A feedforward unitary equivariant neural network. (April 2023)

• Record Type: Journal Article
• Authors: Ma, Pui-Wai; Chan, T.-H. Hubert
• Is Part Of: Neural networks. Volume 161(2023)
• Page Start: 154
• Page End: 164
• Publication Date: 2023-04
• Subjects: Equivariant neural network -- Feedforward neural network -- Unitary equivariant -- Rotational equivariant; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2023.01.042
• Languages: English
• ISSNs: 0893-6080

Abstract

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 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.