{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T17:42:18Z","timestamp":1771954938251,"version":"3.50.1"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"value":"9781643686318","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,21]]},"abstract":"<jats:p>Physics-inspired graph neural networks (PI-GNNs) have been utilized as an efficient unsupervised framework for relaxing combinatorial optimization problems encoded through a specific graph structure and loss, reflecting dependencies between the problem\u2019s variables. While the framework has yielded promising results in various combinatorial problems, we show that the performance of PI-GNNs systematically plummets with an increasing density of the combinatorial problem graphs. Our analysis reveals an interesting phase transition in the PI-GNNs\u2019 training dynamics, associated with degenerate solutions for the denser problems, highlighting a discrepancy between the relaxed, real-valued model outputs and the binary-valued problem solutions. To address the discrepancy, we propose principled alternatives to the naive strategy used in PI-GNNs by building on insights from fuzzy logic and binarized neural networks. Our experiments demonstrate that the portfolio of proposed methods significantly improves the performance of PI-GNNs in increasingly dense settings.<\/jats:p>","DOI":"10.3233\/faia251038","type":"book-chapter","created":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T09:49:39Z","timestamp":1761126579000},"source":"Crossref","is-referenced-by-count":1,"title":["Binarizing Physics-Inspired GNNs for Combinatorial Optimization"],"prefix":"10.3233","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-9710-1147","authenticated-orcid":false,"given":"Martin","family":"Krutsk\u00fd","sequence":"first","affiliation":[{"name":"Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6964-4232","authenticated-orcid":false,"given":"Gustav","family":"\u0160\u00edr","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2229-8824","authenticated-orcid":false,"given":"Vyacheslav","family":"Kungurtsev","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3850-4979","authenticated-orcid":false,"given":"Georgios","family":"Korpas","sequence":"additional","affiliation":[{"name":"Quantum Technologies Group, HSBC Labs, Singapore"},{"name":"Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague"},{"name":"Archimedes Research Unit on AI, Data Science and Algorithms, Athena Research Center"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","ECAI 2025"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA251038","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T09:49:39Z","timestamp":1761126579000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA251038"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,21]]},"ISBN":["9781643686318"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia251038","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,21]]}}}