Batch Normalization for Neural Networks on Complex Domains

TL;DR

This paper introduces batch normalization layers tailored for neural networks operating on complex domains, including less-studied areas like the Siegel disk, enhancing training stability and accuracy.

Contribution

It develops Riemannian batch normalization layers for complex domain neural networks, extending existing methods to new complex domains such as the Siegel disk.

Findings

Improved training stability and accuracy in complex domain neural networks.

Effective on tasks like radar clutter classification, node classification, and action recognition.

Abstract

Riemannian neural networks have proven effective in solving a variety of machine learning tasks. The key to their success lies in the development of principled Riemannian analogs of fundamental building blocks in deep neural networks (DNNs). Among those, Riemannian batch normalization (BN) layers have shown to enhance training stability and improve accuracy. In this paper, we propose BN layers for neural networks on complex domains. The proposed layers have close connections with existing Riemannian BN layers. We derive essential components for practical implementations of BN layers on some complex domains which are less studied in previous works, e.g., the Siegel disk domain. We conduct experiments on radar clutter classification, node classification, and action recognition demonstrating the efficacy of our method.