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[Submitted on 14 Oct 2026] Title:Diminishing Returns of Data in Sparse Autoencoders: Functional Behavior does not Guarantee Feature Reproducibility View a PDF of the paper titled Diminishing Returns of Data in Sparse Autoencoders: Functional Behavior does not Guarantee Feature Reproducibility, by Sambit Ghosh and 3 other authors View PDF HTML (experimental) Abstract:Sparse autoencoders (SAEs) are typically trained on hundreds of millions to billions of activation tokens, yet little work has tested whether this scale is necessary. We study how much activation data SAEs need by training four SAE architectures on three language models with budgets ranging from 5M tokens to a 500M-token reference. We measure two notions of convergence: functional behavior on standard evaluations and one-to-one reproducibility of learned features. Functional data requirements are strongly metric-dependent: reconstruction often approaches the full-data reference at substantially smaller budgets, whereas feature reproducibility continues to improve with data. For Gemma-2-2B BatchTopK, the fraction of strictly matched features rises from 2\% at 5M tokens to 29\% at 50M. Data selection also matters: random sampling better preserves the original activation distribution and generally favors reconstruction, whereas diversity-based sampling frequently improves AutoInterp. A theoretical analysis separates statistical consistency of subsampled training from the stronger identifiability and optimization conditions required for one-to-one feature recovery. Our results show that SAE training can often be made far more data-efficient when budgets are matched to the goal, and feature-level claims are backed by explicit reproducibility checks, paving the way toward cheaper and more reliable SAE research. Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML) Cite as: arXiv:2610.20680 [cs.LG] (or arXiv:2610.20680v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2610.20680 arXiv-issued DOI via DataCite (pending registration) Submission history From: Sambit Ghosh [view email] [v1] Wed, 14 Oct 2026 16:12:42 UTC (108 KB) Full-text links: Access Paper: View a PDF of the paper titled Diminishing Returns of Data in Sparse Autoencoders: Functional Behavior does not Guarantee Feature Reproducibility, by Sambit Ghosh and 3 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG new | recent | 2026-10 Change to browse by: cs stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: 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?)