  Few-shot learning (FSL) aims to recognize novel queries with only a few
support samples through leveraging prior knowledge from a base dataset. In this
paper, we consider the domain shift problem in FSL and aim to address the
domain gap between the support set and the query set. Different from previous
cross-domain FSL work (CD-FSL) that considers the domain shift between base and
novel classes, the new problem, termed cross-domain cross-set FSL (CDSC-FSL),
requires few-shot learners not only to adapt to the new domain, but also to be
consistent between different domains within each novel class. To this end, we
propose a novel approach, namely stabPA, to learn prototypical compact and
cross-domain aligned representations, so that the domain shift and few-shot
learning can be addressed simultaneously. We evaluate our approach on two new
CDCS-FSL benchmarks built from the DomainNet and Office-Home datasets
respectively. Remarkably, our approach outperforms multiple elaborated
baselines by a large margin, e.g., improving 5-shot accuracy by 6.0 points on
average on DomainNet. Code is available at
https://github.com/WentaoChen0813/CDCS-FSL
