Neural networks with superexpressive activations and integer weights

An example of an activation function σ is given such that networks with activations σ, lfloor·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-2β2β+dlog2n for neural network regression estimation of unknown β-H"older continuous function with given n samples.