Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging

[2602.03702] Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging Skip to main content Search Submit Donate Log in Computer Science > Machine Learning arXiv:2602.03702 (cs) [Submitted on 3 Feb 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Anytime Pretraining: Horizon-Free Learning-Rate Schedules with Weight Averaging Authors: Alexandru Meterez , Pranav Ajit Nair , Depen Morwani , Cengiz Pehlevan , Sham Kakade View PDF HTML (experimental) Abstract: Large language models are increasingly trained in continual or open-ended settings, where the total training horizon is not known in advance. Despite this, most existing pretraining recipes are not anytime: they rely on horizon-dependent learning rate schedules and extensive tuning under a fixed compute budget. In this work, we provide a theoretical analysis demonstrating the existence of anytime learning schedules for overparameterized linear regression, and we highlight the central role of weight averaging - also known as model merging - in achieving the minimax convergence rates of stochastic gradient descent. We show that these anytime schedules polynomially decay with time, with the decay rate determined by the source and capacity conditions of the problem. Empirically, we evaluate 150M and 300M parameter language models trained for up to 32x Chinchilla scale, comparing constant and $1/\sqrt{t}$ schedules with weight averaging against a well-tuned cosine schedule. Across the full training range, the anytime schedules achieve comparable final loss to cosine decay. Taken together, our results suggest that weight averaging combined with simple, horizon-free step sizes offers a practical and effective anytime alternative to cosine learning rate schedules for large language model pretraining. Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Optimization and Control (math.OC); Machine Learning (stat.ML) Cite as: arXiv:2602.03702 [cs.LG] (or arXiv:2602.03702v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2602.03702 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alexandru Meterez [ view email ] [v1] Tue, 3 Feb 2026 16:24:05 UTC (212 KB) [v2] Tue, 25 Aug 2026 01:44:43 UTC (250 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG < prev | next > new | recent | 2026-02 Change to browse by: cs cs.AI math math.OC stat stat.ML 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? ) 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)

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