Federated Martingale Posterior Samping

Federated Bayesian neural networks require fixing a prior on the model parameters together with a likelihood. Eliciting meaningful priors on the weight space of modern overparameterized models is notoriously difficult, and misspecification of either component can severely degrade accuracy and calibration. Motivated by the rapid progress of predictive models such as large language models, the martingale posterior, also known as predictive Bayes, replaces the prior--likelihood pair with a predictive distribution and recovers parameter uncertainty by repeatedly drawing predictive samples and refitting the model. A direct federated implementation, however, would require clients to share the local data sets. This letter proposes {federated martingale posterior} (FMP) sampling, a one-shot embarrassingly parallel protocol in which each client uploads a small set of trainable data embeddings and the server runs the predictive sampler centrally. Experiments on MNIST, CIFAR-10, and CIFAR-100 show that FMP closely matches the centralized counterpart and significantly improves calibration over consensus-style baselines.

Low-Rank Gradient Compression with Error Feedback for MIMO Wireless Federated Learning

This paper presents a novel approach to enhance the communication efficiency of federated learning (FL) in multiple input and multiple output (MIMO) wireless systems. The proposed method centers on a low-rank matrix factorization strategy for local gradient compression based on alternating least squares, along with over-the-air computation and error feedback. The proposed protocol, termed over-the-air low-rank compression (Ota-LC), is demonstrated to have lower computation cost and lower communication overhead as compared to existing benchmarks while guaranteeing the same inference performance. As an example, when targeting a test accuracy of 80% on the Cifar-10 dataset, Ota-LC achieves a reduction in total communication costs of at least 30% when contrasted with benchmark schemes, while also reducing the computational complexity order by a factor equal to the sum of the dimension of the gradients.