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.
L. A. Pérez Rey and G. L. Marchetti—Equal Contribution.
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Acknowledgements
This work was supported by the Swedish Research Council, the Knut and Alice Wallenberg Foundation and the European Research Council (ERC-BIRD-884807). This work has also received funding from the NWO-TTW Programme “Efficient Deep Learning” (EDL) P16-25.
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Ethical Statement
The work presented in this paper consists of a theoretical and practical analysis on learning representations that capture the information about symmetry transformations observed in data. Due to the nature of this work as fundamental research, it is challenging to determine any direct adverse ethical implications that might arise. However, we think that any possible ethical implications of these ideas would be a consequence of the possible applications to augmented reality, object recognition, or reinforcement learning among others. The datasets used in this work consist of procedurally generated images with no personal or sensitive information.
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Pérez Rey, L.A., Marchetti, G.L., Kragic, D., Jarnikov, D., Holenderski, M. (2023). Equivariant Representation Learning in the Presence of Stabilizers. In: Koutra, D., Plant, C., Gomez Rodriguez, M., Baralis, E., Bonchi, F. (eds) Machine Learning and Knowledge Discovery in Databases: Research Track. ECML PKDD 2023. Lecture Notes in Computer Science(), vol 14172. Springer, Cham. https://doi.org/10.1007/978-3-031-43421-1_41
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