Transducer is one of the mainstream frameworks for streaming speech recognition. There is a performance gap between the streaming and non-streaming transducer models due to limited context. To reduce this gap, an effective way is to ensure that their hidden and output distributions are consistent, which can be achieved by hierarchical knowledge distillation. However, it is difficult to ensure the distribution consistency simultaneously because the learning of the output distribution depends on the hidden one. In this paper, we propose an adaptive two-stage knowledge distillation method consisting of hidden layer learning and output layer learning. In the former stage, we learn hidden representation with full context by applying mean square error loss function. In the latter stage, we design a power transformation based adaptive smoothness method to learn stable output distribution. It achieved 19\% relative reduction in word error rate, and a faster response for the first token compared with the original streaming model in LibriSpeech corpus.
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