Before revision:  Is there something special about deep convolutional networks that other learning machines do not possess ? Recent results in approximation theory have shown that there is an exponential advantage of deep convolutional-like networks in approximating functions with hierarchical locality in their compositional structure.
After revision:  Is there something special about deep convolutional networks that other learning machines do not possess ? Recent results in approximation theory proved an exponential advantage of deep convolutional-like networks in approximating functions with hierarchical locality in their compositional structure.