On the Subspace Structure of Gradient-Based Meta-Learning

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 adaption 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.