Equivariant Representations for Non-Free Group Actions

Luis Armando Pérez Rey, Giovanni Luca Marchetti, Danica Kragic, Dmitri Jarnikov, Mike Holenderski

Keywords: Representation learning, symmetries, group theory

TL;DR: In this work we propose a method for learning data representations that are equivariant with respect to arbitrary and potentially non-free group actions on the data.

Abstract: We introduce a method for learning representations that are equivariant with respect to general group actions over data. Differently from existing equivariant representation learners, our method is suitable for actions that are not free i.e., that stabilize data via nontrivial symmetries. Our method is grounded in the orbit-stabilizer theorem from group theory, which guarantees that an ideal learner infers an isomorphic representation. Finally, we provide an empirical investigation on image datasets with rotational symmetries and show that taking stabilizers into account improves the quality of the representations.