Batch Normalization for Neural Networks on Complex Domains

2026-05-01

AI Summary

This work addresses the absence of batch normalization methods compatible with Riemannian geometry on complex domains—such as Siegel disks—which has hindered the training stability and performance of Riemannian neural networks. The paper presents the first systematic construction of a batch normalization layer tailored to such complex manifolds, leveraging Riemannian-geometric statistical moment estimation and differential-geometric optimization mechanisms to effectively normalize data in complex domains. This approach substantially extends the applicability of Riemannian batch normalization and consistently improves both model accuracy and training stability across diverse tasks, including 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.

Problem

• Batch Normalization
• Complex Domains
• Riemannian Neural Networks
• Siegel Disk
• Neural Networks

Innovation

• Batch Normalization
• Complex Domains
• Riemannian Neural Networks
• Siegel Disk
• Deep Learning