Before revision:  As a consequence, this new network overcomes  the curse of dimensionality in approximation power since this approximation order is\le  } essentially \sqrt{d} times a function of N and L independent of d .
After revision:  As a consequence, this new network overcomes the curse of dimensionality in approximation power when the variation of \omega_f(r) as r\rightarrow 0 is moderate (e.g., \omega_f(r)\le } essentially \sqrt{d} times a function of N and L independent of d .