[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
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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)
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