Before revision:  The influence of this new similarity measure on the optimization of neural network have been thoroughly analyzed.
After revision:  We first develop a theoretical foundation for AdderNets, by showing that both the single hidden layer AdderNet and the width-bounded deep AdderNet with ReLU activation functions are universal function approximators. An approximation bound for AdderNets with a single hidden layer is also presented. We further analyze the influence of this new similarity measure on the optimization of neural network have been thoroughly analyzed.