Modern speech recognition systems exhibits rapid performance degradation under domain shift. This issue is especially prevalent in data-scarce settings, such as low-resource languages, where diversity of training data is limited. In this work we propose M2DS2, a simple and sample-efficient finetuning strategy for large pretrained speech models, based on mixed source and target domain self-supervision. We find that including source domain self-supervision stabilizes training and avoids mode collapse of the latent representations. For evaluation, we collect HParl, a $120$ hour speech corpus for Greek, consisting of plenary sessions in the Greek Parliament. We merge HParl with two popular Greek corpora to create GREC-MD, a test-bed for multi-domain evaluation of Greek ASR systems. In our experiments we find that, while other Unsupervised Domain Adaptation baselines fail in this resource-constrained environment, M2DS2 yields significant improvements for cross-domain adaptation, even when a only a few hours of in-domain audio are available. When we relax the problem in a weakly supervised setting, we find that independent adaptation for audio using M2DS2 and language using simple LM augmentation techniques is particularly effective, yielding word error rates comparable to the fully supervised baselines.
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