# MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem

arXiv: https://arxiv.org/abs/2402.01199 · HTML: https://mlsanity.com/paper/2402.01199/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 10 references that are in the map.
- First posted on arXiv 2 Feb 2024.

## Builds on (most cited first, 7 of 7)

- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Deep ReLU Networks Have Surprisingly Few Activation Patterns](https://mlsanity.com/paper/1906.00904/) (2019)
- [Exactly Computing the Local Lipschitz Constant of ReLU Networks](https://mlsanity.com/paper/2003.01219/) (2020)

## Built on by (most cited first, 1 of 1)

- [Demystifying Lipschitz verification: positive matrices, negative results](https://mlsanity.com/paper/2603.28113/) (2026)

## 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.