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Recent studies show that integrating syntactic tree models with sequential semantic models can bring improved task performance, while these methods mostly employ shallow integration of syntax and semantics. In this paper, we propose a deep neural communication model between syntax and semantics to improve the performance of text understanding. Local communication is performed between syntactic tree encoder and sequential semantic encoder for mutual learning of information exchange. Global communication can further ensure comprehensive information propagation. Results on multiple syntax-dependent tasks show that our model outperforms strong baselines by a large margin. In-depth analysis indicates that our method is highly effective in composing sentence semantics.