Abstract: Existing federated learning paradigms usually extensively exchange distributed models, rather than original data, 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 plenty of communication rounds in training. Unlike existing paradigms, we introduce an alternative perspective to significantly decrease the federate learning communication cost without leaking original data. In this work, we first present 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 the same training samples to a federated model should also vary. Thus, we introduce a dynamic weight assignment mechanism that enables informative 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 model on the combined meta knowledge that is regarded as a condense form of original data can significantly mitigate the heterogeneity issues. Moreover, to further ameliorate data heterogeneity, we also exchange meta knowledge among clients as conditional initialisation for 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 (\textit{i.e.}, 10 rounds).