# FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet

arXiv: https://arxiv.org/abs/2604.22494 · HTML: https://mlsanity.com/paper/2604.22494/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [FedBN: Federated Learning on Non-IID Features via Local Batch Normalization](https://mlsanity.com/paper/2102.07623/) (2021)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [Riemannian batch normalization for SPD neural networks](https://mlsanity.com/paper/1909.02414/) (2019)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [Is Second-order Information Helpful for Large-scale Visual Recognition?](https://mlsanity.com/paper/1703.08050/) (2017)
- [On Convergence of FedProx: Local Dissimilarity Invariant Bounds, Non-smoothness and Beyond](https://mlsanity.com/paper/2206.05187/) (2022)
- [The largest EEG-based BCI reproducibility study for open science: the MOABB benchmark](https://mlsanity.com/paper/2404.15319/) (2024)
- [Infeasible Deterministic, Stochastic, and Variance-Reduction Algorithms for Optimization under Orthogonality Constraints](https://mlsanity.com/paper/2303.16510/) (2023)
- [Federated Learning on Riemannian Manifolds](https://mlsanity.com/paper/2206.05668/) (2022)
- [Geometric Neural Network based on Phase Space for BCI-EEG decoding](https://mlsanity.com/paper/2403.05645/) (2024)
- [Federated Learning on Riemannian Manifolds with Differential Privacy](https://mlsanity.com/paper/2404.10029/) (2024)
- [Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Data](https://mlsanity.com/paper/2406.08465/) (2024)
- [Riemannian Federated Learning via Averaging Gradient Streams](https://mlsanity.com/paper/2409.07223/) (2024)
- [Classification of Buried Objects from Ground Penetrating Radar Images by using Second Order Deep Learning Models](https://mlsanity.com/paper/2410.07117/) (2024)
- [Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifolds](https://mlsanity.com/paper/2501.11555/) (2025)

## Built on by (most cited first, 2 of 2)

- [A Stable Aggregation Method for Quantum Federated Learning](https://mlsanity.com/paper/2609.00356/) (2026)
- [Personalised federated learning for Riemannian and Euclidean EEG decoding](https://mlsanity.com/paper/2609.29037/) (2026)

## Abstract (arXiv)

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.