A Feedforward Unitary Equivariant Neural Network
This work addresses the need for efficient unitary-equivariant models in physics and machine learning, though it appears incremental as it builds on existing equivariance concepts.
The authors tackled the problem of designing a feedforward neural network that is equivariant to the unitary group U(n) for arbitrary dimensions, and they demonstrated its practicality by applying it to predict atomic motion dynamics with empirical results.
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 $\mathbb{C}^n$ 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.