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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Inter-Layer Alignment Re-Rise Predicts Grokking in Transformers: A Pilot Study

Authors: Carles Marín Muñoz;

Inter-Layer Alignment Re-Rise Predicts Grokking in Transformers: A Pilot Study

Abstract

We identify an internal signal that detects impending grokking ∼3,000 training stepsbefore the accuracy transition without any knowledge of the learned algorithm. Thesignal is a non-monotonic re-rise of inter-layer CKA (Ob01, between layers 0 and 1 ofa small transformer): after an initial drop during memorization, Ob01 begins rising again atstep ≈750 exclusively in models that will grokk. This re-rise discriminates grokking fromnon-grokking in 16/16 vs 0/5 seeds (Fisher exact p = 0.000049; one-sample t = 4.51,p < 0.001), with onset consistently ∼3,297 ± 461 steps before the accuracy jump. The signal replicates across two primes (p = 97, p = 113) and across a structurally distinct modulartask: modular multiplication (6/6 seeds, onset step 750, lead 3,083±186 steps) identical onset to addition despite dierent underlying algorithms. A task-contrast experimentwith k-sparse parity reveals the boundary of the signal's scope: parity generalizes quicklybut Ob01 drops rather than rises the opposite dynamic. This demarcates a meaningfuldistinction: the re-rise is a signature of tasks requiring distributed inter-layer coordination (Fourier-type algorithms), not of grokking or generalization in general. Practically,the re-rise onset provides an early-termination criterion within the modular arithmetic family: runs showing no re-rise by step 1,000 do not grokk in any tested conguration, enablingdiagnosis thousands of steps before any test accuracy signal appears. We motivate Ob01 viaO(X, Y ) = I(X; Y )/H(Y ) and hierarchical predictive coding theory, while being explicitthat CKA is a linear proxy for O, not an estimator of it. Replacing CKA with MINE orkNN MI estimators is the priority follow-up.

Keywords

Fourier algorithm, grokking,, mechanistic interpretability,, centered kernel alignment,, inter-layer coordination,, CKA,, emergent generalization,, utual information,, transformers,, MINE,, modular arithmetic,, utual information,

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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