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[Submitted on 29 Jul 2026] Title:Where Grokking Happens: Distributed Utility and Fourier Recoding Without a Module Switch View a PDF of the paper titled Where Grokking Happens: Distributed Utility and Fourier Recoding Without a Module Switch, by Dekun Yang View PDF HTML (experimental) Abstract:Where in a Transformer is the change from memorization to generalization functionally expressed? We introduce Transition Games--behavior-aligned exact activation games with paired non-generalizing controls--and find distributed utility gain with a prospective block-0 attention bias; selected degree-two modes account for 67--92% of its addition contrast across replacement games, and a disjoint exact path study confirms that block-1 MLP mediates more of their effect than all other tested downstream paths in 12/12 pairs. The sharper "MLP memorizes, attention generalizes" prediction instead reverses (-.331 bits/example at the memory anchor; 0/12 in the predicted direction), while routing onset, global rank collapse, and a prime-invariant architecture ridge also fail, identifying grokking here as spectral recoding of an existing distributed circuit rather than a module switch. Comments: 27 pages, 10 figures. Code and data: this https URL Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) Cite as: arXiv:2609.17571 [cs.LG] (or arXiv:2609.17571v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.17571 arXiv-issued DOI via DataCite Submission history From: Dekun Yang [view email] [v1] Wed, 29 Jul 2026 08:28:42 UTC (1,569 KB) Full-text links: Access Paper: View a PDF of the paper titled Where Grokking Happens: Distributed Utility and Fourier Recoding Without a Module Switch, by Dekun Yang View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs cs.AI 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?)