MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem
arxiv(2024)
摘要
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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