Before revision:  As a consequence, this new class of networks overcome s the curse of dimensionality in approximation power when the variation of \omega_f(r) as r \rightarrow \to 0 is moderate (e.g., \omega_f(r) \lesssim r^\alpha for H \"o lder continuous functions), since the major term to be concerned in our approximation rate is essentially \sqrt{d} times a function of N and L independent of d within the modulus of continuity.
After revision:  As a consequence, this new class of networks overcome s the curse of dimensionality in approximation power when the variation of \omega_f(r) as r \rightarrow \to 0 is moderate (e.g., \omega_f(r) \lesssim r^\alpha for H \"o lder continuous functions), since the major term to be considered in our approximation rate is essentially \sqrt{d} times a function of N and L independent of d within the modulus of continuity.