Nonparametric regression with modified ReLU networks

• URL: http://arxiv.org/abs/2207.08306v1
• Date: Sun, 17 Jul 2022 21:46:06 GMT
• Title: Nonparametric regression with modified ReLU networks
• Authors: Aleksandr Beknazaryan and Hailin Sang
• Abstract summary: We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function $alpha$ before being multiplied by input vectors.
• Score: 77.34726150561087
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function $\alpha$ before being multiplied by input vectors. We give an example of continuous, piecewise linear function $\alpha$ for which the empirical risk minimizers over the classes of modified ReLU networks with $l_1$ and squared $l_2$ penalties attain, up to a logarithmic factor, the minimax rate of prediction of unknown $\beta$-smooth function.

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