Equivariant Representation Learning in the Presence of Stabilizers
This addresses a limitation in equivariant representation learning for non-free group actions, which is important for machine learning applications involving data with inherent symmetries.
The paper tackles the problem of learning equivariant representations for group actions with nontrivial symmetries (stabilizers), introducing Equivariant Isomorphic Networks (EquIN) which theoretically guarantees isomorphic representations through the orbit-stabilizer theorem. Empirical results on image datasets with rotational symmetries show improved representation quality.
We introduce Equivariant Isomorphic Networks (EquIN) -- a method for learning representations that are equivariant with respect to general group actions over data. Differently from existing equivariant representation learners, EquIN is suitable for group actions that are not free, i.e., that stabilize data via nontrivial symmetries. EquIN is theoretically grounded in the orbit-stabilizer theorem from group theory. This guarantees that an ideal learner infers isomorphic representations while trained on equivariance alone and thus fully extracts the geometric structure of data. We provide an empirical investigation on image datasets with rotational symmetries and show that taking stabilizers into account improves the quality of the representations.