Title: Cross-Domain Cross-Set Few-Shot Learning via Learning Compact and Aligned Representations. Abstract: Few-shot learning (FSL) aims to recognize novel query examples with a small support set through leveraging prior knowledge learned from a large-scale training set. In this paper, we extend this task to a more practical setting where the domain shift exists between the support set and query examples and additional unlabeled data in the target domain can be adopted in the meta-training stage. Such new setting, termed cross-domain cross-set FSL (CDSC-FSL), requires the learning system not only to adapt to new classes with few examples but also to be consistent between different domains. To address this paradigm, we propose a novel approach, namely \textit{stab}PA, to learn prototypical compact and cross-domain aligned representations, so that domain shift and few-shot adaptation can be addressed simultaneously. We evaluate our approach on two new CDCS-FSL benchmarks adapted from the DomainNet and Office-Home datasets, respectively. Remarkably, our approach outperforms multiple elaborated baselines by a large margin and improves 5-shot accuracy by up to 4.7 points.