{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T03:13:27Z","timestamp":1773803607698,"version":"3.50.1"},"reference-count":0,"publisher":"Association for the Advancement of Artificial Intelligence (AAAI)","issue":"30","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAAI"],"abstract":"<jats:p>Graph neural networks (GNNs) have shown promise on combinatorial problems such as Max-Clique, yet it remains unclear what algorithmic principles they actually learn. This paper introduces a concept-driven framework for evaluating and interpreting GNNs on such tasks. We begin with a principled benchmark based on synthetic graphs with known difficulty levels\u2014easy, medium, and hard\u2014derived from theoretical thresholds for planted cliques. Using this setup, we show that GNNs reliably learn a simple yet powerful concept: degree-based ranking. This insight motivates a new decoder, Least-Probable Removal (LPR), which significantly outperforms the common top-k strategy, especially on harder and real-world instances. Our analysis pipeline connects latent representations to classical heuristics, improving both interpretability and performance. Finally, we demonstrate cross-domain generalization to sparse PCA, showing that the same GNN architecture and decoding strategy succeed in recovering sparse principal components, revealing a shared underlying principle across domains.<\/jats:p>","DOI":"10.1609\/aaai.v40i30.39734","type":"journal-article","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:01:18Z","timestamp":1773799278000},"page":"25401-25409","source":"Crossref","is-referenced-by-count":0,"title":["Learning to Rank: How GNNs Solve Max-Clique and Sparse PCA"],"prefix":"10.1609","volume":"40","author":[{"given":"Elad","family":"Shoham","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Omri","family":"Haber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Havana","family":"Rika","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dan","family":"Vilenchik","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\/39734\/43695","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/39734\/43695","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:01:18Z","timestamp":1773799278000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/39734"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,14]]},"references-count":0,"journal-issue":{"issue":"30","published-online":{"date-parts":[[2026,3,17]]}},"URL":"https:\/\/doi.org\/10.1609\/aaai.v40i30.39734","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]]}}}