  We propose meta-curvature (MC), a framework to learn curvature information
for better generalization and fast model adaptation. MC expands on the
model-agnostic meta-learner (MAML) by learning to transform the gradients in
the inner optimization such that the transformed gradients achieve better
generalization performance to a new task. For training large scale neural
networks, we decompose the curvature matrix into smaller matrices in a novel
scheme where we capture the dependencies of the model's parameters with a
series of tensor products. We demonstrate the effects of our proposed method on
several few-shot learning tasks and datasets. Without any task specific
techniques and architectures, the proposed method achieves substantial
improvement upon previous MAML variants and outperforms the recent
state-of-the-art methods. Furthermore, we observe faster convergence rates of
the meta-training process. Finally, we present an analysis that explains better
generalization performance with the meta-trained curvature.
