Adapting pre-trained neural models to downstream tasks has become the standard practice for obtaining high-quality models. In this work, we propose a novel model adaptation paradigm, adapting by pruning, which prunes neural connections in the pre-trained model to optimise the performance on the target task; all remaining connections have their weights intact. We formulate adapting-by-pruning as an optimisation problem with a differentiable loss and propose an efficient algorithm to prune the model. We prove that the algorithm is near-optimal under standard assumptions and apply the algorithm to adapt BERT to some GLUE tasks. Results suggest that our method can prune up to 50% weights in BERT while yielding similar performance compared to the fine-tuned full model. We also compare our method with other state-of-the-art pruning methods and study the topological differences of their obtained sub-networks.
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