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Interval analysis (or interval bound propagation, IBP) is a popular technique for verifying and training provably robust deep neural networks, a fundamental challenge in the area of reliable machine learning.
Interval analysis
Ramon E Moore · 1966
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Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints
Patrick Cousot and Radhia Cousot · 1977
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell B. Stinchcombe, and Halbert White · 1989
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Interval arithmetic: From principles to implementation
Timothy Hickey, Qun Ju, and Maarten H Van Emden · 2001
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A rigorous ode solver and smale’s 14th problem
Warwick Tucker · 2002
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian J. Goodfellow, and Rob Fergus · 2013
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Explaining and harnessing adversarial examples
Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy · 2015
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Uri Shaham, Yutaro Yamada, and Sahand Negahban · 2015
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Measuring neural net robustness with constraints
Osbert Bastani, Yani Ioannou, Leonidas Lampropoulos, Dimitrios Vytiniotis, Aditya V. Nori, and Antonio Criminisi · 2016
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End to end learning for self-driving cars
Mariusz Bojarski, Davide Del Testa, Daniel Dworakowski, Bernhard Firner, Beat Flepp, Prasoon Goyal, Lawrence D. Jackel, Mathew Monfort, Urs Muller, Jiakai Zhang, Xin Zhang, Jake Zhao, and Karol Zieba · 2016
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Adversarial examples in the physical world
Alexey Kurakin, Ian J. Goodfellow, and Samy Bengio · 2016
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Transferability in machine learning: from phenomena to black-box attacks using adversarial samples
Nicolas Papernot, Patrick McDaniel, and Ian Goodfellow · 2016
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Distillation as a defense to adversarial perturbations against deep neural networks
Nicolas Papernot, Patrick D. McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami · 2016
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Towards evaluating the robustness of neural networks
Nicholas Carlini and David A. Wagner · 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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Ensemble adversarial training: Attacks and defenses
Florian Tramèr, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, and Patrick McDaniel · 2017
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Provable robustness of relu networks via maximization of linear regions
Francesco Croce, Maksym Andriushchenko, and Matthias Hein · 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
Cited alongside, same era.
Ai2: Safety and robustness certification of neural networks with abstract interpretation
Timon Gehr, Matthew Mirman, Petar Tsankov, Dana Drachsler Cohen, Martin Vechev, and Swarat Chaudhuri · 2018
Cited alongside, same era.
Differentiable abstract interpretation for provably robust neural networks
Matthew Mirman, Timon Gehr, and Martin Vechev · 2018
Cited alongside, same era.
Certified defenses against adversarial examples
Aditi Raghunathan, Jacob Steinhardt, and Percy Liang · 2018
Cited alongside, same era.
Fast and effective robustness certification
Gagandeep Singh, Timon Gehr, Matthew Mirman, Markus Püschel, and Martin Vechev · 2018
Cited alongside, same era.
Fast is better than free: Revisiting adversarial training
Eric Wong, Leslie Rice, and J Zico Kolter · 2019
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Wasserstein adversarial examples via projected sinkhorn iterations
Eric Wong, Frank Schmidt, and Zico Kolter · 2019
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Training for faster adversarial robustness verification via inducing relu stability
Kai Xiao, Vincent Tjeng, Nur Muhammad Shafiullah, and Aleksander Madry · 2019
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Universal approximation with certified networks
Maximilian Baader, Matthew Mirman, and Martin Vechev · 2020
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Adversarial training and provable defenses: Bridging the gap
Mislav Balunovic and Martin Vechev · 2020
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Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks
Francesco Croce and Matthias Hein · 2020
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Provable defenses against adversarial examples via the convex outer adversarial polytope
Eric Wong and Zico Kolter · 2018
Cited alongside, same era.
Efficient formal safety analysis of neural networks
Shiqi Wang, Kexin Pei, Justin Whitehouse, Junfeng Yang, and Suman Jana · 2018
Cited alongside, same era.
Scaling provable adversarial defenses
Eric Wong, Frank Schmidt, Jan Hendrik Metzen, and J Zico Kolter · 2018
Cited alongside, same era.
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.
Certifying geometric robustness of neural networks
Mislav Balunovic, Maximilian Baader, Gagandeep Singh, Timon Gehr, and Martin Vechev · 2019
Cited alongside, same era.
Cnn-cert: An efficient framework for certifying robustness of convolutional neural networks
Akhilan Boopathy, Tsui-Wei Weng, Pin-Yu Chen, Sijia Liu, and Luca Daniel · 2019
Cited alongside, same era.
Provable robustness against all adversarial l p l_{p} -perturbations for p >= 1 p>=1
Francesco Croce and Matthias Hein · 2019
Cited alongside, same era.
Later among the works it cites.
A survey of safety and trustworthiness of deep neural networks: Verification, testing, adversarial attack and defence, and interpretability
Xiaowei Huang, Daniel Kroening, Wenjie Ruan, James Sharp, Youcheng Sun, Emese Thamo, Min Wu, and Xinping Yi · 2020
Later among the works it cites.
Confidence-calibrated adversarial training: Generalizing to unseen attacks
David Stutz, Matthias Hein, and Bernt Schiele · 2020
Later among the works it cites.
Interval universal approximation for neural networks
Zi Wang, Aws Albarghouthi, Gautam Prakriya, and Somesh Jha · 2020
Later among the works it cites.
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
Later among the works it cites.
Fast training of provably robust neural networks by singleprop
Akhilan Boopathy, Tsui-Wei Weng, Sijia Liu, Pin-Yu Chen, Gaoyuan Zhang, and Luca Daniel · 2021
Closest in time.
Certified robustness against physically-realizable patch attack via randomized cropping
Wan-Yi Lin, Fatemeh Sheikholeslami, Leslie Rice, J Zico Kolter, et al · 2021
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Training provably robust models by polyhedral envelope regularization
Chen Liu, Mathieu Salzmann, and Sabine Süsstrunk · 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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Fast and Complete: Enabling complete neural network verification with rapid and massively parallel incomplete verifiers
Kaidi Xu, Huan Zhang, Shiqi Wang, Yihan Wang, Suman Jana, Xue Lin, and Cho-Jui Hsieh · 2021
Closest in time.
Certified robustness to programmable transformations in lstms
Yuhao Zhang, Aws Albarghouthi, and Loris D’Antoni · 2021
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On the convergence of certified robust training with interval bound propagation
Anonymous · 2022
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