A tight, mechanism-agnostic early predictor of grokking: crossing coincident with the generalization jump on 5 seeds × 3 tasks

In the grokking setup, small networks trained on algorithmic tasks (e.g. modular arithmetic) fit the training set long before validation accuracy jumps. For a candidate scalar progress measure $m(t)$ computed only from weights/activations (mechanism-agnostic), define its crossing time $t_c$ as the step at which $m(t)$ crosses a pre-registered threshold, and the generalization time $t_g$ as the step at which validation accuracy first exceeds $0.9$. Define the cross-fraction $\phi = t_c/t_g$ (so $\phi \to 1^-$ means the crossing is tightly coincident with, and slightly leads, generalization; $\phi \to 0$ means it fires far too early to be informative). Find a mechanism-agnostic measure whose mean cross-fraction lies in $[0.7,1.0]$ AND that positively leads ($t_c \le t_g$) on all 5/5 seeds across each of 3 tasks — or establish a NEGATIVE result over a clearly stated candidate set that none does both.

Acceptance. Protocol must be pre-registered and mechanically checkable: fixed architecture, 3 named tasks, 5 seeds each, a threshold rule and the $\phi=t_c/t_g$ definition fixed in advance (state the threshold-crossing convention, the $t_g$ definition = first step val-acc exceeds 0.9, and any smoothing). FULLY RESOLVES: a measure with mean cross-fraction $\phi \in [0.7,1.0]$ AND positive lead ($t_c \le t_g$) on all 15/15 runs, reported as a table of $\phi$ (mean + per seed/task), lead-time (steps $t_g-t_c$, $\ge 0$ on every run), and the Spearman correlation between $t_c$ and $t_g$ across runs, with a runnable script. NEGATIVE RESOLUTION: the same protocol over $\ge 3$ named candidate measures, with the full table, showing none meets both bars. PARTIAL: the reproducible protocol + table for $\ge 1$ measure. Metric: mean cross-fraction, per-run lead-time, and Spearman($t_c,t_g$).