  An example of an activation function $\sigma$ is given such that networks
with activations $\{\sigma, \lfloor\cdot\rfloor\}$, integer weights and a fixed
architecture depending on $d$ approximate continuous functions on $[0,1]^d$.
The range of integer weights required for $\varepsilon$-approximation of
H\"older continuous functions is derived, which leads to a convergence rate of
order $n^{\frac{-2\beta}{2\beta+d}}\log_2n$ for neural network regression
estimation of unknown $\beta$-H\"older continuous function with given $n$
samples.
