Structure-Specific Representational Priors Causally Control the Grokking Delay

Grokking -- generalization long after training-set interpolation -- has been accelerated by structure-agnostic interventions (gradient filtering, weight-norm clamping, geometric penalties). Whether the delay specifically measures the time to form task-structured representations has remained observational. We test it causally by injecting representational priors of varying content into a one-layer transformer learning modular addition, via a supervised-contrastive loss whose positives encode (i) the task's true structure ((a+b) bmod p), (ii) a coherent-but-wrong sibling ((a-b) bmod p), or (iii) a random partition -- all with identical loss form, strength, class sizes, and geometry. Whether generalization occurs follows a clean gradation: true 22/30 runs, sibling (same periodic features, wrong combination) 14/15, random (only memorizable) 0/20 (Fisher p=1.3×10-7). A weight-norm-matched control replaying the norm trajectory onto plain cross-entropy generalizes 0/15, ruling out the norm as mediator. Probes show structure formation precedes and predicts generalization in all runs. Only the true structure also accelerates grokking (up to 2.75×), but this is dose-dependent and bimodal. We then confirm the mechanism by prediction: because the acceleration is gated by a weight-norm side-effect, clamping the norm during training yields a reliable, standalone accelerator with a median 8.6× speedup (up to 22× on the fastest seeds, under 1000 epochs), growing monotonically as the norm is held lower; the residual stalls also vanish, though significant only pooled over the two mitigations run at both strengths (0/40 vs 6/20, p=7.7×10-4), not per method. The grokking delay is, causally, the time to form the right representational structure -- decided at the level of features, not labels.