bibkey: “boursierpesmedragomir2025grokking” authors: “Etienne Boursier; Scott Pesme; Radu-Alexandru Dragomir” year: 2025 title: “A Theoretical Framework for Grokking: Interpolation followed by Riemannian Norm Minimisation” doi: null claim: “Gradient flow with small weight decay first tracks the unregularized flow to an interpolation manifold and then follows a slow-time Riemannian norm-minimization flow on it; in linear regression the null coordinates decay exactly as exp(-lambda t).” strata_touched: [] license: “citation-only” triage: “anchor” url: “https://arxiv.org/abs/2505.20172”

A Theoretical Framework for Grokking: Interpolation followed by Riemannian Norm Minimisation

Verified locator

NeurIPS 2025; arXiv:2505.20172. Proposition 2 proves convergence, as the decay vanishes, of the rescaled trajectory to the reduced flow d theta/d tau = -P_{T M} theta on a smooth attracting critical manifold under a Morse-Bott condition; Appendix C, Eqs. (23)-(24), separates positive-singular-value coordinates from null coordinates and gives z_i(t) = exp(-lambda t) z_i(0) for the latter. This is the direct prior for the pure weight-decay manifold flow and for the null-coordinate decay used in the fiber-law volume; the volume uses only the pointwise statement and the exact linear solution.

Declared identifiers: https://arxiv.org/abs/2505.20172.