Recent work on speech self-supervised learning (speech SSL) demonstrated the benefits of scale in learning rich and transferable representations for Automatic Speech Recognition (ASR) with limited parallel data. It is then natural to investigate the existence of sparse and transferrable subnetworks in pre-trained speech SSL models that can achieve even better low-resource ASR performance. However, directly applying widely adopted pruning methods such as the Lottery Ticket Hypothesis (LTH) is suboptimal in the computational cost needed. Moreover, contrary to what LTH predicts, the discovered subnetworks yield minimal performance gain compared to the original dense network. In this work, we propose Prune-Adjust- Re-Prune (PARP), which discovers and finetunes subnetworks for much better ASR performance, while only requiring a single downstream finetuning run. PARP is inspired by our surprising observation that subnetworks pruned for pre-training tasks only needed to be slightly adjusted to achieve a sizeable performance boost in downstream ASR tasks. Extensive experiments on low-resource English and multi-lingual ASR show (1) sparse subnetworks exist in pre-trained speech SSL, and (2) the computational advantage and performance gain of PARP over baseline pruning methods. On the 10min Librispeech split without LM decoding, PARP discovers subnetworks from wav2vec 2.0 with an absolute 10.9%/12.6% WER decrease compared to the full model. We demonstrate PARP mitigates performance degradation in cross-lingual mask transfer, and investigate the possibility of discovering a single subnetwork for 10 spoken languages in one run.
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