15
0

Nonparametric regression with modified ReLU networks

Abstract

We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function α\alpha before being multiplied by input vectors. We give an example of continuous, piecewise linear function α\alpha for which the empirical risk minimizers over the classes of modified ReLU networks with l1l_1 and squared l2l_2 penalties attain, up to a logarithmic factor, the minimax rate of prediction of unknown β\beta-smooth function.

View on arXiv
Comments on this paper