Curvature generation in curved spaces for few-shot learning

Few-shot learning describes the challenging problem of recognizing samples from unseen classes given very few labeled examples. In many cases, few-shot learning is cast as learning an embedding space that assigns test samples to their corresponding class prototypes. Previous methods assume that data of all few-shot learning tasks comply with a fixed geometrical structure, mostly a Euclidean structure. Questioning this assumption that is clearly difficult to hold in real-world scenarios and incurs distortions to data, we propose to learn a task-aware curved embedding space by making use of the hyperbolic geometry. As a result, task-specific embedding spaces where suitable curvatures are generated to match the characteristics of data are constructed, leading to more generic embedding spaces. We then leverage on intra-class and inter-class context information in the embedding space to generate class prototypes for discriminative classification. We conduct a comprehensive set of experiments on inductive and transductive few-shot learning, demonstrating the benefits of our proposed method over existing embedding methods.