A new network with super approximation power is introduced. This network is built with Floor (\lfloor x\rfloor) or ReLU (\max\{0,x\}) activation function in each neuron and hence we call such networks as Floor-ReLU networks. {For any hyper-parameters N\inN^+ and L\inN^+,} it is shown that Floor-ReLU networks with  width \max\{d,\, 5N+13\} and  depth 64dL+3 can {uniformly approximate a H{\"o}lder function f on [0,1]^d with an approximation rate 3\lambda d^{\alpha/2}N^{-\alphaL}, where \alpha \in(0,1] and \lambda are the H{\"o}lder order and constant, respectively.} More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f(d\,N^{-L})+2\omega_f(d){N^{-L}}. 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) %DIFDELCMD < \le %%% {\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. }
A new network with super approximation power is introduced. This network is built with Floor (\lfloor x\rfloor) or ReLU (\max\{0,x\}) activation function in each neuron and hence we call such networks Floor-ReLU networks. {For any hyper-parameters N\inN^+ and L\inN^+,} it is shown that Floor-ReLU networks with a width \max\{d,\, 5N+13\} and a depth 64dL+3 can {uniformly approximate a H{\"o}lder function f on [0,1]^d with an approximation rate 3\lambda d^{\alpha/2}N^{-\alphaL}, where \alpha \in(0,1] and \lambda are the H{\"o}lder order and constant, respectively.} More generally for an arbitrary continuous function f on [0,1]^d with a modulus of continuity \omega_f(\cdot), the constructive approximation rate is \omega_f(d\,N^{-L})+2\omega_f(d){N^{-L}}. 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) %DIFDELCMD < \le %%% {\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. }
D
as
A
a
A
a
A
s