mlsanityData to 7 Oct 2026

Federated Learning on Riemannian Manifolds with Differential Privacy

arXiv 2404.10029 ↗First posted 15 Apr 2024math.OC cs.CR cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

In recent years, federated learning (FL) has emerged as a prominent paradigm in distributed machine learning. Despite the partial safeguarding of agents' information within FL systems, a malicious adversary can potentially infer sensitive information through various means. In this paper, we propose a generic private FL framework defined on Riemannian manifolds (PriRFed) based on the differential privacy (DP) technique. We analyze the privacy guarantee while establishing the convergence properties. To the best of our knowledge, this is the first federated learning framework on Riemannian manifold with a privacy guarantee and convergence results. Numerical simulations are performed on synthetic and real-world datasets to showcase the efficacy of the proposed PriRFed approach.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 32 of its 62 references that are in the map. First posted on arXiv 15 Apr 2024.

Builds on

32 of 62 references.

References · 32

  1. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,592
  2. 2018Federated Optimization in Heterogeneous Networkscited by 2,971
  3. 2016Federated Learning: Strategies for Improving Communication Efficiencycited by 1,461
  4. 2019On the Convergence of FedAvg on Non-IID Datacited by 1,220
  5. 2021MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classificationcited by 682
  6. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  7. 2016Federated Optimization: Distributed Machine Learning for On-Device Intelligencecited by 558
  8. 2017Differentially Private Federated Learning: A Client Level Perspectivecited by 451
  9. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  10. 2018Beyond Inferring Class Representatives: User-Level Privacy Leakage From Federated Learningcited by 242
  11. 2018Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergencescited by 237
  12. 2019Hyperbolic Image Embeddingscited by 219
20 more
  1. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 155
  2. 2018Differentially Private Empirical Risk Minimization Revisited: Faster and More Generalcited by 127
  3. 2021Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradientscited by 122
  4. 2013Manopt, a Matlab toolbox for optimization on manifoldscited by 112
  5. 2016First-order Methods for Geodesically Convex Optimizationcited by 92
  6. 2016Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifoldscited by 64
  7. 2017Riemannian approach to batch normalizationcited by 35
  8. 2019A Continuous-time Perspective for Modeling Acceleration in Riemannian Optimizationcited by 25
  9. 2022Fully Adaptive Composition in Differential Privacycited by 22
  10. 2014Characterizing the Sample Complexity of Private Learnerscited by 19
  11. 2015Fast and Simple PCA via Convex Optimizationcited by 16
  12. 2021Differential Privacy Over Riemannian Manifoldscited by 16
  13. 2022Federated Learning on Riemannian Manifoldscited by 13
  14. 2019Benefits and Pitfalls of the Exponential Mechanism with Applications to Hilbert Spaces and Functional PCAcited by 10
  15. 2022Differentially Private Fr'echet Mean on the Manifold of Symmetric Positive Definite (SPD) Matrices with log-Euclidean Metriccited by 8
  16. 2014Lognormal Distributions and Geometric Averages of Positive Definite Matricescited by 7
  17. 2022Shape And Structure Preserving Differential Privacycited by 6
  18. 2023Gaussian Differential Privacy on Riemannian Manifoldscited by 6
  19. 2015Robust Shift-and-Invert Preconditioning: Faster and More Sample Efficient Algorithms for Eigenvector Computationcited by 5
  20. 2020Hyperbolic Manifold Regressioncited by 5

Built on by

Cited by year (2026 to 7 Oct)

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

5 papers.

  1. 2024Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Datacited by 5
  2. 2024Riemannian coordinate descent algorithms on matrix manifoldscited by 4
  3. 2024Riemannian Federated Learning via Averaging Gradient Streamscited by 4
  4. 2026FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnetcited by 2
  5. 2025Federated Learning on Riemannian Manifolds: A Gradient-Free Projection-Based Approachcited by 1