[2608.14492] Approximate Muon with low-rank adapters Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.14492 (cs) [Submitted on 14 Aug 2026] Title: Approximate Muon with low-rank adapters Authors: Ben Anson , Conor Houghton , Edward Milsom View a PDF of the paper titled Approximate Muon with low-rank adapters, by Ben Anson and Conor Houghton and Edward Milsom View PDF HTML (experimental) Abstract: The Muon optimizer shows clear benefits versus alternatives when pretraining neural networks. However, it is used less frequently for parameter-efficient fine-tuning (PEFT). One potential reason is that the most common PEFT method, LoRA, does not naturally combine with Muon since it is not mathematically possible to orthogonalize the weight update given by a low-rank parameterization. In this paper, we address this issue by approximating the solution to a relaxed Muon objective in the low-rank setting via linearization and then least-squares. We provide an efficient implementation that uses matmul operations only, as opposed to more complex linear algebra decomposition routines. Our method, sMuon (small Muon), performs favourably across SFT and a ReLoRA pretraining experiment. While results are model- and eval-dependent, we find overall that using Muon for low-rank fine-tuning provides moderate performance improvements. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2608.14492 [cs.LG] (or arXiv:2608.14492v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.14492 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ben Anson [ view email ] [v1] Fri, 14 Aug 2026 17:07:37 UTC (69 KB) Full-text links: Access Paper: View a PDF of the paper titled Approximate Muon with low-rank adapters, by Ben Anson and Conor Houghton and Edward Milsom View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 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