Do Classical Early-Warning Signals Forecast Grokking? A Prospective Audit with an Interventional Stability Probe

Critical slowing down (CSD)—rising lag-1 autocorrelation and variance as a stochastic system approaches a fold bifurcation—is a standard early warning signal (EWS) in the ecology and climate science toolkit. Grokking, the delayed and abrupt onset of generalization in neural net- works, is widely called a training-time “phase transition,” making it natural to ask whether CSD indicators can forecast it. We test this hypothesis prospectively and adversarially, under three disciplines: a positive control the instrument must first pass, negative controls and baselines against which every claim is measured, and an interventional stability probe of the assumed mechanism. We first validate the EWS instrument on a ramped stochastic fold where CSD is mathematically guaranteed: across five seeds the indicators lead the transition by a median of ∼8,000 steps, produce zero false alarms on a matched null, and—using an independence-safe (non-overlapping-window) trend test—rise with median p ≈ 4 × 10−10; a parameter-free consis- tency check of the autocorrelation–recovery relation ρ1 = e−∆t/τrec holds at r = 0.887–0.969. We then apply the identical alarm rule, frozen in a version-controlled config before the held- out seeds existed, to grokking of modular addition in a one-layer transformer. The result is a clean negative. Calibrated on no-grokking control runs (weight decay = 0), the EWS battery produces zero detections across twenty grokking runs, five distinct training observables, and three window sizes—including on ten held-out seeds trained only after the detector configura- tion was committed—and an FFT comparator inspired by a prior loss-oscillation proposal is also silent under the same protocol. The apparent pre-transition trend that motivates CSD vanishes once the trend test respects window overlap (p: 0.016 → 0.39; only 1 of 10 dev seeds trends upward), and the smooth transition score has negative Brier skill relative to climatology. An interventional stability probe indicates why: before the transition small weight perturba- tions are amplified under identically replayed batches (a pattern replicated across five seeds and three kick sizes and persisting under an optimizer-state-reset control)—and bounded recovery appears only intermittently after grokking, tracking the post-transition loss-spike cycle rather than switching on at t∗. This is consistent with escape from an unstable, degenerate manifold rather than the collapse of a stable basin, so the fold premise behind CSD does not hold. We conclude that training-time emergence monitors should measure divergence rates, not relaxation rates. All code, logs, and tests are available on request and will be released publicly.