MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem
Not on the map. Why?
Abstract (arXiv)
It is well established that to ensure or certify the robustness of a neural network, its Lipschitz constant plays a prominent role. However, its calculation is NP-hard. In this note, by taking into account activation regions at each layer as new constraints, we propose new quadratically constrained MIP formulations for the neural network Lipschitz estimation problem. The solutions of these problems give lower bounds and upper bounds of the Lipschitz constant and we detail conditions when they coincide with the exact Lipschitz constant.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 7 of its 10 references that are in the map. First posted on arXiv 2 Feb 2024.
Builds on
7 of 10 references.
References · 7
- 2017Spectrally-normalized margin bounds for neural networkscited by 681
- 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
- 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 311
- 2017Parseval Networks: Improving Robustness to Adversarial Examplescited by 288
- 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
- 2019Deep ReLU Networks Have Surprisingly Few Activation Patternscited by 160
- 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
Built on by
Citing papers per year: 2026: 1.
1 paper.