Critical Windows of Complexity Control: When Transformers Decide to Reason or Memorize

Recent work has shown that Transformers' compositional generalization is governed by \emph{complexity control}, initialization scale and weight decay, which steers training toward low-complexity reasoning solutions rather than high-complexity memorization. Existing analyses, however, treat complexity control as a single static hyperparameter choice, leaving open \emph{when} during training this control is actually decisive. We show that the memorization-versus-reasoning fate of a Transformer is determined within a sharp, identifiable window of training. On a controlled compositional task we find that (i)~weight decay applied for a single 25%-of-training window matches full-training weight decay in out-of-distribution (OOD) accuracy ($0.93$ vs $0.91$); (ii)~holding total regularization budget constant, placing it in the middle of training yields $5{-}9\times$ higher OOD accuracy than placing it early; (iii)~the boundary of the critical window is remarkably sharp, window onset shifted by as little as $100$ optimization steps causes mean OOD to jump from chance ($0.15$) to reasoning-regime ($0.61$); (iv)~the window's position depends systematically on initialization scale, but the basin of attraction for reasoning solutions \emph{shrinks} at small initialization, contradicting the prevailing recommendation that smaller initialization is uniformly better. We further show that the critical-window phenomenon is task-specific: it does not appear on grokking with modular arithmetic, where properly tuned constant weight decay matches scheduled weight decay.