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.

翻译：我们针对经典SPDnet模型提出了两种联邦学习框架，该模型作用于对称正定(SPD)矩阵且带有Stiefel约束参数。与破坏正交性的标准欧氏平均不同，我们的方法通过两种高效的聚合策略保持几何结构：ProjAvg（将算术均值投影到Stiefel流形上）和RLAvg（通过收缩与提升近似切空间均值）。两种方法计算效率高、独立于优化器，并能以可扩展的联邦学习方式处理特征为SPD矩阵的信号处理应用。在脑电图运动想象基准上的仿真表明，FedSPDnet在F1分数、对联邦学习与部分参与的鲁棒性方面均优于联邦EEGnet，且每轮通信使用的参数更少。