A Feedforward Unitary Equivariant Neural Network

TL;DR

This paper introduces a novel feedforward neural network that is equivariant under the unitary group, capable of handling complex vector inputs of arbitrary dimension without convolution layers, and demonstrates its effectiveness in predicting atomic motion dynamics.

Contribution

The paper presents a new unitary equivariant neural network architecture that avoids convolution layers and truncation errors, with efficient implementation and practical application to atomic motion prediction.

Findings

Successfully predicts atomic motion dynamics

Efficient layer implementation using simple calculations

Demonstrates practicality of the proposed 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 $\mathbb{C}^n$ 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.