{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T03:04:30Z","timestamp":1773803070214,"version":"3.50.1"},"reference-count":0,"publisher":"Association for the Advancement of Artificial Intelligence (AAAI)","issue":"26","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAAI"],"abstract":"<jats:p>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 Coherent Ising Machines (CIMs) to estimate the global Lipschitz constant. \nWe 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. \nOur 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. \nIn 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.\nThese findings highlight the promising utility of small-scale quantum devices in advancing the estimation of neural network robustness.<\/jats:p>","DOI":"10.1609\/aaai.v40i26.39312","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T01:28:21Z","timestamp":1773797301000},"page":"21628-21636","source":"Crossref","is-referenced-by-count":0,"title":["HiQ-Lip: A Hierarchical Quantum-Classical Method for Global Lipschitz Constant Estimation of ReLU Networks"],"prefix":"10.1609","volume":"40","author":[{"given":"Haoqi","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenzhi","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruoying","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaokai","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Wen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9382","published-online":{"date-parts":[[2026,3,14]]},"container-title":["Proceedings of the AAAI Conference on Artificial Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/39312\/43273","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/39312\/43273","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T01:28:21Z","timestamp":1773797301000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/39312"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,14]]},"references-count":0,"journal-issue":{"issue":"26","published-online":{"date-parts":[[2026,3,17]]}},"URL":"https:\/\/doi.org\/10.1609\/aaai.v40i26.39312","relation":{},"ISSN":["2374-3468","2159-5399"],"issn-type":[{"value":"2374-3468","type":"electronic"},{"value":"2159-5399","type":"print"}],"subject":[],"published":{"date-parts":[[2026,3,14]]}}}