The huge size of the widely used BERT family models has led to recent efforts about model distillation. The main goal of distillation is to create a task-agnostic pre-trained model that can be fine-tuned on downstream tasks without fine-tuning its full-sized version. Despite the progress of distillation, to what degree and for what reason a task-agnostic model can be created from distillation has not been well studied. Also, the mechanisms behind transfer learning of those BERT models are not well investigated either. Therefore, this work focuses on analyzing the acceptable deduction when distillation for guiding the future distillation procedure. Specifically, we first inspect the prunability of the Transformer heads in RoBERTa and ALBERT using their head importance estimation proposed by Michel et al. (2019), and then check the coherence of the important heads between the pre-trained task and downstream tasks. Hence, the acceptable deduction of performance on the pre-trained task when distilling a model can be derived from the results, and we further compare the behavior of the pruned model before and after fine-tuning. Our studies provide guidance for future directions about BERT family model distillation.
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