Transformer-based models have demonstrated their effectiveness in automatic speech recognition (ASR) tasks and even shown superior performance over the conventional hybrid framework. The main idea of Transformers is to capture the long-range global context within an utterance by self-attention layers. However, for scenarios like conversational speech, such utterance-level modeling will neglect contextual dependencies that span across utterances. In this paper, we propose to explicitly model the inter-sentential information in a Transformer based end-to-end architecture for conversational speech recognition. Specifically, for the encoder network, we capture the contexts of previous speech and incorporate such historic information into current input by a context-aware residual attention mechanism. For the decoder, the prediction of current utterance is also conditioned on the historic linguistic information through a conditional decoder framework. We show the effectiveness of our proposed method on several open-source dialogue corpora and the proposed method consistently improved the performance from the utterance-level Transformer-based ASR models.
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