Function approximation by deep neural networks with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$

In this paper it is shown that $C_\beta$-smooth functions can be approximated by neural networks with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$. 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 $[-1,1]$.