Streaming automatic speech recognition (ASR) models are restricted from accessing future context, which results in worse performance compared to the non-streaming models. To improve the performance of streaming ASR, knowledge distillation (KD) from the non-streaming to streaming model has been studied, mainly focusing on aligning the output token probabilities. In this paper, we propose a layer-to-layer KD from the teacher encoder to the student encoder. To ensure that features are extracted using the same context, we insert auxiliary non-streaming branches to the student and perform KD from the non-streaming teacher layer to the non-streaming auxiliary layer. We design a special KD loss that leverages the autoregressive predictive coding (APC) mechanism to encourage the streaming model to predict unseen future contexts. Experimental results show that the proposed method can significantly reduce the word error rate compared to previous token probability distillation methods.

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