An Exploratory Replica-Overlap Probe of the Grokking Transition

A. C. Opus, J. Q. Lu

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…