qile Zhu , Rajendra Rana Bhat, and Xiaolin Li . 2017 . Adversarial Examples : Attacks and Defenses for Deep Learning. CoRR abs\/1712.07107 (2017). arXiv:1712.07107 http:\/\/arxiv.org\/abs\/1712.07107. Xiaoyong Yuan, Pan He, Qile Zhu, Rajendra Rana Bhat, and Xiaolin Li. 2017. Adversarial Examples: Attacks and Defenses for Deep Learning. CoRR abs\/1712.07107 (2017). arXiv:1712.07107 http:\/\/arxiv.org\/abs\/1712.07107."},{"key":"e_1_3_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1145\/2619239.2631434"},{"key":"e_1_3_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1109\/TST.2016.7399288"}],"event":{"name":"PLDI '19: 40th ACM SIGPLAN Conference on Programming Language Design and Implementation","sponsor":["SIGPLAN ACM Special Interest Group on Programming Languages"],"location":"Phoenix AZ USA","acronym":"PLDI '19"},"container-title":["Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3314221.3314614","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3314221.3314614","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:53:22Z","timestamp":1750204402000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3314221.3314614"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,8]]},"references-count":57,"alternative-id":["10.1145\/3314221.3314614","10.1145\/3314221"],"URL":"https:\/\/doi.org\/10.1145\/3314221.3314614","relation":{},"subject":[],"published":{"date-parts":[[2019,6,8]]},"assertion":[{"value":"2019-06-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}