Class-Adaptive Characteristic Function Matching for Cross-Domain Few-Shot Learning

Under domain shift, successful few-shot recognition requires not only transferable source-trained features but also a comparison rule appropriate for novel target classes. Most metric-based approaches to cross-domain few-shot learning (CD-FSL) construct class prototypes from target support examples, yet evaluate all queries using a shared Euclidean or cosine metric. Target supervision therefore adapts the class representatives but leaves the comparison function unchanged across classes. We address this asymmetry with Class-Adaptive Characteristic Function Matching, a plug-and-play metric module that uses target support examples to adapt both class representation and query-class comparison. Our key observation is that the frequency arguments of an empirical characteristic function can parameterize the comparison rule: each frequency induces a nonlinear response to a feature projection, while a finite set of frequencies forms a compact representation of the support class. For each candidate class, a lightweight KL-regularized stochastic generator conditions on its support set and produces a compact set of class-specific frequency arguments. Given a query, we tentatively include it in each candidate support set and measure the resulting change between the original and query-augmented empirical characteristic-function representations. This change serves as the membership score, allowing the same query to be evaluated through a distinct support-conditioned comparison for every novel target class. The proposed module can replace conventional point-based similarities without modifying the feature backbone or the target-domain adaptation procedure of the host method. Experiments across four CD-FSL benchmarks, three base learners, and multiple pretrained backbones demonstrate consistent improvements with only a small parameter overhead. Code and models will be publicly released.