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arXiv · 2503.16342

HiQ-Lip: A Hierarchical Quantum-Classical Method for Global Lipschitz Constant Estimation of ReLU Networks

Haoqi He·Yan Xiao·Wenzhi Xu·Ruoying Liu·Xiaokai Lin·Kai Wen
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Abstract

Estimating the global Lipschitz constant of neural networks is crucial for understanding and improving their robustness and generalization capabilities. However, precise calculations are NP-hard, and current semidefinite programming (SDP) methods face challenges such as high memory usage and slow processing speeds. In this paper, we propose HiQ-Lip, a hybrid quantum-classical hierarchical method that leverages quantum computing to estimate the global Lipschitz constant. We tackle the estimation by converting it into a Quadratic Unconstrained Binary Optimization problem and implement a multilevel graph coarsening and refinement strategy to adapt to the constraints of contemporary quantum hardware. Our experimental evaluations on fully connected neural networks demonstrate that HiQ-Lip not only provides estimates comparable to state-of-the-art methods but also significantly accelerates the computation process. In specific tests involving two-layer neural networks with 256 hidden neurons, HiQ-Lip doubles the solving speed and offers more accurate upper bounds than the existing best method, LiPopt. These findings highlight the promising utility of small-scale quantum devices in advancing the estimation of neural network robustness.

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Haoqi He, Yan Xiao, Wenzhi Xu, Ruoying Liu, Xiaokai Lin, Kai Wen. 2026-01-09. HiQ-Lip: A Hierarchical Quantum-Classical Method for Global Lipschitz Constant Estimation of ReLU Networks. https://arxiv.org/abs/2503.16342

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