{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T13:12:36Z","timestamp":1788441156947,"version":"build-2803163510"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2026,3,22]]},"abstract":"<jats:p>In traditional models of supervised learning, the goal of a learner-- given examples from an arbitrary joint distribution on $\\mathbb{R}^d \\times \\{\\pm 1\\}$-- is to output a hypothesis that is competitive (to within $\u03b5$) of the best fitting concept from some class. In order to escape strong hardness results for learning even simple concept classes, we introduce a smoothed-analysis framework that requires a learner to compete only with the best classifier that is robust to small random Gaussian perturbation.   This subtle change allows us to give a wide array of learning results for any concept that (1) depends on a low-dimensional subspace (aka multi-index model) and (2) has a bounded Gaussian surface area. This class includes functions of halfspaces and (low-dimensional) convex sets, cases that are only known to be learnable in non-smoothed settings with respect to highly structured distributions such as Gaussians.   Our definition of smoothed agnostic learning is an interpolation between the case where the instance distribution $D$ and the optimal classifier can be arbitrarily coupled (which corresponds to agnostic learning and $\u03c3= 0$) and completely decoupled (when $\u03c3= \\infty$). This decoupling allows us to avoid worst-case concepts that can encode complexity-theoretic primitives.   Surprisingly, our analysis also yields new results for traditional non-smoothed frameworks such as learning with margin. In particular, we obtain the first algorithm for agnostically learning intersections of $k$-halfspaces in time $k^{\\mathrm{poly}(\\frac{\\log k}{\u03b5\u03b3}) }$ where $\u03b3$ is the margin parameter. Before our work, the best-known runtime was exponential in $k$ (Arriaga and Vempala, FOCS' 99).<\/jats:p>\n                  <jats:p>50 pages. This is the TheoretiCS journal version<\/jats:p>","DOI":"10.46298\/theoretics.26.13","type":"journal-article","created":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T12:15:12Z","timestamp":1788437712000},"source":"Crossref","is-referenced-by-count":0,"title":["Smoothed Analysis for Learning Concepts with Low Intrinsic Dimension"],"prefix":"10.46298","volume":"Volume 5","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-2443-8675","authenticated-orcid":false,"given":"Gautam","family":"Chandrasekaran","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6960-2235","authenticated-orcid":false,"given":"Adam","family":"Klivans","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2229-1879","authenticated-orcid":false,"given":"Vasilis","family":"Kontonis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-7676-2762","authenticated-orcid":false,"given":"Raghu","family":"Meka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2643-4298","authenticated-orcid":false,"given":"Konstantinos","family":"Stavropoulos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"25203","published-online":{"date-parts":[[2026,9,3]]},"container-title":["TheoretiCS"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2407.00966v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2407.00966v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T12:15:12Z","timestamp":1788437712000},"score":1,"resource":{"primary":{"URL":"https:\/\/theoretics.episciences.org\/15633"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,3]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/theoretics.26.13","relation":{"has-preprint":[{"id-type":"arxiv","id":"2407.00966v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2407.00966","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2407.00966","asserted-by":"subject"}]},"ISSN":["2751-4838"],"issn-type":[{"value":"2751-4838","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,3]]},"article-number":"15633"}}