Where Grokking Happens: Distributed Utility and Fourier Recoding Without a Module Switch

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.

27 pages, 10 figures. Code and data: this https URL

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2609.17571 [cs.LG]

(or arXiv:2609.17571v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.17571 Focus to learn more arXiv-issued DOI via DataCite

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