Approximating smooth functions by deep neural networks with sigmoid activation function

We study the power of deep neural networks (DNNs) with sigmoid activation function. Recently, it was shown that DNNs approximate any d-dimensional, smooth function on a compact set rate order W?p?d, where W is number nonzero weights in network and p smoothness Unfortunately, these rates only hold for special class sparsely connected DNNs. ask ourselves if we can show same approximation simpler more general class, i.e., which are defined by its width depth. In this article fixed depth Md achieve an M?2p. As conclusion quantitatively characterize terms overall W0 W0?p?d. This result finally helps us to understand topology guarantees target accuracy.