  Existing federated learning paradigms usually extensively exchange
distributed models at a central solver to achieve a more powerful model.
However, this would incur severe communication burden between a server and
multiple clients especially when data distributions are heterogeneous. As a
result, current federated learning methods often require a large number of
communication rounds in training. Unlike existing paradigms, we introduce an
alternative perspective to significantly decrease the communication cost in
federate learning. In this work, we first introduce a meta knowledge
representation method that extracts meta knowledge from distributed clients.
The extracted meta knowledge encodes essential information that can be used to
improve the current model. As the training progresses, the contributions of
training samples to a federated model also vary. Thus, we introduce a dynamic
weight assignment mechanism that enables samples to contribute adaptively to
the current model update. Then, informative meta knowledge from all active
clients is sent to the server for model update. Training a model on the
combined meta knowledge without exposing original data among different clients
can significantly mitigate the heterogeneity issues. Moreover, to further
ameliorate data heterogeneity, we also exchange meta knowledge among clients as
conditional initialization for local meta knowledge extraction. Extensive
experiments demonstrate the effectiveness and efficiency of our proposed
method. Remarkably, our method outperforms the state-of-the-art by a large
margin (from $74.07\%$ to $92.95\%$) on MNIST with a restricted communication
budget (i.e. 10 rounds).
