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
arXiv:2603. 20986v2 Announce Type: replace Abstract: Phase-field modeling links thermodynamics and kinetics to microstructural evolution, but multiphysics frameworks such as MOOSE require expertise to construct inputs, manage campaigns, diagnose failures, and validate results.
By Sukriti Manna, Henry Chan, Subramanian K. R. S. Sankaranarayanan
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 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:2607. 23967v1 Announce Type: new Abstract: Delayed generalization, or grokking, remains poorly understood despite extensive empirical study.
By Taeyoung Kim
arXiv:2606. 30789v1 Announce Type: new Abstract: Group Relative Policy Optimization (GRPO) has become a standard tool for improving the reasoning ability of large language models, yet its training dynamics are still described empirically: reward trajectories are fit with low-parameter functional forms whose constants carry no mechanistic meaning, and hyperparameter choices remain a matter of trial and error.
By Rajat Ghosh, Datta Nimmaturi, Aryan Singhal, Vaishnavi Bhargava, Henry Wong, Johnu George, Debojyoti Dutta
arXiv:2607. 10285v1 Announce Type: new Abstract: We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process.
By Max Weinmann, Miriam Klopotek
arXiv:2607. 11116v1 Announce Type: cross Abstract: Deep equilibrium models promise input-adaptive implicit computation: harder problems should demand more solver iterations, and the solved equilibrium should encode the result of genuine iterative inference.
By Joyjeet Singh
arXiv:2607. 20552v1 Announce Type: new Abstract: Grokking -- the delayed generalization of neural networks long after they have memorized their training data -- wastes thousands of training epochs and is notoriously unpredictable.
By Chitraansh Pandey
arXiv:2608. 06597v1 Announce Type: cross Abstract: A scientific theory of deep learning, comprising learning dynamics and statistical properties of learned models, is rapidly gaining attention.
By Bj\"orn Ladewig, Ibrahim Talha Ersoy, Karoline Wiesner
arXiv:2608.23889v1 Announce Type: cross
Abstract: Plasticity under changing environments is central to both evolutionary biology and continual learning. Motivated by recent work on genotype--phenotyp...
By Owen Skriloff
arXiv:2606. 30064v1 Announce Type: new Abstract: We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures.
By L. U. Abdullaev, F. Herrera, U. A. Rozikov, M. V. Velasco