# Information-Geometric Barycenters for Bayesian Federated Learning

arXiv: https://arxiv.org/abs/2412.11646 · HTML: https://mlsanity.com/paper/2412.11646/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 47 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 30 of 34)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning on Non-IID Data Silos: An Experimental Study](https://mlsanity.com/paper/2102.02079/) (2021)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Bayesian Nonparametric Federated Learning of Neural Networks](https://mlsanity.com/paper/1905.12022/) (2019)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Personalized Federated Learning: A Meta-Learning Approach](https://mlsanity.com/paper/2002.07948/) (2020)
- [FedBE: Making Bayesian Model Ensemble Applicable to Federated Learning](https://mlsanity.com/paper/2009.01974/) (2020)
- [Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms](https://mlsanity.com/paper/2010.05273/) (2020)
- [Practical One-Shot Federated Learning for Cross-Silo Setting](https://mlsanity.com/paper/2010.01017/) (2020)
- [Personalized Federated Learning via Variational Bayesian Inference](https://mlsanity.com/paper/2206.07977/) (2022)
- [Variational Learning is Effective for Large Deep Networks](https://mlsanity.com/paper/2402.17641/) (2024)
- [Revisiting Weighted Aggregation in Federated Learning with Neural Networks](https://mlsanity.com/paper/2302.10911/) (2023)
- [A Bayesian Federated Learning Framework with Online Laplace Approximation](https://mlsanity.com/paper/2102.01936/) (2021)
- [FedPop: A Bayesian Approach for Personalised Federated Learning](https://mlsanity.com/paper/2206.03611/) (2022)
- [Fusion of Probability Density Functions](https://mlsanity.com/paper/2202.11633/) (2022)
- [Bayesian Federated Learning: A Survey](https://mlsanity.com/paper/2304.13267/) (2023)
- [GIFAIR-FL: A Framework for Group and Individual Fairness in Federated Learning](https://mlsanity.com/paper/2108.02741/) (2021)
- [Proportional Fairness in Federated Learning](https://mlsanity.com/paper/2202.01666/) (2022)
- [Federated Learning as Variational Inference: A Scalable Expectation Propagation Approach](https://mlsanity.com/paper/2302.04228/) (2023)
- [Confidence-aware Personalized Federated Learning via Variational Expectation Maximization](https://mlsanity.com/paper/2305.12557/) (2023)
- [The Relevance of Bayesian Layer Positioning to Model Uncertainty in Deep Bayesian Active Learning](https://mlsanity.com/paper/1811.12535/) (2018)
- [Bayesian Learning with Wasserstein Barycenters](https://mlsanity.com/paper/1805.10833/) (2018)
- [Federated Learning with Uncertainty via Distilled Predictive Distributions](https://mlsanity.com/paper/2206.07562/) (2022)

## Built on by (most cited first, 1 of 1)

- [Cost-Free Personalization via Information-Geometric Projection in Bayesian Federated Learning](https://mlsanity.com/paper/2509.10132/) (2025)

## Abstract (arXiv)

Federated learning (FL) is a widely used and impactful distributed optimization framework that achieves consensus through averaging locally trained models. While effective, this approach may not align well with Bayesian inference, where the model space has the structure of a distribution space. Taking an information-geometric perspective, we reinterpret FL aggregation as the problem of finding the barycenter of local posteriors using a prespecified divergence metric, minimizing the average discrepancy across clients. This perspective provides a unifying framework that generalizes many existing methods and offers crisp insights into their theoretical underpinnings. We then propose BA-BFL, an algorithm that retains the convergence properties of Federated Averaging in non-convex settings. In non-independent and identically distributed scenarios, we conduct extensive comparisons with statistical aggregation techniques, showing that BA-BFL achieves performance comparable to state-of-the-art methods while offering a geometric interpretation of the aggregation phase. Additionally, we extend our analysis to Hybrid Bayesian Deep Learning, exploring the impact of Bayesian layers on uncertainty quantification and model calibration.