  We show that $d$-variate polynomials of degree $R$ can be represented on
$[0,1]^d$ as shallow neural networks of width $2(R+d)^d$. Also, by SNN
representation of localized Taylor polynomials of univariate $C^\beta$-smooth
functions, we derive for shallow networks the minimax optimal rate of
convergence, up to a logarithmic factor, to unknown univariate regression
function.
