Bayes-optimal Learning of Deep Random Networks of Extensive-width

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width are proportionally large. We propose a closed-form expression for the Bayes-optimal test error, for regression and classification tasks. We further compute closed-form expressions for the test errors of ridge regression, kernel and random featu...