FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet

arXiv cs.LG / 4/27/2026

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Key Points

The paper proposes two federated learning frameworks tailored to the SPDnet model, targeting symmetric positive definite (SPD) matrix data with Stiefel-constrained parameters.
Instead of standard Euclidean averaging (which breaks orthogonality), it introduces ProjAvg and RLAvg to preserve the model’s geometric structure during aggregation.
ProjAvg restores orthogonality by projecting arithmetic means onto the Stiefel manifold, while RLAvg performs an approximate tangent-space averaging using retractions and liftings.
The aggregation methods are designed to be computationally efficient, optimizer-independent, and suitable for scalable federated learning in signal processing scenarios where features are SPD matrices.
Experiments on EEG motor imagery benchmarks indicate FedSPDnet improves F1 score and robustness under federation and partial client participation compared with federated EEGnet, while reducing communication-round parameter usage.

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.