Dual-Geometry Graph Network: Unifying Local and Global Priors for Few-Shot Learning

Abstract

In few-shot learning, utilizing local and global geometric priors to capture both subtle local class metrics and coarse global structures within the meta-task are important to obtain discriminative embeddings. However, existing graph-based and curvature-based few-shot approaches only focus on either one kind of geometric prior but neglect the other. To effectively utilize the pros of these two paradigms, we propose a novel Dual-Geometry Graph Network (DGGN) to adaptively integrate the local and global geometric priors via two key pathways. Specifically, the local-wise metric modeling pathway utilizes Ollivier-Ricci curvature to capture task-specific local class metrics among the instances, and the global-wise connectivity modeling pathway utilizes resistive embedding to capture global instance distributions and connectivity patterns of the entire meta-task. In addition, we introduce two new regularization loss functions to explicitly enhance the geometric representation ability of the local and global pathways respectively. We validate that DGGN