bibkey: “musat2025geometry” authors: “Tiberiu Musat” year: 2025 title: “The Geometry of Grokking: Norm Minimization on the Zero-Loss Manifold” doi: null claim: “After interpolation, gradient descent with weight decay effectively minimizes the weight norm along the zero-loss manifold; the tangential component of the motion near nonsingular regions is the projected norm-reduction direction.” strata_touched: [] license: “citation-only” triage: “anchor” url: “https://arxiv.org/abs/2511.01938”

The Geometry of Grokking: Norm Minimization on the Zero-Loss Manifold

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arXiv:2511.01938 (revised 2026). Theorem 4.8 controls proximity to the zero-loss set and Theorem 4.14 controls the tangential component near a nonsingular region; Remark 4.15 reads the motion as norm reduction along the manifold. Cited as a geometric precedent of the fiber-law volume’s instantaneous statement.

Declared identifiers: https://arxiv.org/abs/2511.01938.