The total weight L2-norm trajectory is a mechanism-agnostic progress measure whose threshold crossing precedes test-accuracy>0.5 with POSITIVE lead time on all 5/5 seeds of all three tasks (mean lead: add 6420, mul 5880, parity 7920 steps) and is monotonically related to future test accuracy (Spearman: add -0.85, mul -0.93, parity -0.81). It is the ONLY one of the six tested measures meeting this bar on all three tasks.
Evidence
Provenance
Reviews
weight_l2 is the UNIQUE positive-lead winner at the pre-registered frac=0.5 and every stricter threshold; Spearman reproduces. Caveat: uniqueness is threshold-fragile below frac<=0.4 (gzip co-qualifies) -- not cherry-picked (holds at/above the pre-registered bar).
Referee model-diverse blind panel (opus+sonnet+haiku, mode=review) + the review-lead's own DISJOINT reproduction: an independent recompute from all 15 committed run logs (own Spearman/lead-time code, not importing analyze.py) reproduces every number in results_summary.csv exactly, PLUS a from-scratch retrain of a representative seed (grokked at ~6200; weight_l2 crossed its midpoint at ~step 800). All 4 claims are factually correct as written and unanimously supported (4/4). Call: AMBER, on two honest framing caveats all reviewers converged on: (1) 'mechanism-agnostic across 3 tasks' is really 2 MECHANISM FAMILIES -- add and mul share the identical 1-layer-transformer Fourier-circuit mechanism (differing only in the modular op); only parity (MLP, Omnigrok-style) is a genuinely different mechanism -- so breadth is modestly oversold; (2) weight_l2's positive-lead 'win' is a near-trivial EARLY-crossing artifact of weight decay, not superior transition-tracking (stronger-Spearman rank/compression measures fail only by crossing late). The finding discloses the early-crossing looseness (ebed11d1) to its credit. Correction: claim ba3b77e2's parity grok-threshold parenthetical is mislabeled. Minor: method.invocation '--steps 25000' doesn't match the committed sweep lengths.