A feedforward unitary equivariant neural network.

Abstract

We devise a new type of feedforward neural network. It is equivariant with respect to the unitary group U(n). The input and output can be vectors in ℂⁿ with arbitrary dimension n. No convolution layer is required in our implementation. We avoid errors due to truncated higher order terms in Fourier-like transformation. The implementation of each layer can be done efficiently using simple calculations. As a proof of concept, we have given empirical results on the prediction of the dynamics of atomic motion to demonstrate the practicality of our approach.