FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet
Thibault Pautrel, Florent Bouchard, Ammar Mian, Guillaume Ginolhac
TLDR
FedSPDnet introduces geometry-aware federated learning for SPD matrices, using novel aggregation to outperform existing methods in signal processing.
Key contributions
- Introduces ProjAvg and RLAvg, two geometry-aware aggregation strategies for federated SPDnet.
- Preserves the geometric structure of Stiefel-constrained parameters, avoiding orthogonality violations.
- Achieves computational efficiency, optimizer independence, and scalability for SPD matrix applications.
- Demonstrates superior F1 score and robustness over federated EEGnet on EEG motor imagery benchmarks.
Why it matters
This paper addresses the critical issue of geometric structure preservation in federated learning for SPD matrices. By introducing efficient, geometry-aware aggregation, it significantly improves performance and robustness for signal processing applications. This opens new avenues for secure and distributed learning with complex data.
Original 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.
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