arXiv Machine Learning By Lorenzo Rizzi, Arie Wortsman Zurich, Bruno Loureiro

Learning between the peaks: sharp asymptotics for kernel ridge regression under power-law anisotropy

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arXiv:2608. 28564v1 Announce Type: cross Abstract: We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels.

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arXiv Machine Learning
Jul 14

Exact Dynamics of Multi-class Stochastic Gradient Descent

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
arXiv Machine Learning
Sep 23

A Spectral Theory of Grokking: Weight Decay induces Feature Learning

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