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Certified defenses based on convex relaxations are an established technique for training provably robust models.
Quadratic programming with one negative eigenvalue is np-hard
Panos M Pardalos and Stephen A Vavasis · 1991
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Discontinuous piecewise linear optimization
Andrew R Conn and Marcel Mongeau · 1998
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Minimization of discontinuous cost functions by smoothing
José Mario Martínez · 2002
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Global optimization of rational functions: a semidefinite programming approach
Dorina Jibetean and Etienne de Klerk · 2006
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Rational function optimization using genetic algorithms
MJ Valadan Zoej, Mehdi Mokhtarzade, Ali Mansourian, Hamid Ebadi, and S Sadeghian · 2007
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Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot and Yoshua Bengio · 2010
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2013
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Exact solutions to the nonlinear dynamics of learning in deep linear neural networks
Andrew M. Saxe, James L. McClelland, and Surya Ganguli · 2014
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Global optimization of bounded factorable functions with discontinuities
Achim Wechsung and Paul I Barton · 2014
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Explaining and harnessing adversarial examples
Ian Goodfellow, Jonathon Shlens, and Christian Szegedy · 2015
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Formal verification of piece-wise linear feed-forward neural networks
Rüdiger Ehlers · 2017
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Reluplex: An efficient smt solver for verifying deep neural networks
Guy Katz, Clark Barrett, David L Dill, Kyle Julian, and Mykel J Kochenderfer · 2017
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Ai2: Safety and robustness certification of neural networks with abstract interpretation
Timon Gehr, Matthew Mirman, Dana Drachsler-Cohen, Petar Tsankov, Swarat Chaudhuri, and Martin Vechev · 2018
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On the effectiveness of interval bound propagation for training verifiably robust models
Sven Gowal, Krishnamurthy Dvijotham, Robert Stanforth, Rudy Bunel, Chongli Qin, Jonathan Uesato, Timothy Mann, and Pushmeet Kohli · 2018
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Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2018
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Differentiable abstract interpretation for provably robust neural networks
Matthew Mirman, Timon Gehr, and Martin Vechev · 2018
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Fast and effective robustness certification
Gagandeep Singh, Timon Gehr, Matthew Mirman, Markus Püschel, and Martin Vechev · 2018
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Towards fast computation of certified robustness for ReLU networks
Lily Weng, Huan Zhang, Hongge Chen, Zhao Song, Cho-Jui Hsieh, Luca Daniel, Duane Boning, and Inderjit Dhillon · 2018
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Provable defenses against adversarial examples via the convex outer adversarial polytope
Eric Wong and Zico Kolter · 2018
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Scaling provable adversarial defenses
Eric Wong, Frank Schmidt, Jan Hendrik Metzen, and J. Zico Kolter · 2018
Enabling certification of verification-agnostic networks via memory-efficient semidefinite programming
Sumanth Dathathri, Krishnamurthy Dvijotham, Alexey Kurakin, Aditi Raghunathan, Jonathan Uesato, Rudy Bunel, Shreya Shankar, Jacob Steinhardt, Ian J. Goodfellow, Percy Liang, and Pushmeet Kohli · 2020
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Sok: Certified robustness for deep neural networks
Linyi Li, Xiangyu Qi, Tao Xie, and Bo Li · 2020
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The convex relaxation barrier, revisited: Tightened single-neuron relaxations for neural network verification
Christian Tjandraatmadja, Ross Anderson, Joey Huchette, Will Ma, Krunal Patel, and Juan Pablo Vielma · 2020
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Automatic perturbation analysis for scalable certified robustness and beyond
Kaidi Xu, Zhouxing Shi, Huan Zhang, Yihan Wang, Kai-Wei Chang, Minlie Huang, Bhavya Kailkhura, Xue Lin, and Cho-Jui Hsieh · 2020
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Randomized smoothing of all shapes and sizes
Greg Yang, Tony Duan, J. Edward Hu, Hadi Salman, Ilya P. Razenshteyn, and Jerry Li · 2020
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Efficient neural network robustness certification with general activation functions
Huan Zhang, Tsui-Wei Weng, Pin-Yu Chen, Cho-Jui Hsieh, and Luca Daniel · 2018
Cited alongside, same era.
Certified adversarial robustness via randomized smoothing
Jeremy Cohen, Elan Rosenfeld, and Zico Kolter · 2019
Cited alongside, same era.
A dual approach to verify and train deep networks
Sven Gowal, Krishnamurthy Dvijotham, Robert Stanforth, Timothy Mann, and Pushmeet Kohli · 2019
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Evaluating robustness of neural networks with mixed integer programming
Vincent Tjeng, Kai Y. Xiao, and Russ Tedrake · 2019
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Universal approximation with certified networks
Maximilian Baader, Matthew Mirman, and Martin T. Vechev · 2020
Cited alongside, same era.
Adversarial training and provable defenses: Bridging the gap
Mislav Balunovic and Martin Vechev · 2020
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Towards stable and efficient training of verifiably robust neural networks
Huan Zhang, Hongge Chen, Chaowei Xiao, Sven Gowal, Robert Stanforth, Bo Li, Duane Boning, and Cho-Jui Hsieh · 2020
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Towards better understanding of training certifiably robust models against adversarial examples
Sungyoon Lee, Woojin Lee, Jinseong Park, and Jaewook Lee · 2021
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Towards evaluating and training verifiably robust neural networks
Zhaoyang Lyu, Minghao Guo, Tong Wu, Guodong Xu, Kehuan Zhang, and Dahua Lin · 2021
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Prima: Precise and general neural network certification via multi-neuron convex relaxations, 2021
Mark Niklas Müller, Gleb Makarchuk, Gagandeep Singh, Markus Püschel, and Martin Vechev · 2021
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Scaling polyhedral neural network verification on GPUs
François Serre, Christoph Müller, Gagandeep Singh, Markus Püschel, and Martin Vechev · 2021
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Fast certified robust training with short warmup
Zhouxing Shi, Yihan Wang, Huan Zhang, Jinfeng Yi, and Cho-Jui Hsieh · 2021
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Towards certifying l-infinity robustness using neural networks with l-inf-dist neurons
Bohang Zhang, Tianle Cai, Zhou Lu, Di He, and Liwei Wang · 2021
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Boosting the certified robustness of l-infinity distance nets
Bohang Zhang, Du Jiang, Di He, and Liwei Wang · 2022
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