Title: Probabilistic Federated Neural Matching. Abstract: In federated learning problems, data is scattered across different servers and exchanging or pooling it is often impractical or prohibited. We develop a Bayesian nonparametric framework for federated learning with neural networks. Each data server is assumed to train local neural network weights, which are modeled through our framework. We then develop an inference approach that allows us to synthesize a more expressive global network without additional supervision or data pooling. We then demonstrate the efficacy of our approach on federated learning problems simulated from two popular image classification datasets.