Batch Normalization for Neural Networks on Complex Domains
For practitioners using Riemannian neural networks, this work extends batch normalization to complex-valued domains, addressing a gap in existing methods.
The paper proposes batch normalization layers for neural networks on complex domains, including less studied ones like the Siegel disk domain, and demonstrates improved training stability and accuracy on tasks such as radar clutter classification, node classification, and action recognition.
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.