Asymptotics of feature learning in two-layer networks after one gradient-step

In this manuscript we investigate the problem of how two-layer neural networks learn features from data, and improve over the kernel regime, after being trained with a single gradient descent step. Leveraging a connection from (Ba et al., 2022) with a non-linear spiked matrix model and recent progress on Gaussian universality (Dandi et al., 2023), we provide an exact asymptotic description of the generalization error in the high-dimensional limit where the number of samples $n$, the width $p$ and the …

cond-mat.dis-nn cs.lg data feature features gradient kernel layer learn linear matrix networks neural networks non-linear progress stat.ml