  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.
