Equivariant Representation Learning via Class-Pose Decomposition

Giovanni Luca Marchetti, Gustaf Tegnér, Anastasiia Varava, Danica Kragic
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:4745-4756, 2023.

Abstract

We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-marchetti23b, title = {Equivariant Representation Learning via Class-Pose Decomposition}, author = {Marchetti, Giovanni Luca and Tegn\'er, Gustaf and Varava, Anastasiia and Kragic, Danica}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {4745--4756}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/marchetti23b/marchetti23b.pdf}, url = {https://proceedings.mlr.press/v206/marchetti23b.html}, abstract = {We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from 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.} }
Endnote
%0 Conference Paper %T Equivariant Representation Learning via Class-Pose Decomposition %A Giovanni Luca Marchetti %A Gustaf Tegnér %A Anastasiia Varava %A Danica Kragic %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-marchetti23b %I PMLR %P 4745--4756 %U https://proceedings.mlr.press/v206/marchetti23b.html %V 206 %X We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from 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.
APA
Marchetti, G.L., Tegnér, G., Varava, A. & Kragic, D.. (2023). Equivariant Representation Learning via Class-Pose Decomposition. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:4745-4756 Available from https://proceedings.mlr.press/v206/marchetti23b.html.

Related Material