{"paper":{"title":"Efficient and Minimax Optimal In-context Nonparametric Regression with Transformers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Ioana Popescu, Michelle Ching, Nico Smith, Richard J. Samworth, Tianyi Ma, William G. Underwood","submitted_at":"2026-01-21T14:13:38Z","abstract_excerpt":"We study in-context learning for nonparametric regression with $\\alpha$-H\\\"older smooth regression functions, for some $\\alpha>0$. We prove that, with $n$ in-context examples and $d$-dimensional regression covariates, a pretrained transformer with $\\Theta(\\log n)$ parameters and $\\Omega\\bigl(n^{2\\alpha/(2\\alpha+d)}\\log^3 n\\bigr)$ pretraining sequences can achieve the minimax optimal rate of convergence $O\\bigl(n^{-2\\alpha/(2\\alpha+d)}\\bigr)$ in mean squared error. Our result requires substantially fewer transformer parameters and pretraining sequences than previous results in the literature. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.15014","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.15014/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}