Title: GAML: geometry-aware meta-learning via a fully adaptive preconditioner. Abstract: Model-Agnostic Meta-Learning (MAML) is one of the most successful meta-learning algorithms. It has a bi-level optimization structure, where the outer-loop process learns the shared initialization and the inner-loop process optimizes the task-specific weights. Although MAML relies on the standard gradient descent in the inner-loop, recent works have shown that it can be beneficial to control the inner loop's gradient descent with a meta-learned preconditioner. The existing preconditioners, however, cannot adapt in a task-specific and path-dependent way at the same time. Also, most of them do not consider the geometry of the loss surface. In this work, we propose Geometry-Aware Meta-Learning (GAML) that can overcome the limitations. GAML can efficiently meta-learn a preconditioner that is dependent on the task-specific parameters and its preconditioner can be shown to be a Riemannian metric that defines the geometry of the loss surface. Therefore, we can perform a fully-adaptive and geometry-aware optimization in the inner-loop. Experiment results show that GAML outperforms the state-of-the-art MAML family and PGD-MAML family for a variety of few-shot learning tasks.