@article {665054, title = {Universality Laws for High-Dimensional Learning with Random Features}, journal = {IEEE Transactions on Information Theory, in press}, year = {2022}, abstract = {We prove a universality theorem for learning with random features. Our result shows that, in terms of training and generalization errors, the random feature model with a nonlinear activation function is asymptotically equivalent to a surrogate Gaussian model with a matching covariance matrix. This settles a conjecture based on which several recent papers develop their results. Our method for proving the universality builds on the classical Lindeberg approach. Major ingredients of the proof include a leave-one-out analysis for the optimization problem associated with the training process and a central limit theorem, obtained via Stein{\textquoteright}s method, for weakly correlated random variables.}, url = {https://arxiv.org/abs/2009.07669}, author = {Hong Hu and Yue M. Lu} }