{"type":"ScholarlyArticle","title":"Certified Robustness via Randomized Smoothing over Multiplicative Parameters of Input Transformations","authors":[{"name":"Nikita Muravev","slug":"nikita-muravev","given":"Nikita","family":"Muravev","affiliation":"Huawei Moscow Research Center; Lomonosov Moscow State University"},{"name":"Aleksandr Petiushko","slug":"aleksandr-petiushko","given":"Aleksandr","family":"Petiushko","affiliation":"Lomonosov Moscow State University; Nuro , Inc."}],"abstract":"Currently the most popular method of providing robustness certificates is randomized smoothing where an input is smoothed via some probability distribution. We propose a novel approach to randomized smoothing over multiplicative parameters. Using this method we construct certifiably robust classifiers with respect to a gamma correction perturbation and compare the result with classifiers obtained via other smoothing distributions (Gaussian, Laplace, uniform). The experiments show that asymmetrical Rayleigh distribution allows to obtain better certificates for some values of perturbation parameters. To the best of our knowledge it is the first work concerning certified robustness against the multiplicative gamma correction transformation and the first to study effects of asymmetrical distributions in randomized smoothing.","doi":"10.24963/ijcai.2022/467","url":"https://ijcai.org/proceedings/2022/467","pdf":"https://ijcai.org/proceedings/2022/0467.pdf","markdown":"https://ijcai.org/proceedings/2022/467.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/467","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Machine Learning","track":"Main Track","number":467,"pages":{"first":3366,"last":3372},"keywords":["Machine Learning: Classification","Machine Learning: Robustness"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986844","length_sec":86,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984987","length_sec":313,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Agarwal and Mahajan, 2017] Monika Agarwal and Rashima Mahajan. Medical images contrast enhance- ment using quad weighted histogram equalization with adaptive gama correction and homomorphic filtering. Procedia Computer Science, 115:509-517, 2017. 7th International Conference on Advances in Computing & Communications, ICACC-2017, 22-24 August 2017, Cochin, India.","title":"Medical images contrast enhancement using quad weighted histogram equalization with adaptive gama correction and homomorphic filtering","authors":"Monika Agarwal, Rashima Mahajan","year":"2017","venue":"International Conference on Advances in Computing & Communications, ICACC-2017","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Alfarra et al., 2021] Motasem Alfarra, Adel Bibi, Naeemul- lah Khan, Philip H. S. Torr, and Bernard Ghanem. De- formrs: Certifying input deformations with randomized smoothing. ArXiv, 2021.","title":"Deformrs: Certifying input deformations with randomized smoothing","authors":"Alfarra","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Athalye et al., 2018] Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial exam- ples. In Jennifer Dy and Andreas Krause, editors, Pro- ceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 274-283, Stockholmsmässan, Stockholm Sweden, 10-15 Jul 2018. PMLR.","title":"Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples","authors":"Anish Athalye, Nicholas Carlini, David Wagner","year":"2018","venue":"Proceedings of the 35th International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Carlini and Wagner, 2017] Nicholas Carlini and David Wagner. Adversarial examples are not easily detected: Bypassing ten detection methods. In Proceedings of the 10th ACM Workshop on Artificial Intelligence and Security, AISec '17, page 3-14, New York, NY, USA, 2017. Association for Computing Machinery.","title":"Adversarial examples are not easily detected: Bypassing ten detection methods","authors":"Wagner Carlini, Nicholas Carlini, David Wagner","year":"2017","venue":"Proceedings of the 10th ACM Workshop on Artificial Intelligence and Security, AISec '17","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Clopper and Pearson, 1934] C. J. Clopper and E. S. Pear- son. The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26(4):404-413, 1934.","title":"The use of confidence or fiducial limits illustrated in the case of the binomial","authors":"C J Clopper, E S Pearson","year":"1934","venue":"Biometrika","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Cohen et al., 2019] Jeremy M. Cohen, Elan Rosenfeld, and J. Zico Kolter. Certified adversarial robustness via ran- domized smoothing. Proceedings of Machine Learning Research, 97:1310-1320, 2019.","title":"Certified adversarial robustness via randomized smoothing","authors":"Jeremy M Cohen, Elan Rosenfeld, J Zico Kolter","year":"2019","venue":"Proceedings of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Deng et al., 2009] Jia Deng, Wei Dong, Richard Socher, Li- Jia Li, Kai Li, and Fei-Fei Li. Imagenet: a large-scale hierarchical image database. IEEE Conference on Com- puter Vision and Pattern Recognition, pages 248-255, 06 2009.","title":"Imagenet: a large-scale hierarchical image database","authors":"Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, Fei-Fei Li","year":"2009","venue":"IEEE Conference on Computer Vision and Pattern Recognition","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Fischer et al., 2020] Marc Fischer, Maximilian Baader, and Martin Vechev. Certified defense to image transformations via randomized smoothing. Advances in Neural Informa- tion Processing Systems, 33:8404-8417, 2020.","title":"Certified defense to image transformations via randomized smoothing","authors":"Fischer","year":"2020","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Goodfellow et al., 2015] Ian Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adver- sarial examples. In International Conference on Learning Representations, 2015.","title":"Explaining and harnessing adversarial examples","authors":"Ian Goodfellow, Jonathon Shlens, Christian Szegedy","year":"2015","venue":"International Conference on Learning Representations","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Hayes, 2020] J. Hayes. Extensions and limitations of ran- domized smoothing for robustness guarantees. In 2020 IEEE/CVF Conference on Computer Vision and Pat- tern Recognition Workshops (CVPRW), pages 3413-3421, 2020.","title":"Extensions and limitations of randomized smoothing for robustness guarantees","authors":"J Hayes","year":"2020","venue":"IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Jeong and Shin, 2020] Jongheon Jeong and Jinwoo Shin. Consistency regularization for certified robustness of smoothed classifiers. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 10558-10570.","title":"Consistency regularization for certified robustness of smoothed classifiers","authors":"Shin ; ] Jongheon Jeong, Jinwoo Jeong, Shin","year":"2020","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"Curran Associates, Inc., 2020.","title":null,"authors":"Curran Associates, Inc","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Kurakin and Ian Goodfellow, 2017] Alexey Kurakin and Samy Bengio Ian Goodfellow. Adversarial machine learn- ing at scale. ArXiv, 2017.","title":"Adversarial machine learning at scale","authors":"Alexey Kurakin, Samy Bengio, Ian Goodfellow","year":"2017","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Lecuyer et al., 2019] M. Lecuyer, V. Atlidakis, R. Geam- basu, D. Hsu, and S Jana. Certified robustness to adversar- ial examples with differential privacy. In IEEE Symposium on Security and Privacy (SP), 2019.","title":"Certified robustness to adversarial examples with differential privacy","authors":"M Lecuyer, V Atlidakis, R Geambasu, D Hsu, Jana","year":"2019","venue":"IEEE Symposium on Security and Privacy (SP)","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Li et al., 2019] Bai Li, Changyou Chen, Wenlin Wang, and Lawrence Carin. Certified adversarial robustness with ad- ditive noise. Advances in Neural Information Processing Systems, 32, 2019.","title":"Certified adversarial robustness with additive noise","authors":"Bai Li, Changyou Chen, Wenlin Wang, Lawrence Carin","year":"2019","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Li et al., 2021] Linyi Li, Maurice Weber, Xiaojun Xu, Luka Rimanic, Bhavya Kailkhura, Tao Xie, Ce Zhang, and Bo Li. Tss: Transformation-specific smoothing for ro- bustness certification. In Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, CCS '21, page 535-557, New York, NY, USA, 2021. Association for Computing Machinery.","title":"Tss: Transformation-specific smoothing for robustness certification","authors":"Li","year":"2021","venue":"Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, CCS '21","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Liu et al., 2018] Xuanqing Liu, Minhao Cheng, Huan Zhang, and Cho-Jui Hsieh. Towards robust neural net- works via random self-ensemble. In Proceedings of the European Conference on Computer Vision (ECCV), September 2018.","title":"Towards robust neural networks via random self-ensemble","authors":"Liu","year":"2018","venue":"Proceedings of the European Conference on Computer Vision (ECCV)","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Somasundaram and Kalavathi, 2011] Karuppanagounder Somasundaram and Palanisamy Kalavathi. Medical image contrast enhancement based on gamma correction. International Journal of Knowledge Management and e-Learning, 3:15-18, 02 2011.","title":"Karuppanagounder Somasundaram and Palanisamy Kalavathi. Medical image contrast enhancement based on gamma correction","authors":"Kalavathi Somasundaram","year":"2011","venue":"International Journal of Knowledge Management and e-Learning","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Szegedy et al., 2014] Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Er- han, J. Ian Goodfellow, and Rob Fergus. Intriguing properties of neural networks. international conference on learning representations, 2014.","title":"Intriguing properties of neural networks","authors":"Szegedy","year":"2014","venue":"international conference on learning representations","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Veluchamy and Subramani, 2019] Magudeeswaran Veluchamy and Bharath Subramani. Image contrast and color enhancement using adaptive gamma correction and histogram equalization. Optik, 183:329-337, 2019.","title":"Magudeeswaran Veluchamy and Bharath Subramani. Image contrast and color enhancement using adaptive gamma correction and histogram equalization","authors":"Subramani Veluchamy","year":"2019","venue":"Optik","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Wong and Kolter, 2018] Eric Wong and Zico Kolter. Prov- able defenses against adversarial examples via the con- vex outer adversarial polytope. In Jennifer Dy and An- dreas Krause, editors, Proceedings of the 35th Interna- tional Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 5286- 5295, Stockholmsmässan, Stockholm Sweden, 10-15 Jul 2018. PMLR.","title":"Provable defenses against adversarial examples via the convex outer adversarial polytope","authors":"Kolter Wong, Eric Wong, Zico Kolter","year":"2018","venue":"Proceedings of the 35th International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Zhang et al., 2020] Dinghuai Zhang, Mao Ye, Chengyue Gong, Zhanxing Zhu, and Qiang Liu. Black-box certifica- tion with randomized smoothing: A functional optimiza- tion based framework. Advances in Neural Information Processing Systems, 33:2316-2326, 2020.","title":"Black-box certification with randomized smoothing: A functional optimization based framework","authors":"Zhang","year":"2020","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}