Parameter-efficient fine-tuning approaches have recently garnered a lot of attention. Having considerably lower number of trainable weights, these methods can bring about scalability and computational effectiveness. In this paper, we look for optimal sub-networks and investigate the capability of different transformer modules in transferring knowledge from a pre-trained model to a downstream task. Our empirical results suggest that every transformer module in BERT can act as a winning ticket: fine-tuning each specific module while keeping the rest of the network frozen can lead to comparable performance to the full fine-tuning. Among different modules, LayerNorms exhibit the best capacity for knowledge transfer with limited trainable weights, to the extent that, with only 0.003% of all parameters in the layer-wise analysis, they show acceptable performance on various target tasks. On the reasons behind their effectiveness, we argue that their notable performance could be attributed to their high-magnitude weights compared to that of the other modules in the pre-trained BERT.
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