Generating semantically coherent responses is still a major challenge in dialogue generation. Different from conventional text generation tasks, the mapping between inputs and responses in conversations is more complicated, which highly demands the understanding of utterance-level semantic dependency, a relation between the whole meanings of inputs and outputs. To address this problem, we propose an Auto-Encoder Matching (AEM) model to learn such dependency. The model contains two auto-encoders and one mapping module. The auto-encoders learn the semantic representations of inputs and responses, and the mapping module learns to connect the utterance-level representations. Experimental results from automatic and human evaluations demonstrate that our model is capable of generating responses of high coherence and fluency compared to baseline models. The code is available at https://github.com/lancopku/AMM
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