On the Subspace Structure of Gradient-Based Meta-Learning

TL;DR

This paper analyzes the subspace structure of parameters in gradient-based meta-learning, revealing that adaptation occurs in low-dimensional subspaces and enabling estimation of task space dimensions.

Contribution

It introduces a general subspace perspective for GBML, extending previous findings to regression and providing a method to estimate task space intrinsic dimensions.

Findings

Parameters adapt within low-dimensional subspaces

The subspace structure applies to regression tasks

Method for estimating intrinsic task dimensions

Abstract

In this work we provide an analysis of the distribution of the post-adaptation parameters of Gradient-Based Meta-Learning (GBML) methods. Previous work has noticed how, for the case of image-classification, this adaptation only takes place on the last layers of the network. We propose the more general notion that parameters are updated over a low-dimensional \emph{subspace} of the same dimensionality as the task-space and show that this holds for regression as well. Furthermore, the induced subspace structure provides a method to estimate the intrinsic dimension of the space of tasks of common few-shot learning datasets.