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However, designing a precise and scalable verifier which can handle different activation functions, realistic network architectures and relevant specifications remains an open and difficult challenge.<\/jats:p>\n          <jats:p>\n            In this paper, we take a major step forward in addressing this challenge and present a new verification framework, called PRIMA. PRIMA is both (i) general: it handles any non-linear activation function, and (ii) precise: it computes precise convex abstractions involving\n            <jats:italic>multiple<\/jats:italic>\n            neurons via novel convex hull approximation algorithms that leverage concepts from computational geometry. The algorithms have polynomial complexity, yield fewer constraints, and minimize precision loss.\n          <\/jats:p>\n          <jats:p>We evaluate the effectiveness of PRIMA on a variety of challenging tasks from prior work. Our results show that PRIMA is significantly more precise than the state-of-the-art, verifying robustness to input perturbations for up to 20%, 30%, and 34% more images than existing work on ReLU-, Sigmoid-, and Tanh-based networks, respectively. Further, PRIMA enables, for the first time, the precise verification of a realistic neural network for autonomous driving within a few minutes.<\/jats:p>","DOI":"10.1145\/3498704","type":"journal-article","created":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T17:03:12Z","timestamp":1642006992000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":70,"title":["PRIMA: general and precise neural network certification via scalable convex hull approximations"],"prefix":"10.1145","volume":"6","author":[{"given":"Mark Niklas","family":"M\u00fcller","sequence":"first","affiliation":[{"name":"ETH Zurich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9802-3299","authenticated-orcid":false,"given":"Gleb","family":"Makarchuk","sequence":"additional","affiliation":[{"name":"ETH Zurich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gagandeep","family":"Singh","sequence":"additional","affiliation":[{"name":"VMware Research, USA \/ University of Illinois at Urbana-Champaign, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Markus","family":"P\u00fcschel","sequence":"additional","affiliation":[{"name":"ETH Zurich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Vechev","sequence":"additional","affiliation":[{"name":"ETH Zurich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2022,1,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3314221.3314614"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-020-01474-5"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0893-9659(91)90141-H"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02293050"},{"key":"e_1_2_2_5_1","volume-title":"Certifying Geometric Robustness of Neural Networks. 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Wallach, Hugo Larochelle, Kristen Grauman, Nicol\u00f2 Cesa-Bianchi, and Roman Garnett (Eds.). 10825\u201310836. https:\/\/proceedings.neurips.cc\/paper\/2018\/hash\/f2f446980d8e971ef3da97af089481c3-Abstract.html Gagandeep Singh, Timon Gehr, Matthew Mirman, Markus P\u00fcschel, and Martin T. Vechev. 2018. Fast and Effective Robustness Certification. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montr\u00e9al, Canada, Samy Bengio, Hanna M. Wallach, Hugo Larochelle, Kristen Grauman, Nicol\u00f2 Cesa-Bianchi, and Roman Garnett (Eds.). 10825\u201310836. https:\/\/proceedings.neurips.cc\/paper\/2018\/hash\/f2f446980d8e971ef3da97af089481c3-Abstract.html"},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/3290354"},{"key":"e_1_2_2_54_1","volume-title":"Boosting Robustness Certification of Neural Networks. 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OpenReview.net. https:\/\/openreview.net\/forum?id=HJgeEh09KQ"},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/3009837.3009885"},{"key":"e_1_2_2_56_1","volume-title":"2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings, Yoshua Bengio and Yann LeCun (Eds.). arxiv:1312","author":"Szegedy Christian","year":"2014","unstructured":"Christian Szegedy , Wojciech Zaremba , Ilya Sutskever , Joan Bruna , Dumitru Erhan , Ian J. Goodfellow , and Rob Fergus . 2014 . Intriguing properties of neural networks . In 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings, Yoshua Bengio and Yann LeCun (Eds.). arxiv:1312 .6199 Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian J. Goodfellow, and Rob Fergus. 2014. Intriguing properties of neural networks. 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In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020 , NeurIPS 2020, December 6-12, 2020, virtual, Hugo Larochelle, Marc\u2019Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (Eds.). https:\/\/proceedings.neurips.cc\/paper\/2020\/hash\/f6c2a0c4b566bc99d596e58638e342b0-Abstract.html Christian Tjandraatmadja, Ross Anderson, Joey Huchette, Will Ma, Krunal Patel, and Juan Pablo Vielma. 2020. The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, Hugo Larochelle, Marc\u2019Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (Eds.). https:\/\/proceedings.neurips.cc\/paper\/2020\/hash\/f6c2a0c4b566bc99d596e58638e342b0-Abstract.html"},{"key":"e_1_2_2_58_1","volume-title":"Evaluating Robustness of Neural Networks with Mixed Integer Programming. In 7th International Conference on Learning Representations, ICLR 2019","author":"Tjeng Vincent","year":"2019","unstructured":"Vincent Tjeng , Kai Y. Xiao , and Russ Tedrake . 2019 . Evaluating Robustness of Neural Networks with Mixed Integer Programming. In 7th International Conference on Learning Representations, ICLR 2019 , New Orleans, LA, USA , May 6-9, 2019. OpenReview.net. https:\/\/openreview.net\/forum?id=HyGIdiRqtm Vincent Tjeng, Kai Y. Xiao, and Russ Tedrake. 2019. Evaluating Robustness of Neural Networks with Mixed Integer Programming. In 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, May 6-9, 2019. OpenReview.net. https:\/\/openreview.net\/forum?id=HyGIdiRqtm"},{"key":"e_1_2_2_59_1","unstructured":"Udacity. 2016. Using Deep Learning to Predict Steering Angles. https:\/\/github.com\/udacity\/self-driving-car  Udacity. 2016. Using Deep Learning to Predict Steering Angles. https:\/\/github.com\/udacity\/self-driving-car"},{"key":"e_1_2_2_60_1","volume-title":"A Review of Formal Methods applied to Machine Learning. ArXiv preprint, abs\/2104.02466","author":"Urban Caterina","year":"2021","unstructured":"Caterina Urban and Antoine Min\u00e9 . 2021. A Review of Formal Methods applied to Machine Learning. ArXiv preprint, abs\/2104.02466 ( 2021 ), arxiv:2104.02466 Caterina Urban and Antoine Min\u00e9. 2021. A Review of Formal Methods applied to Machine Learning. 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Efficient Formal Safety Analysis of Neural Networks. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montr\u00e9al, Canada, Samy Bengio, Hanna M. Wallach, Hugo Larochelle, Kristen Grauman, Nicol\u00f2 Cesa-Bianchi, and Roman Garnett (Eds.). 6369\u20136379. https:\/\/proceedings.neurips.cc\/paper\/2018\/hash\/2ecd2bd94734e5dd392d8678bc64cdab-Abstract.html"},{"key":"e_1_2_2_62_1","volume-title":"Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Verification. ArXiv preprint, abs\/2103.06624","author":"Wang Shiqi","year":"2021","unstructured":"Shiqi Wang , Huan Zhang , Kaidi Xu , Xue Lin , Suman Jana , Cho-Jui Hsieh , and J Zico Kolter . 2021. Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Verification. 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PMLR, 5273\u20135282. http:\/\/proceedings.mlr.press\/v80\/weng18a.html Tsui-Wei Weng, Huan Zhang, Hongge Chen, Zhao Song, Cho-Jui Hsieh, Luca Daniel, Duane S. Boning, and Inderjit S. Dhillon. 2018. Towards Fast Computation of Certified Robustness for ReLU Networks. In Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsm\u00e4ssan, Stockholm, Sweden, July 10-15, 2018, Jennifer G. Dy and Andreas Krause (Eds.) (Proceedings of Machine Learning Research, Vol. 80). PMLR, 5273\u20135282. http:\/\/proceedings.mlr.press\/v80\/weng18a.html"},{"key":"e_1_2_2_64_1","volume-title":"Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018","author":"Wong Eric","year":"2018","unstructured":"Eric Wong , Frank R. Schmidt , Jan Hendrik Metzen , and J. Zico Kolter . 2018. Scaling provable adversarial defenses . In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018 , NeurIPS 2018 , December 3-8, 2018, Montr\u00e9al, Canada, Samy Bengio, Hanna M. Wallach, Hugo Larochelle, Kristen Grauman, Nicol\u00f2 Cesa-Bianchi, and Roman Garnett (Eds.). 8410\u20138419. https:\/\/proceedings.neurips.cc\/paper\/2018\/hash\/358f9e7be09177c17d0d17ff73584307-Abstract.html Eric Wong, Frank R. Schmidt, Jan Hendrik Metzen, and J. Zico Kolter. 2018. Scaling provable adversarial defenses. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montr\u00e9al, Canada, Samy Bengio, Hanna M. Wallach, Hugo Larochelle, Kristen Grauman, Nicol\u00f2 Cesa-Bianchi, and Roman Garnett (Eds.). 8410\u20138419. https:\/\/proceedings.neurips.cc\/paper\/2018\/hash\/358f9e7be09177c17d0d17ff73584307-Abstract.html"},{"key":"e_1_2_2_65_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2018.2808470"},{"key":"e_1_2_2_66_1","volume-title":"Automatic Perturbation Analysis for Scalable Certified Robustness and Beyond. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020","author":"Xu Kaidi","year":"2020","unstructured":"Kaidi Xu , Zhouxing Shi , Huan Zhang , Yihan Wang , Kai-Wei Chang , Minlie Huang , Bhavya Kailkhura , Xue Lin , and Cho-Jui Hsieh . 2020 . Automatic Perturbation Analysis for Scalable Certified Robustness and Beyond. 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In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, Hugo Larochelle, Marc\u2019Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (Eds.). https:\/\/proceedings.neurips.cc\/paper\/2020\/hash\/0cbc5671ae26f67871cb914d81ef8fc1-Abstract.html"},{"key":"e_1_2_2_67_1","volume-title":"Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers. In 9th International Conference on Learning Representations, ICLR 2021","author":"Xu Kaidi","year":"2021","unstructured":"Kaidi Xu , Huan Zhang , Shiqi Wang , Yihan Wang , Suman Jana , Xue Lin , and Cho-Jui Hsieh . 2021 . Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers. In 9th International Conference on Learning Representations, ICLR 2021 , Virtual Event, Austria , May 3-7, 2021. 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