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.

翻译：联邦贝叶斯神经网络需要为模型参数指定先验分布及似然函数。在现代过参数化模型的权重空间中设置具有意义的先验分布极为困难，而这两个组件中任一设定错误都会严重降低模型精度与校准性能。受大语言模型等预测模型快速发展的启发，鞅后验（亦称预测贝叶斯）方法用预测分布替代先验-似然对，通过重复抽取预测样本并重新拟合模型来恢复参数不确定性。然而，直接实现联邦化要求客户端共享本地数据集。本文提出联邦鞅后验抽样（FMP），这是一种单轮、极度并行的协议：各客户端仅上传少量可训练的数据嵌入，由服务器端运行预测采样器。在MNIST、CIFAR-10和CIFAR-100数据集上的实验表明，FMP与集中式方法性能接近，且在校准质量上显著优于基于共识的基线方法。