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.

翻译：黎曼神经网络在多种机器学习任务中展现出有效性，其成功关键在于为深度神经网络基本构建模块开发了原则性的黎曼类比方法。其中，黎曼批量归一化层已被证明能增强训练稳定性并提升精度。本文针对复数域神经网络提出了批量归一化层，该层与现有黎曼批量归一化层存在密切联系。我们推导了在部分前人研究较少的复数域（如西格尔圆盘域）中实现批量归一化层的必要组件。通过在雷达杂波分类、节点分类和动作识别任务上的实验，验证了所提方法的有效性。