Scaling Laws for Dynamic Mini-Batch SGD in Sketched Linear Regression

[2605.24316] Scaling Laws for Dynamic Mini-Batch SGD in Sketched Linear Regression Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2605.24316 (cs) [Submitted on 23 May 2026 ( v1 ), last revised 15 Aug 2026 (this version, v3)] Title: Scaling Laws for Dynamic Mini-Batch SGD in Sketched Linear Regression Authors: Ziyan Chen , Zhongzhu Zhou , Ding-Xuan Zhou View a PDF of the paper titled Scaling Laws for Dynamic Mini-Batch SGD in Sketched Linear Regression, by Ziyan Chen and 2 other authors View PDF HTML (experimental) Abstract: Mini-batching is central to large-scale optimization, yet its role in statistical scaling laws remains limited. We study one-pass and multi-pass batch SGD for sketched linear regression under power-law spectral and source conditions. Our analysis reveals a two-horizon phenomenon induced by warmup--stable--decay schedules: deterministic learning is governed by the full optimization trajectory, while stochastic error retains only a shorter terminal memory. For dynamic batch schedules, the individual batch sizes enter through influence-weighted summaries that measure how strongly each update affects the final risk. Consequently, batching leaves the approximation and optimization-bias laws unchanged at a fixed update horizon, but controls the one-pass variance and the multi-pass fluctuation around full-batch gradient descent. We obtain matching one-pass variance bounds and nearly matching multi-pass fluctuation bounds, recover static-batch and full-batch behavior as special cases, and derive an oracle square-root rule for allocating a fixed iteration budget. These results identify WSD horizon separation and final-risk influence as the mechanisms governing dynamic mini-batch scaling. Comments: 62 pages, 4 figures Subjects: Machine Learning (cs.LG) Cite as: arXiv:2605.24316 [cs.LG] (or arXiv:2605.24316v3 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2605.24316 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ziyan Chen [ view email ] [v1] Sat, 23 May 2026 00:48:36 UTC (106 KB) [v2] Thu, 25 Jun 2026 06:26:55 UTC (160 KB) [v3] Sat, 15 Aug 2026 04:36:40 UTC (575 KB) Full-text links: Access Paper: View a PDF of the paper titled Scaling Laws for Dynamic Mini-Batch SGD in Sketched Linear Regression, by Ziyan Chen and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-05 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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) Major funding support from

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