An Exploratory Replica-Overlap Probe of the Grokking Transition

arXiv:2609.25634v1 Announce Type: cross Abstract: We trained 64 independently seeded networks in four configurations, continuing each to sustained convergence or a 40,000-epoch ceiling. We then asked whether an RSB-inspired distribution of pairwise weight overlaps changes across the grokking transition. It is the alignment step, not the overlap statistic, that determines what this registered probe can report. The registered implementation permutes hidden units without the corresponding bias and head-internal permutations and therefore does not preserve the network function. Every q_wt value computed through this alignment inherits the defect; q_fn does not, because it is computed from predictions of the unpermuted models. The numerical-precision requirement also failed, and an audit found protocol deviations. Consequently, the pre-registered rule gives no verdict: registered outcome UNDETERMINED (reason code C0_INSTRUMENT_INVALID). These data provide neither a confirmatory null nor a validated reading of the Parisi order parameter. Only frac40 cleared the 12/16 checkpoint-completeness requirement. For this configuration, a post-hoc criterion applied to the same data gave a Hartigan-dip interval containing zero (95% CI for Delta dip = [-0.017, 0.034]), whereas the overlap standard deviation increased by a factor of about 5.6. A post-hoc calibration assigns the dip test zero power at the simulated separations; the interval is therefore uninformative, not evidence of no change. The standard-deviation ratio is the only statistic here with power at the observed effect. Ensemble loss was near-flat only under the pre-specified 1% threshold. Finally, grokking rates of 0/16, 11/16 and 16/16 remain descriptive because train fraction is confounded with split identity.

Abstract:We trained 64 independently seeded networks in four configurations, continuing each to sustained convergence or a 40,000-epoch ceiling. We then asked whether an RSB-inspired distribution of pairwise weight overlaps changes across the grokking transition. It is the alignment step, not the overlap statistic, that determines what this registered probe can report. The registered implementation permutes hidden units without the corresponding bias and head-internal permutations and therefore does not preserve the network function. Every q_wt value computed through this alignment inherits the defect; q_fn does not, because it is computed from predictions of the unpermuted models. The numerical-precision requirement also failed, and an audit found protocol deviations. Consequently, the pre-registered rule gives no verdict: registered outcome UNDETERMINED (reason code C0_INSTRUMENT_INVALID). These data provide neither a confirmatory null nor a validated reading of the Parisi order parameter. Only frac40 cleared the 12/16 checkpoint-completeness requirement. For this configuration, a post-hoc criterion applied to the same data gave a Hartigan-dip interval containing zero (95% CI for Delta dip = [-0.017, 0.034]), whereas the overlap standard deviation increased by a factor of about 5.6. A post-hoc calibration assigns the dip test zero power at the simulated separations; the interval is therefore uninformative, not evidence of no change. The standard-deviation ratio is the only statistic here with power at the observed effect. Ensemble loss was near-flat only under the pre-specified 1% threshold. Finally, grokking rates of 0/16, 11/16 and 16/16 remain descriptive because train fraction is confounded with split identity.

13 pages, 5 figures. Pre-registered study; the registered decision rule returns UNDETERMINED (reason code C0_INSTRUMENT_INVALID) because the registered alignment implementation is not function-preserving. Reported as an honest negative/instrument-invalid result

Machine Learning (cs.LG); Disordered Systems and Neural Networks (cond-mat.dis-nn); Artificial Intelligence (cs.AI)

arXiv:2609.25634 [cs.LG]

(or arXiv:2609.25634v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.25634 arXiv-issued DOI via DataCite (pending registration)

From: J. Q. Lu [view email] [v1] Tue, 22 Sep 2026 03:44:55 UTC (329 KB)

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An Exploratory Replica-Overlap Probe of the Grokking Transition

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