Siegel Neural Networks

Xuan Son Nguyen, Aymeric Histace, Nistor Grozavu

Keywords: Neural networks, Siegel spaces, Symmetric spaces, Riemannian manifolds

Abstract:

Riemannian symmetric spaces (RSS) such as hyperbolic spaces and symmetric positive definite (SPD) manifolds have become popular spaces for representation learning. In this paper, we propose a novel approach for building discriminative neural networks on Siegel spaces, a family of RSS that is largely unexplored in machine learning tasks. For classification applications, one focus of recent works is the construction of multiclass logistic regression (MLR) and fully-connected (FC) layers for hyperbolic and SPD neural networks. Here we show how to build such layers for Siegel neural networks. Our approach relies on the quotient structure of those spaces and the notation of vector-valued distance on
RSS. We demonstrate the relevance of our approach on two applications, i.e., radar signal classification and node classification. Our results successfully demonstrate state-of-the-art performance across all datasets.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 20629