{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-graph-theoretic-framework-for-understanding-1","title":"A Graph-Theoretic Framework for Understanding Open-World Semi-Supervised Learning","arxiv_id":"2311.03524","date":"2023-11-06","proceeding":"NeurIPS 2023 11","authors":["Yiyou Sun","Zhenmei Shi","Yixuan Li"],"abstract":"Open-world semi-supervised learning aims at inferring both known and novel classes in unlabeled data, by harnessing prior knowledge from a labeled set with known classes. Despite its importance, there is a lack of theoretical foundations for this problem. This paper bridges the gap by formalizing a graph-theoretic framework tailored for the open-world setting, where the clustering can be theoretically characterized by graph factorization. Our graph-theoretic framework illuminates practical algorithms and provides guarantees. In particular, based on our graph formulation, we apply the algorithm called Spectral Open-world Representation Learning (SORL), and show that minimizing our loss is equivalent to performing spectral decomposition on the graph. Such equivalence allows us to derive a provable error bound on the clustering performance for both known and novel classes, and analyze rigorously when labeled data helps. Empirically, SORL can match or outperform several strong baselines on common benchmark datasets, which is appealing for practical usage while enjoying theoretical guarantees.","url_abs":"https://arxiv.org/abs/2311.03524v1","url_pdf":"https://arxiv.org/pdf/2311.03524v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-graph-theoretic-framework-for-understanding-1","repo_url":"https://github.com/deeplearning-wisc/sorl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"open-world-semi-supervised-learning","task_name":"Open-World Semi-Supervised Learning"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2311.03524","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2311.03524"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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