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The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models.
An automatic method for solving discrete programming problems
Ailsa H. Land and Alison G. Doig · 1960
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Software Engineering Techniques: Report on a Conference Sponsored by the NATO Science Committee
John N Buxton and Brian Randell · 1970
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A hierarchy of relaxations and convex hull characterizations for mixed-integer zero—one programming problems
Hanif D Sherali and Warren P Adams · 1994
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Grasp: A search algorithm for propositional satisfiability
João P Marques-Silva and Karem A Sakallah · 1999
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Interval arithmetic: From principles to implementation
Timothy Hickey, Qun Ju, and Maarten H Van Emden · 2001
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Verification of a trained neural network accuracy
Radosiaw R Zakrzewski · 2001
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Splitting on demand in sat modulo theories
Clark Barrett, Robert Nieuwenhuis, Albert Oliveras, and Cesare Tinelli · 2006
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Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot and Yoshua Bengio · 2010
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Measuring neural net robustness with constraints
Osbert Bastani, Yani Ioannou, Leonidas Lampropoulos, Dimitrios Vytiniotis, Aditya Nori, and Antonio Criminisi · 2016
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Learning to branch in mixed integer programming
Elias Boutros Khalil, Pierre Le Bodic, Le Song, George Nemhauser, and Bistra Dilkina · 2016
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Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning
D. R. Morrison, S. H. Jacobson, J. J. Sauppe, and E. C Sewell · 2016
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Towards evaluating the robustness of neural networks
Nicholas Carlini and David Wagner · 2017
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Formal guarantees on the robustness of a classifier against adversarial manipulation
Matthias Hein and Maksym Andriushchenko · 2017
Cited alongside, same era.
Safety verification of deep neural networks
Xiaowei Huang, Marta Kwiatkowska, Sen Wang, and Min Wu · 2017
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An approach to reachability analysis for feed-forward relu neural networks
A dual approach to scalable verification of deep networks
Krishnamurthy Dvijotham, Robert Stanforth, Sven Gowal, Timothy Mann, and Pushmeet Kohli · 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
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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Strong mixed-integer programming formulations for trained neural networks
Ross Anderson, Joey Huchette, Christian Tjandraatmadja, and Juan Pablo Vielma · 2019
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Alessio Lomuscio and Lalit Maganti · 2017
Cited alongside, same era.
Verifying properties of binarized deep neural networks
Nina Narodytska, Shiva Prasad Kasiviswanathan, Leonid Ryzhyk, Mooly Sagiv, and Toby Walsh · 2017
Cited alongside, same era.
Output reachable set estimation and verification for multi-layer neural networks
Weiming Xiang, Hoang-Dung Tran, and Taylor T Johnson · 2017
Cited alongside, same era.
Reachability analysis for neural agent-environment systems
Michael Akintunde, Alessio Lomuscio, Lalit Maganti, and Edoardo Pirovano · 2018
Cited alongside, same era.
Maximum resilience of artificial neural networks
Chih-Hong Cheng, Georg Nührenberg, and Harald Ruess
Cited in the paper.
Verification of binarized neural networks
Chih-Hong Cheng, Georg Nührenberg, and Harald Ruess
Cited in the paper.
Formal verification of piece-wise linear feed-forward neural networks
Ruediger Ehlers
Cited in the paper.
Vicenc Rubies Royo, Roberto Calandra, Dusan M Stipanovic, and Claire Tomlin · 2019
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Verifying neural networks with mixed integer programming
Vincent Tjeng and Russ Tedrake · 2019
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A statistical approach to assessing neural network robustness
Stefan Webb, Tom Rainforth, Yee Whye Teh, and M. Pawan Kumar · 2019
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Neural network branching for neural network verification
Jingyue Lu and M. Pawan Kumar · 2020
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