mlsanityData to 7 Oct 2026

Federated Learning on Riemannian Manifolds

arXiv 2206.05668 ↗First posted 12 Jun 2022cs.LG math.OCcited by 13

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Abstract (arXiv)

Federated learning (FL) has found many important applications in smart-phone-APP based machine learning applications. Although many algorithms have been studied for FL, to the best of our knowledge, algorithms for FL with nonconvex constraints have not been studied. This paper studies FL over Riemannian manifolds, which finds important applications such as federated PCA and federated kPCA. We propose a Riemannian federated SVRG (RFedSVRG) method to solve federated optimization over Riemannian manifolds. We analyze its convergence rate under different scenarios. Numerical experiments are conducted to compare RFedSVRG with the Riemannian counterparts of FedAvg and FedProx. We observed from the numerical experiments that the advantages of RFedSVRG are significant.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 19 of its 32 references that are in the map. First posted on arXiv 12 Jun 2022.

Builds on

19 of 32 references.

References · 19

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,592
  2. 2019Advances and Open Problems in Federated Learningcited by 3,021
  3. 2018Federated Optimization in Heterogeneous Networkscited by 2,971
  4. 2019On the Convergence of FedAvg on Non-IID Datacited by 1,220
  5. 2020Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimizationcited by 897
  6. 2016Federated Optimization: Distributed Machine Learning for On-Device Intelligencecited by 558
  7. 2021Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradientscited by 122
  8. 2013Manopt, a Matlab toolbox for optimization on manifoldscited by 112
  9. 2020FedSplit: An algorithmic framework for fast federated optimizationcited by 108
  10. 2016Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiationcited by 93
  11. 2016First-order Methods for Geodesically Convex Optimizationcited by 92
  12. 2020From Local SGD to Local Fixed-Point Methods for Federated Learningcited by 74
7 more
  1. 2016Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifoldscited by 64
  2. 2016Global rates of convergence for nonconvex optimization on manifoldscited by 61
  3. 2021Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learningcited by 52
  4. 2021Decentralized Riemannian Gradient Descent on the Stiefel Manifoldcited by 33
  5. 2021On the Local Linear Rate of Consensus on the Stiefel Manifoldcited by 8
  6. 2021Distributed Principal Component Analysis with Limited Communicationcited by 6
  7. 2017Distributed Optimization on Riemannian Manifolds for multi-agent networkscited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 5; 2025: 4; 2026: 3.

13 papers.

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  1. 2024Federated Learning on Riemannian Manifolds with Differential Privacycited by 5
  2. 2024Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Datacited by 5
  3. 2024Riemannian coordinate descent algorithms on matrix manifoldscited by 4
  4. 2024Riemannian Federated Learning via Averaging Gradient Streamscited by 4
  5. 2026FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnetcited by 2
  6. 2024Streamlining in the Riemannian Realm: Efficient Riemannian Optimization with Loopless Variance Reductioncited by 1
  7. 2025Aggregation on Learnable Manifolds for Asynchronous Federated Optimizationcited by 1
  8. 2025New Insights on Unfolding and Fine-tuning Quantum Federated Learningcited by 1
  9. 2025Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approachcited by 1
  10. 2023Federated Classification in Hyperbolic Spaces via Secure Aggregation of Convex Hullscited by 0
  11. 2025ONG: Orthogonal Natural Gradient Descentcited by 0
  12. 2026Sheaf-Based Federated Representation Learningcited by 0
1 more
  1. 2026A Stable Aggregation Method for Quantum Federated Learningcited by 0