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
The paper presents a spectral theory explaining the phenomenon of grokking, where an initial fit to training data is followed by a delayed improvement in generalization. It shows that for homogeneous networks trained with squared loss and L₂ weight decay, residuals after memorization influence the neural tangent kernel (NTK) dynamics, leading to a transition from lazy to rich learning. The theory predicts that grokking timescales depend on the product of learning rate and weight decay, and that stronger decay can halt fitting, with empirical validation on modular addition tasks using MLPs and Transformers.
By Lenz Pracher, Pascal de Jong, Oskar Lieshaus, Alan Jeffares, Steffen Rulands
arXiv:2608.25813v3 Announce Type: replace
Abstract: For overparameterized neural networks, many solutions can fit the training data equally well while behaving very differently on unseen samples. Gro...
By Yiming Lin, Yuxuan Wang
arXiv:2607. 23967v1 Announce Type: new Abstract: Delayed generalization, or grokking, remains poorly understood despite extensive empirical study.
By Taeyoung Kim
arXiv:2608. 01833v1 Announce Type: cross Abstract: Grokking is a striking phenomenon in neural network training, where a model can undergo a prolonged period of pure memorization before abrupt generalization.
By Lai Shun Chan, Xiaotian Zhang, Yue Shang, Ge Zhang, Entao Yang
The paper investigates whether flatter loss landscapes drive better generalization in the context of Grokking. It shows that sharpness‑aware minimization (SAM) alone does not reliably induce the transition to generalization, but when combined with weight decay, SAM can accelerate this transition up to four times faster. The authors provide a theoretical analysis using a minimal two‑layer ReLU model, demonstrating that flatness alone cannot distinguish memorizing from generalizing solutions, while weight decay favors generalization and a local stability window explains SAM’s effect.
By Mohnish Harwani