Title: Towards Representative Subset Selection for Self-Supervised Speech Recognition. Abstract: Self-supervised speech recognition models require considerable labeled training data for learning high-fidelity representations for Automatic Speech Recognition (ASR) which is computationally demanding and time-consuming, thereby hindering the usage of these models in resource-constrained environments. We consider the task of identifying an optimal subset of data to train self-supervised speech models for ASR. We make a surprising observation that the dataset pruning strategies used in vision tasks for sampling the most informative examples do not perform better than random subset selection on the task of fine-tuning self-supervised ASR. We then present the COWERAGE algorithm for better subset selection in self-supervised ASR, which is based on our finding that ensuring the coverage of examples based on training Word Error Rate (WER) in the early training epochs leads to better generalization performance. Extensive experiments on the wav2vec 2.0 model and TIMIT, Librispeech, and LJSpeech datasets show the effectiveness of COWERAGE, with up to 17% absolute WER improvement over existing dataset pruning methods and random sampling. We also demonstrate that the coverage of training instances in terms of WER ensures inclusion of phonemically diverse examples which leads to better test accuracy in self-supervised speech recognition models.