# Riemannian Federated Learning via Averaging Gradient Streams

arXiv: https://arxiv.org/abs/2409.07223 · HTML: https://mlsanity.com/paper/2409.07223/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 70 references that are in the map.
- First posted on arXiv 11 Sep 2024.

## Builds on (most cited first, 30 of 34)

- [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)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Achieving Linear Speedup with Partial Worker Participation in Non-IID Federated Learning](https://mlsanity.com/paper/2101.11203/) (2021)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronization](https://mlsanity.com/paper/1910.13598/) (2019)
- [First-order Methods for Geodesically Convex Optimization](https://mlsanity.com/paper/1602.06053/) (2016)
- [On the convergence properties of a K-step averaging stochastic gradient descent algorithm for nonconvex optimization](https://mlsanity.com/paper/1708.01012/) (2017)
- [Fast Federated Learning in the Presence of Arbitrary Device Unavailability](https://mlsanity.com/paper/2106.04159/) (2021)
- [Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds](https://mlsanity.com/paper/1605.07147/) (2016)
- [Global rates of convergence for nonconvex optimization on manifolds](https://mlsanity.com/paper/1605.08101/) (2016)
- [A Unified Analysis of Federated Learning with Arbitrary Client Participation](https://mlsanity.com/paper/2205.13648/) (2022)
- [Averaging Stochastic Gradient Descent on Riemannian Manifolds](https://mlsanity.com/paper/1802.09128/) (2018)
- [On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry](https://mlsanity.com/paper/2106.00286/) (2021)
- [Federated Learning Under Intermittent Client Availability and Time-Varying Communication Constraints](https://mlsanity.com/paper/2205.06730/) (2022)
- [Federated Learning under Importance Sampling](https://mlsanity.com/paper/2012.07383/) (2020)
- [Why (and When) does Local SGD Generalize Better than SGD?](https://mlsanity.com/paper/2303.01215/) (2023)
- [DeEPCA: Decentralized Exact PCA with Linear Convergence Rate](https://mlsanity.com/paper/2102.03990/) (2021)
- [Fast and Simple PCA via Convex Optimization](https://mlsanity.com/paper/1509.05647/) (2015)
- [Federated Learning on Riemannian Manifolds](https://mlsanity.com/paper/2206.05668/) (2022)
- [Differentially private Riemannian optimization](https://mlsanity.com/paper/2205.09494/) (2022)
- [R3MC: A Riemannian three-factor algorithm for low-rank matrix completion](https://mlsanity.com/paper/1306.2672/) (2013)
- [Towards Bias Correction of FedAvg over Nonuniform and Time-Varying Communications](https://mlsanity.com/paper/2306.00280/) (2023)
- [Hyperbolic Manifold Regression](https://mlsanity.com/paper/2005.13885/) (2020)

## Built on by (most cited first, 4 of 4)

- [FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet](https://mlsanity.com/paper/2604.22494/) (2026)
- [New Insights on Unfolding and Fine-tuning Quantum Federated Learning](https://mlsanity.com/paper/2506.20016/) (2025)
- [Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approach](https://mlsanity.com/paper/2507.22855/) (2025)
- [A Stable Aggregation Method for Quantum Federated Learning](https://mlsanity.com/paper/2609.00356/) (2026)

## Abstract (arXiv)

Federated learning (FL) as a distributed learning paradigm has a significant advantage in addressing large-scale machine learning tasks. In the Euclidean setting, FL algorithms have been extensively studied with both theoretical and empirical success. However, there exist few works that investigate federated learning algorithms in the Riemannian setting. In particular, critical challenges such as partial participation and data heterogeneity among agents are not explored in the Riemannian federated setting. This paper presents and analyzes a Riemannian FL algorithm, called RFedAGS, based on a new efficient server aggregation -- averaging gradient streams, which can simultaneously handle partial participation and data heterogeneity. We theoretically show that the proposed RFedAGS has global convergence and sublinear convergence rate under decaying step sizes cases; and converges sublinearly/linearly to a neighborhood of a stationary point/solution under fixed step sizes cases. These analyses are based on a vital and non-trivial assumption induced by partial participation, which is shown to hold with high probability. Extensive experiments conducted on synthetic and real-world data demonstrate the good performance of RFedAGS.