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

• URL: http://arxiv.org/abs/2503.16342v1
• Date: Thu, 20 Mar 2025 16:58:40 GMT
• Title: HiQ-Lip: The First Quantum-Classical Hierarchical Method for Global Lipschitz Constant Estimation of ReLU Networks
• Authors: Haoqi He, Yan Xiao,
• Abstract summary: Estimating the global Lipschitz constant of neural networks is crucial for understanding and improving their robustness and generalization capabilities.<n>We propose textbfHiQ-Lip, a hybrid quantum-classical hierarchical method that leverages Coherent Ising Machines (CIMs) to estimate the global Lipschitz constant.
• Score: 2.44505480142099
• License: http://creativecommons.org/licenses/by/4.0/
• 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 \textbf{HiQ-Lip}, a hybrid quantum-classical hierarchical method that leverages Coherent Ising Machines (CIMs) to estimate the global Lipschitz constant. We tackle the estimation by converting it into a Quadratic Unconstrained Binary Optimization (QUBO) 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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