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Verification of neural networks enables us to gauge their robustness against adversarial attacks.
Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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ECOS: An SOCP solver for embedded systems
A. Domahidi, E. Chu, and S. Boyd · 2013
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Convex analysis
Ralph Tyrell Rockafellar · 2015
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Towards verification of artificial neural networks
Karsten Scheibler, Leonore Winterer, Ralf Wimmer, and Bernd Becker · 2015
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CVXPY: A Python-embedded modeling language for convex optimization
Steven Diamond and Stephen Boyd · 2016
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Provably minimally-distorted adversarial examples
Nicholas Carlini, Guy Katz, Clark Barrett, and David L Dill · 2017
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Maximum resilience of artificial neural networks
Chih-Hong Cheng, Georg Nührenberg, and Harald Ruess · 2017
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Formal verification of piece-wise linear feed-forward neural networks
Ruediger Ehlers · 2017
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Deep neural networks as 0-1 mixed integer linear programs: A feasibility study
Matteo Fischetti and Jason Jo · 2017
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Formal guarantees on the robustness of a classifier against adversarial manipulation
Matthias Hein and Maksym Andriushchenko · 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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An approach to reachability analysis for feed-forward relu neural networks
Alessio Lomuscio and Lalit Maganti · 2017
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Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2017
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Strong convex relaxations and mixed-integer programming formulations for trained neural networks
Ross Anderson, Joey Huchette, Christian Tjandraatmadja, and Juan Pablo Vielma · 2018
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A unified view of piecewise linear neural network verification
Rudy R Bunel, Ilker Turkaslan, Philip Torr, Pushmeet Kohli, and Pawan K Mudigonda · 2018
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Output range analysis for deep feedforward neural networks
Souradeep Dutta, Susmit Jha, Sriram Sankaranarayanan, and Ashish Tiwari · 2018
Towards fast computation of certified robustness for ReLU networks
Tsui-Wei Weng, Huan Zhang, Hongge Chen, Zhao Song, Cho-Jui Hsieh, Duane Boning, Inderjit S Dhillon, and Luca Daniel · 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
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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
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Certified adversarial robustness via randomized smoothing
Jeremy M Cohen, Elan Rosenfeld, and J Zico Kolter · 2019
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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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Certified robustness to adversarial examples with differential privacy
Mathias Lecuyer, Vaggelis Atlidakis, Roxana Geambasu, Daniel Hsu, and Suman Jana · 2018
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Second-order adversarial attack and certifiable robustness
Bai Li, Changyou Chen, Wenlin Wang, and Lawrence Carin · 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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Training verified learners with learned verifiers
Krishnamurthy Dvijotham, Sven Gowal, Robert Stanforth, Relja Arandjelovic, Brendan O’Donoghue, Jonathan Uesato, and Pushmeet Kohli
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Verification of non-linear specifications for neural networks
Chongli Qin, Krishnamurthy Dj Dvijotham, Brendan O’Donoghue, Rudy Bunel, Robert Stanforth, Sven Gowal, Jonathan Uesato, Grzegorz Swirszcz, and Pushmeet Kohli · 2019
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Provably robust deep learning via adversarially trained smoothed classifiers
Hadi Salman, Jerry Li, Ilya Razenshteyn, Pengchuan Zhang, Huan Zhang, Sebastien Bubeck, and Greg Yang · 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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Training for faster adversarial robustness verification via inducing reLU stability
Kai Y. Xiao, Vincent Tjeng, Nur Muhammad (Mahi) Shafiullah, and Aleksander Madry · 2019
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Huan Zhang, Pengchuan Zhang, and Cho-Jui Hsieh · 2019
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