Despite the recent works on knowledge distillation (KD) have achieved a further improvement through elaborately modeling the decision boundary as the posterior knowledge, their performance is still dependent on the hypothesis that the target network has a powerful capacity (representation ability). In this paper, we propose a knowledge representing (KR) framework mainly focusing on modeling the parameters distribution as prior knowledge. Firstly, we suggest a knowledge aggregation scheme in order to answer how to represent the prior knowledge from teacher network. Through aggregating the parameters distribution from teacher network into more abstract level, the scheme is able to alleviate the phenomenon of residual accumulation in the deeper layers. Secondly, as the critical issue of what the most important prior knowledge is for better distilling, we design a sparse recoding penalty for constraining the student network to learn with the penalized gradients. With the proposed penalty, the student network can effectively avoid the over-regularization during knowledge distilling and converge faster. The quantitative experiments exhibit that the proposed framework achieves the state-ofthe-arts performance, even though the target network does not have the expected capacity. Moreover, the framework is flexible enough for combining with other KD methods based on the posterior knowledge.
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