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State-of-the-art performance on language understanding tasks is now achievedwith increasingly large networks; the current record holder has billions ofparameters. Given a language model pre-trained on massive unlabeled textcorpora, only very light supervised fine-tuning is needed to learn a task: thenumber of fine-tuning steps is typically five orders of magnitude lower thanthe total parameter count. Does this mean that fine-tuning only introducessmall differences from the pre-trained model in the parameter space? If so, canone avoid storing and computing an entire model for each task? In this work, weaddress these questions by using Bidirectional Encoder Representations fromTransformers (BERT) as an example. As expected, we find that the fine-tunedmodels are close in parameter space to the pre-trained one, with the closenessvarying from layer to layer. We show that it suffices to fine-tune only themost critical layers. Further, we find that there are surprisingly many goodsolutions in the set of sparsified versions of the pre-trained model. As aresult, fine-tuning of huge language models can be achieved by simply setting acertain number of entries in certain layers of the pre-trained parameters tozero, saving both task-specific parameter storage and computational cost.

How fine can fine-tuning be? Learning efficient language models