Fetching the paper…
Reading the bibliography…
Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning controllers.
The mnist database of handwritten digits
Yann LeCun · 1998
Earlier work this paper cites.
Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
Earlier work this paper cites.
Cvx: Matlab software for disciplined convex programming, 2008
Michael Grant, Stephen Boyd, and Yinyu Ye · 2008
Earlier work this paper cites.
Observers for systems with nonlinearities satisfying incremental quadratic constraints
Behçet Açıkmeşe and Martin Corless · 2011
Earlier work this paper cites.
Provably safe and robust learning-based model predictive control
Anil Aswani, Humberto Gonzalez, S Shankar Sastry, and Claire Tomlin · 2013
Earlier work this paper cites.
Introductory lectures on convex optimization: A basic course
Yurii Nesterov · 2013
Earlier work this paper cites.
Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2013
Earlier work this paper cites.
Explaining and harnessing adversarial examples (2014)
Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy · 2014
Earlier work this paper cites.
Measuring neural net robustness with constraints
Osbert Bastani, Yani Ioannou, Leonidas Lampropoulos, Dimitrios Vytiniotis, Aditya Nori, and Antonio Criminisi · 2016
Earlier work this paper cites.
Adversarial machine learning at scale
Alexey Kurakin, Ian Goodfellow, and Samy Bengio · 2016
Earlier work this paper cites.
Distillation as a defense to adversarial perturbations against deep neural networks
Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami · 2016
Earlier work this paper cites.
Primer on monotone operator methods
Ernest K Ryu and Stephen Boyd · 2016
Earlier work this paper cites.
Improving the robustness of deep neural networks via stability training
Stephan Zheng, Yang Song, Thomas Leung, and Ian Goodfellow · 2016
Earlier work this paper cites.
The MOSEK optimization toolbox for MATLAB manual. Version 8.1
MOSEK ApS · 2017
Earlier work this paper cites.
Lipschitz properties for deep convolutional networks
Radu Balan, Maneesh Singh, and Dongmian Zou · 2017
Cited alongside, same era.
Spectrally-normalized margin bounds for neural networks
Peter L Bartlett, Dylan J Foster, and Matus J Telgarsky · 2017
Cited alongside, same era.
Safe model-based reinforcement learning with stability guarantees
Felix Berkenkamp, Matteo Turchetta, Angela Schoellig, and Andreas Krause · 2017
Cited alongside, same era.
UCI machine learning repository, 2017
Dheeru Dua and Casey Graff · 2017
Cited alongside, same era.
Provable defenses against adversarial examples via the convex outer adversarial polytope
J Zico Kolter and Eric Wong · 2017
Cited alongside, same era.
Certified defenses against adversarial examples
Aditi Raghunathan, Jacob Steinhardt, and Percy Liang · 2018
Later among the works it cites.
Semidefinite relaxations for certifying robustness to adversarial examples
Aditi Raghunathan, Jacob Steinhardt, and Percy S Liang · 2018
Later among the works it cites.
Reachability analysis of deep neural networks with provable guarantees
Wenjie Ruan, Xiaowei Huang, and Marta Kwiatkowska · 2018
Later among the works it cites.
Fast and effective robustness certification
Gagandeep Singh, Timon Gehr, Matthew Mirman, Markus Püschel, and Martin Vechev · 2018
Later among the works it cites.
Lipschitz-margin training: Scalable certification of perturbation invariance for deep neural networks
Yusuke Tsuzuku, Issei Sato, and Masashi Sugiyama · 2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2017
Cited alongside, same era.
Lower bounds on the robustness to adversarial perturbations
Jonathan Peck, Joris Roels, Bart Goossens, and Yvan Saeys · 2017
Cited alongside, same era.
Evaluating robustness of neural networks with mixed integer programming
Vincent Tjeng, Kai Xiao, and Russ Tedrake · 2017
Cited alongside, same era.
Output range analysis for deep feedforward neural networks
Souradeep Dutta, Susmit Jha, Sriram Sankaranarayanan, and Ashish Tiwari · 2018
Cited alongside, same era.
Analysis of optimization algorithms via integral quadratic constraints: Nonstrongly convex problems
Mahyar Fazlyab, Alejandro Ribeiro, Manfred Morari, and Victor M Preciado · 2018
Cited alongside, same era.
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
Cited alongside, same era.
Limitations of the lipschitz constant as a defense against adversarial examples
Todd Huster, Cho-Yu Jason Chiang, and Ritu Chadha · 2018
Cited alongside, same era.
Lipschitz regularity of deep neural networks: analysis and efficient estimation
Aladin Virmaux and Kevin Scaman · 2018
Later among the works it cites.
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
Later among the works it cites.
Evaluating the robustness of neural networks: An extreme value theory approach
Tsui-Wei Weng, Huan Zhang, Pin-Yu Chen, Jinfeng Yi, Dong Su, Yupeng Gao, Cho-Jui Hsieh, and Luca Daniel · 2018
Later among the works it cites.
Scaling provable adversarial defenses
Eric Wong, Frank Schmidt, Jan Hendrik Metzen, and J Zico Kolter · 2018
Later among the works it cites.
Efficient neural network robustness certification with general activation functions
Huan Zhang, Tsui-Wei Weng, Pin-Yu Chen, Cho-Jui Hsieh, and Luca Daniel · 2018
Later among the works it cites.
On lipschitz bounds of general convolutional neural networks
Dongmian Zou, Radu Balan, and Maneesh Singh · 2018
Later among the works it cites.
Lipschitz certificates for neural network structures driven by averaged activation operators
Patrick L. Combettes and Jean-Christophe Pesquet · 2019
Closest in time.
Mahyar Fazlyab, Manfred Morari, and George J Pappas · 2019
Closest in time.
Provable certificates for adversarial examples: Fitting a ball in the union of polytopes
Matt Jordan, Justin Lewis, and Alexandros G Dimakis · 2019
Closest in time.