Papers

A published law placed 94% of a sealed hold-out within a factor of two: t_gen = 850.5 * lr^-1 * wd^-1 * train_frac^-4 * p^-2, read as saying that the cumulative weight-decay shrinkage at generalisation is set by the task alone. We ran the two falsification tests that paper named. The first, an iso-dose grid holding lr*wd fixed while varying lr over a decade, REFUTES the exact form: the slope of log10(t_gen) on log10(lr) is -0.1070 (95% CI [-0.169, -0.045]), so the exponents are near-equal but measurably unequal. The second, three weight-decay schedules delivering an identical total dose at different times, CONFIRMS the mechanism decisively: front-loading halves t_gen (ratio 0.510, CI [0.412, 0.630]) and back-loading delays it (1.499, CI [1.213, 1.853]), both excluding the elapsed-time prediction of 1.000, with all three arms landing within 6.4% of numbers fixed before execution. Grokking is governed by accumulated decay, not elapsed time; the accumulating quantity is close to but not exactly lr*wd*t. We also report two methodological measurements. Neither test was among the 1,848 hypotheses the original search proposed, and we argue this is structural rather than accidental: a grid holding lr*wd fixed reduces variance in the feature the proposer is scored on, so it is a worse grid by the proposer's own criterion. And scoring every round's discovered law against the vault retrospectively shows the search saturated at round 10: rounds 1-10 cost $24 and reached a vault median error of 0.0792; rounds 11-114 cost $252 and reached 0.0784.

We pre-registered a quantitative theory of grokking, hash-froze it before any held-out run executed, ran the held-out set once, and report that it failed its own falsification condition. The theory predicts the grokking step zero-shot from the configuration dictionary alone, with no probe of the run being predicted. Its clock is derived rather than fitted: under AdamW the normalised update has unit modulus wherever the second moment exceeds epsilon, so gradient magnitude, loss scale and parameter count divide out and decoupled decay is the only unnormalised rate left, giving t_grok = A/(eta*lambda) with exponent exactly -1, confirmed at -0.98, -1.11, -0.73 and -0.96 across four training fractions. On 80 configurations it placed 0.550 of rows within a factor of two against a committed 0.61: falsified. The failure is structured, not diffuse. Inside the task families it was fitted on it is unbiased (mean error +0.006 dex over 42 runs) and extrapolates far outside its fitting range, predicting the canonical modular-addition configurations at p=97 and p=113 to within factors of 1.2 to 1.7 having never seen a modulus above 59 or a two-layer model. On eight unseen task families it is biased +1.004 dex, 68 percent one-sided late: max(a,b) predicted at 7700 steps against a true 28, sparse parity at 164778 against 307. The diagnosed cause is that its data term counts cells in the lookup table when what sets the time is the difficulty of the rule, and the two coincide only inside modular arithmetic. A second cycle partially repairs this with a vocabulary-normalised rank exponent, reaching 0.538 under leave-one-task-family-out and turning parity from 2.677 dex wrong into a median error of 0.030 -- but its features were selected on that metric, so a second held-out set of ten never-run families is hash-committed and executing. We release the harness, 396 runs and both registries.