FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet

2026-04-24

AI Summary

This work addresses the limitation of conventional federated learning, which employs Euclidean averaging for SPD matrix models with Stiefel constraints, thereby compromising their orthogonality and intrinsic geometric structure. To overcome this, the study introduces, for the first time, a manifold-aware aggregation mechanism into the SPDnet federated learning framework, proposing two geometry-preserving strategies: ProjAvg, which projects aggregated updates onto the Stiefel manifold, and RLAvg, which approximates averaging in the tangent space. Both methods are optimizer-agnostic and computationally efficient, leveraging projection, retraction, and lifting operations on the Stiefel manifold. Evaluated on EEG motor imagery tasks, the proposed approach achieves higher F1 scores than federated EEGNet with significantly fewer communication parameters and demonstrates strong robustness to data heterogeneity and partial client participation.

Technology Category

Machine Learning: Distributed Machine Learning & Federated LearningMultiagent Systems: Mechanism DesignConstraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

User Modeling, Personalization and Recommendation: Federated recommendation systems and personalizationResponsible Web: Machine-in-the-loop, human agency and autonomySystems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing

Abstract

We introduce two federated learning frameworks for the classical SPDnet model operating on symmetric positive definite (SPD) matrices with Stiefel-constrained parameters. Unlike standard Euclidean averaging, which violates orthogonality, our approach preserves geometric structure through two efficient aggregation strategies: ProjAvg, projecting arithmetic means onto the Stiefel manifold, and RLAvg, approximating tangent-space averaging via retractions and liftings. Both methods are computationally efficient, independent of the optimizer, and enable scalable federated learning for signal processing applications whose features are SPD matrices. Simulations on EEG motor imagery benchmarks show that FedSPDnet outperforms federated EEGnet in F1 score and robustness to federation and partial participation, while using fewer parameters per communication round.

Problem

• federated learning
• SPD matrices
• Stiefel manifold
• geometric structure preservation
• EEG signal processing

Innovation

• Federated Learning
• SPD Manifold
• Stiefel Manifold
• Geometric Aggregation
• EEG Signal Processing