bibkey: “kim2026weightdecayclock” authors: “Taeyoung Kim” year: 2026 title: “Grokking on the Weight-Decay Clock: A Rate Hierarchy from Softly Broken Symmetries” doi: null claim: “Delayed generalization in a solvable model is governed by weight-decay relaxation of the component in the empirical observability null space that remains population-visible; population-risk excess has a single-root term and a doubled-root term, and rescaling that component shifts the delay linearly in its logarithm.” strata_touched: [] license: “citation-only” triage: “anchor” url: “https://arxiv.org/abs/2607.23967”

Grokking on the Weight-Decay Clock: A Rate Hierarchy from Softly Broken Symmetries

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arXiv:2607.23967. Section 2.3, Eqs. (6)-(8), defines empirical and population observability Grams and identifies the quotient of their null spaces as the intrinsic object; Theorem 4 and Corollary 5 give the slow-mode threshold clock; Theorem 20, Eqs. (34)-(37), gives the single-root versus doubled-root rate dichotomy; Section 7.4 rescales the empirical-null component after interpolation and measures a delay shift linear in log c. Direct prior for the training-invisible-quotient framing and the rate dichotomy of the fiber-law volume, which contributes only the escape-set formulation with an explicit witness.

Declared identifiers: https://arxiv.org/abs/2607.23967.