Improved generalization bounds for binary linear classification via isoperimetry

[2505.16713] Improved generalization bounds for binary linear classification via isoperimetry Skip to main content Search Submit Donate Log in Statistics > Machine Learning arXiv:2505.16713 (stat) [Submitted on 22 May 2025 ( v1 ), last revised 25 Aug 2026 (this version, v4)] Title: Improved generalization bounds for binary linear classification via isoperimetry Authors: Shogo Nakakita View PDF HTML (experimental) Abstract: We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument. In particular, we establish Poincaré and log-Sobolev inequalities for the joint distribution of the output labels and the label-weighted input vectors, which we apply to derive concentration bounds. The derived results improve upon existing bounds obtained from general unbounded empirical processes, as well as that tailored specifically to logistic regression. In asymptotic analysis, we also show that almost sure convergence of uniform generalization errors to their expectation occurs in very broad settings, such as proportionally high-dimensional regimes. Using this convergence, we establish uniform laws of large numbers under dimension-free conditions. Comments: 39 pages, 3 figures; corrected tail bounds via functional inequalities; the fix introduces a subexponential term and updated constants in the main results Subjects: Machine Learning (stat.ML) ; Machine Learning (cs.LG); Statistics Theory (math.ST) Cite as: arXiv:2505.16713 [stat.ML] (or arXiv:2505.16713v4 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2505.16713 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shogo Nakakita [ view email ] [v1] Thu, 22 May 2025 14:14:50 UTC (26 KB) [v2] Thu, 26 Jun 2025 06:57:11 UTC (27 KB) [v3] Mon, 6 Jul 2026 07:38:46 UTC (201 KB) [v4] Tue, 25 Aug 2026 06:13:20 UTC (205 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2025-05 Change to browse by: cs cs.LG math math.ST stat stat.TH References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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