Geometry-adaptive Meta-learning in Riemannian Manifolds
Zhi Feng Gao · 2024
Meta-learning aims to empower machines to quickly adapt to new tasks by learning prior knowledge from seen tasks [5]. In the adaptation process, the matching degree between the geometry of space and the geometric structure of data plays an important role. Real-world data exhibits various forms of non-Euclidean geometric structures [1, 2], such as hierarchical structures in natural language and cyclical structures in facial images, as shown in Figure 1. Previous research has shown that the non-Euclidean structure of real-world data is consistent with Riemannian manifold structures [6], providing theoretical feasibility for modeling data using Riemannian manifolds [3, 4]. This paper studies geometry-adaptive meta-learning methods in Riemannian manifolds, as shown in Figure 2. It explores how to quickly adapt the geometry of data space in Riemannian backbones and Riemannian classifiers to the non-Euclidean structure of data. In addition, the paper generates a large amount of training data and learns efficient Riemannian optimizers in the adaptation process, achieving better generalization for new tasks.