arXiv Machine Learning By Yiming Lin

Canalization Before Generalization: Grokking as a Dynamical Probe

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The paper investigates how overparameterized neural networks can fit training data in many different ways yet generalize differently. By applying short, fixed‑duration weight‑decay pulses during the grokking plateau, the authors show that early in training the pulses produce unordered shifts in generalization time, but later a clear dose ordering emerges: larger weight‑decay increases lead to earlier generalization, while larger decreases delay it. This ordering appears before visible generalization and persists even as test‑loss barriers collapse, a phenomenon the authors term the canalization of function selection.

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arXiv Machine Learning
Sep 11

Quantifying the Memorization-to-Generalization Transition: Scaling Laws and Phase Structure in Grokking

The study investigates the delayed transition from memorization to generalization—known as grokking—in two‑hidden‑layer MLPs trained on modular arithmetic. By exploring 384 hyperparameter configurations, the authors derive a power‑law scaling relation for the onset time of generalization, showing that data complexity dominates over model capacity. A clear phase boundary at weight decay around 1.0 separates grokking from non‑grokking regimes, and weight norm trajectories indicate implicit regularization during the transition.

By Anish Kataria