Grokking on the Weight-Decay Clock: A Rate Hierarchy from Softly Broken Symmetries
Delayed generalization, or grokking, remains poorly understood despite extensive empirical study. We identify an exactly solvable late-time relaxation mechanism for grokking in linear models trained with full-batch heavy-ball optimization and weight decay, together with a locally quadratic extension to nonlinear neural networks. Our analysis reveals a distinguished population-active component of the empirical null space, which we call the grokking subspace. Along this subspace, the training predictions remain unchanged, leaving weight decay as the sole restoring force and giving rise to a slow dissipative relaxation governed by an exact discrete-time and continuous-time law. We show that ...
| Authors | Taeyoung Kim |
|---|---|
| Primary category | cs.AI |
| Published | 27 July 2026 |
| Last updated at source | 27 July 2026 |
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