Most existing few-shot classification methods only consider generalization on one dataset (i.e., single-domain), failing to transfer across various seen and unseen domains. In this paper, we consider the more realistic multi-domain few-shot classification problem to investigate the crossdomain generalization. Two challenges exist in this new setting: (1) how to efficiently generate multi-domain feature representation, and (2) how to explore domain correlations for better cross-domain generalization. We propose a parameter-efficient multi-mode modulator to address both challenges. First, the modulator is designed to maintain multiple modulation parameters (one for each domain) in a single network, thus achieving single-network multi-domain representation. Given a particular domain, domain-aware features can be efficiently generated with the well-devised separative selection module and cooperative query module. Second, we further divide the modulation parameters into
the domain-specific set and the domain-cooperative set to explore the intra-domain information and inter-domain correlations, respectively. The intra-domain information describes each domain independently to prevent negative interference. The inter-domain correlations guide information sharing among relevant domains to enrich their own representation. Moreover, unseen domains can utilize the correlations to obtain an adaptive combination of seen domains for extrapolation. We demonstrate that the proposed multi-mode modulator achieves state-of-the-art results on the challenging META-DATASET benchmark, especially for unseen test domains.