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 since this approximation order is\le r^\alpha for H } essentially \sqrt{d} times a function of N and L independent of d .