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In this paper it is shown that $C_\beta$-smooth functions can be approximatedby deep neural networks with ReLU activation function and with parameters$\{0,\pm \frac{1}{2}, \pm 1, 2\}$. The $l_0$ and $l_1$ parameter norms ofconsidered networks are thus equivalent. The depth, width and the number ofactive parameters of the constructed networks have, up to a logarithmic factor,the same dependence on the approximation error as the networks with parametersin $[-1,1]$. In particular, this means that the nonparametric regressionestimation with the constructed networks attains the same convergence rate aswith sparse networks with parameters in $[-1,1]$.

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