# Meta-Curvature

## TL;DR

Meta-Curvature (MC) is a novel framework that enhances model-agnostic meta-learning by learning to transform gradients through a curvature-aware approach, leading to improved generalization, faster convergence, and superior few-shot learning performance.

## Contribution

MC introduces a new way to learn curvature information by decomposing the curvature matrix into smaller tensors, improving meta-learning efficiency and effectiveness.

## Key findings

- Outperforms previous MAML variants and state-of-the-art methods.
- Achieves faster convergence in meta-training.
- Enhances generalization in few-shot learning tasks.

## Abstract

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.