The Norm-Separation Delay Law of Grokking: A First-Principles Theory of Delayed Generalization
Grokking -- the sudden generalisation that appears long after a model has perfectly memorised its training data -- has been widely observed but lacks a quantitative theory explaining the length of the delay. We show that grokking is a norm-driven representational phase transition in regularised training dynamics, and establish the Norm-Separation Delay Law: $T_{\mathrm{grok}} - T_{\mathrm{mem}} = Θ(γ_{\mathrm{eff}}^{-1} \log(\|θ_{\mathrm{mem}}\|^2 / \|θ_{\mathrm{post}}\|^2))$, where $γ_{\mathrm{eff}}$ is the optimiser's effective contraction rate ($γ_{\mathrm{eff}} = ηλ$ for SGD, $γ_{\mathrm{eff}} \ge ηλ$ for AdamW). The upper bound follows from a discrete Lyapunov contraction argument; t...
| Authors | Truong Xuan Khanh, Truong Quynh Hoa, Luu Duc Trung et al. |
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| Primary category | cs.AI |
| Published | 5 March 2026 |
| Last updated at source | 2 May 2026 |
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