Before revision:  As a consequence, this new {class of networks} overcome  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)  {\lesssim} r^\alpha for H{\"o}lder continuous functions), since the major term to be concerned in our approximation rate is {essentially 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 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 d times a function of N and L independent of d within the modulus of continuity. }