Scaling Laws and Spectra of Shallow Neural Networks in the Feature Learning Regime

arXiv:2509.24882v2 Announce Type: replace Abstract: Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and diagonal neural networks in the feature learning regime. Leveraging connections with matrix compressed sensing and LASSO, we derive a detailed phase diagram for the scaling exponents of the excess risk as a function of sample complexity and weight decay. This analysis uncovers crossovers between distinct scaling

Source: arXiv cs.LG — read the full report at the original publisher.

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