Federated learning enables collaborative model training without sharing raw data, but the transmitted updates can still reveal information about individual records. Ensuring differential privacy is particularly challenging when model parameters lie on a Riemannian manifold, as existing methods often rely on geometry-dependent noise calibration and computationally demanding intrinsic operations.
In this talk, I will present DP-RFedProj, a record-level differentially private federated learning framework for compact submanifolds. The method combines projection-based aggregation with gradient perturbation in a fixed ambient space, yielding a closed-form privacy guarantee that is independent of the manifold geometry, aggregation rule, and local optimizer. We establish convergence guarantees for Riemannian SGD and show that the leading privacy term depends on the intrinsic dimension of the manifold. Experiments on EEG motor-imagery classification with SPDNet demonstrate strong utility–privacy trade-offs, outperforming a Euclidean baseline across privacy budgets while requiring substantially less noise than previous manifold-aware approaches.