Bayesian Federated Learning (BFL) combines uncertainty modeling with decentralized training, enabling the development of personalized and reliable models in the presence of data heterogeneity and privacy constraints. Existing approaches typically rely on Markov Chain Monte Carlo (MCMC) sampling or variational inference, often incorporating personalization mechanisms to better adapt to the local data distributions. In this work, we propose an information-geometric projection framework for personalization in parametric BFL. By projecting the global model onto a neighborhood of the user’s local model, our method enables a tunable trade-off between global generalization and local specialization. Under mild assumptions, we show that this projection step is equivalent to computing a barycenter in the statistical manifold, allowing us to derive closed-form solutions and achieve costfree personalization. We apply the proposed approach within a variational learning setup using the Improved Variational Online Newton (IVON) optimizer and extend it to general aggregation schemes in BFL. Empirical evaluations under heterogeneous data distributions confirm that our method effectively balances global and local performance with minimal computational overhead. Code is available at https://github.com/NourJamoussi/ Information-Geometry-for-Bayesian-Federated-Learning.
