arXiv:2510. 14074v2 Announce Type: replace-cross Abstract: We develop a framework for analyzing the learning dynamics of high-dimensional problems trained using one-pass stochastic gradient descent (SGD) with data from multiple anisotropic classes.
By Elizabeth Collins-Woodfin, Inbar Seroussi
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. 07281v1 Announce Type: cross Abstract: This paper investigates the asymptotic behavior of the out-of-sample prediction risk of the high-dimensional ridgeless least-squares estimator when the feature dimension $p$ and the sample size $n$ grow proportionally.
By Zhijun Liu, Dandan Jiang
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
By Andrea Montanari, Kangjie Zhou
arXiv:2602.06797v3 Announce Type: replace-cross
Abstract: We study optimal learning rate (LR) schedules under the functional scaling law (FSL) framework (Li et al., 2025), which decomposes training d...
By Binghui Li, Zilin Wang, Fengling Chen, Shiyang Zhao, Ruiheng Zheng, Lei Wu
arXiv:2510.14878v3 Announce Type: replace-cross
Abstract: We study kernel regression with common rotation-invariant kernels on real datasets including CIFAR-5m, SVHN, and ImageNet. We give a theoreti...
By Dhruva Karkada, Joseph Turnbull, Yuxi Liu, James B. Simon