Unsupervised Domain Adaptation (UDA) transfers predictive models from a fully-labeled source domain to an unlabeled target domain. In some applications, however, it is expensive even to collect labels in the source domain, making most previous works impractical. To cope with this problem, recent work performed instance-wise cross-domain self-supervised learning, followed by an additional fine-tuning stage. However, the instance-wise self-supervised learning only learns and aligns low-level discriminative features. In this paper, we propose an end-to-end Prototypical Cross-domain Self-Supervised Learning (PCS) framework for Few-shot Unsupervised Domain Adaptation (FUDA). PCS not only performs cross-domain low-level feature alignment, but it also encodes and aligns semantic structures in the shared embedding space across domains. Our framework captures category-wise semantic structures of the data by in-domain prototypical contrastive learning; and performs feature alignment through cross-domain prototypical self-supervision. Compared with state-of-the-art methods, PCS improves the mean classification accuracy over different domain pairs on FUDA by 10.5%, 3.5%, 9.0%, and 13.2% on Office, Office-Home, VisDA-2017, and DomainNet, respectively. Our project page is at http://xyue.io/pcs-fuda/index.html
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