Nonparametric regression with modified ReLU networks

07/17/2022

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by   Aleksandr Beknazaryan, et al.

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We consider regression estimation with modified ReLU neural networks in which network weight matrices are first modified by a function α before being multiplied by input vectors. We give an example of continuous, piecewise linear function α 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 β-smooth function.