Function approximation by deep neural networks with parameters {0,±1/2, ± 1, 2}

03/15/2021

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by   Aleksandr Beknazaryan, et al.

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In this paper it is shown that C_β-smooth functions can be approximated by neural networks with parameters {0,±1/2, ± 1, 2}. The depth, width and the number of active parameters of constructed networks have, up to a logarithimc factor, the same dependence on the approximation error as the networks with parameters in [-1,1]. In particular, this means that the nonparametric regression estimation with constructed networks attain the same convergence rate as with the sparse networks with parameters in [-1,1].