  In federated learning, models trained on local clients are distilled into a
global model. Due to the permutation invariance arises in neural networks, it
is necessary to match the hidden neurons first when executing federated
learning with neural networks. Through the Bayesian nonparametric framework,
Probabilistic Federated Neural Matching (PFNM) matches and fuses local neural
networks so as to adapt to varying global model size and the heterogeneity of
the data. In this paper, we propose a new method which extends the PFNM with a
Kullback-Leibler (KL) divergence over neural components product, in order to
make inference exploiting posterior information in both local and global
levels. We also show theoretically that The additional part can be seamlessly
concatenated into the match-and-fuse progress. Through a series of simulations,
it indicates that our new method outperforms popular state-of-the-art federated
learning methods in both single communication round and additional
communication rounds situation.
