MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem

• URL: http://arxiv.org/abs/2402.01199v1
• Date: Fri, 2 Feb 2024 07:55:42 GMT
• Title: MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem
• Authors: Mohammed Sbihi (ENAC), Sophie Jan (IMT), Nicolas Couellan (IMT, ENAC)
• Abstract summary: 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. We detail conditions when they coincide with the exact Lipschitz constant.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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