FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet

TL;DR

This paper presents FedSPDnet, a federated learning framework for SPD matrices that maintains geometric structure and improves performance in signal processing tasks like EEG analysis.

Contribution

It introduces two geometry-aware aggregation strategies for federated SPDnet, enhancing scalability and robustness over existing methods.

Findings

FedSPDnet outperforms federated EEGnet in F1 score.

It is more robust to federation and partial participation.

Uses fewer parameters per communication round.

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.