Equivariant Representation Learning via Class-Pose Decomposition

We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space in an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is self-supervised and infers these semantics based on relative symmetry information. The approach is motivated by theoretical results from group theory and guarantees representations that are lossless, interpretable and disentangled. We provide an empirical investigation via experiments involving datasets with a variety of symmetries. Results show that our representations capture the geometry of data and outperform other equivariant representation learning frameworks.

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.