Equivariant Representation Learning in the Presence of Stabilizers

• URL: http://arxiv.org/abs/2301.05231v2
• Date: Sat, 16 Sep 2023 20:56:32 GMT
• Title: Equivariant Representation Learning in the Presence of Stabilizers
• Authors: Luis Armando P\'erez Rey, Giovanni Luca Marchetti, Danica Kragic, Dmitri Jarnikov, Mike Holenderski
• Abstract summary: 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.
• Score: 13.11108596589607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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