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We propose a novel method for computing exact pointwise robustness of deep neural networks for all convex $\ell_p$ norms.
A new polynomial-time algorithm for linear programming
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An extension of karmarkar’s projective algorithm for convex quadratic programming
Yinyu Ye and Edison Tse · 1989
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An algorithm for finding the chebyshev center of a convex polyhedron
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Lectures on Polytopes
Günter M Ziegler · 1995
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Theory of Linear and Integer Programming
Alexander Schrijver · 1998
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Convex Optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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An introduction to hyperplane arrangements
Richard P Stanley · 2004
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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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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Osbert Bastani, Yani Ioannou, Leonidas Lampropoulos, Dimitrios Vytiniotis, Aditya Nori, and Antonio Criminisi · 2016
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Towards evaluating the robustness of neural networks
Nicholas Carlini and David A. Wagner · 2016
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Chih-Hong Cheng, Georg Nührenberg, and Harald Ruess · 2017
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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 Dill, Kyle Julian, and Mykel Kochenderfer · 2017
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An approach to reachability analysis for feed-forward relu neural networks
Output range analysis for deep feedforward neural networks
Souradeep Dutta, Susmit Jha, Sriram Sankaranarayanan, and Ashish Tiwari · 2018
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Deep neural networks and mixed integer linear optimization
Matteo Fischetti and Jason Jo · 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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Certified defenses against adversarial examples
Aditi Raghunathan, Jacob Steinhardt, and Percy Liang · 2018
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Certified defenses against adversarial examples
Aditi Raghunathan, Jacob Steinhardt, and Percy Liang · 2018
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Lipschitz-Margin training: Scalable certification of perturbation invariance for deep neural networks
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Vincent Tjeng, Kai Xiao, and Russ Tedrake · 2017
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Provable robustness of relu networks via maximization of linear regions
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Formal security analysis of neural networks using symbolic intervals
Shiqi Wang, Kexin Pei, Justin Whitehouse, Junfeng Yang, and Suman Jana
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Yusuke Tsuzuku, Issei Sato, and Masashi Sugiyama · 2018
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Lipschitz regularity of deep neural networks: analysis and efficient estimation
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Efficient formal safety analysis of neural networks
Shiqi Wang, Kexin Pei, Justin Whitehouse, Junfeng Yang, and Suman Jana · 2018
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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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A convex relaxation barrier to tight robustness verification of neural networks
Hadi Salman, Greg Yang, Huan Zhang, Cho-Jui Hsieh, and Pengchuan Zhang · 2019
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Robustness certificates against adversarial examples for relu networks
Sahil Singla and Soheil Feizi · 2019
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