Homomorphism AutoEncoder -- Learning Group Structured Representations from Observed Transitions

Hamza Keurti, Hsiao-Ru Pan, Michel Besserve, Benjamin F Grewe, Bernhard Schölkopf
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:16190-16215, 2023.

Abstract

How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional knowledge, we study this problem using tools from representation learning and group theory. We propose methods enabling an agent acting upon the world to learn internal representations of sensory information that are consistent with actions that modify it. We use an autoencoder equipped with a group representation acting on its latent space, trained using an equivariance-derived loss in order to enforce a suitable homomorphism property on the group representation. In contrast to existing work, our approach does not require prior knowledge of the group and does not restrict the set of actions the agent can perform. We motivate our method theoretically, and show empirically that it can learn a group representation of the actions, thereby capturing the structure of the set of transformations applied to the environment. We further show that this allows agents to predict the effect of sequences of future actions with improved accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-keurti23a, title = {Homomorphism {A}uto{E}ncoder -- Learning Group Structured Representations from Observed Transitions}, author = {Keurti, Hamza and Pan, Hsiao-Ru and Besserve, Michel and Grewe, Benjamin F and Sch\"{o}lkopf, Bernhard}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {16190--16215}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/keurti23a/keurti23a.pdf}, url = {https://proceedings.mlr.press/v202/keurti23a.html}, abstract = {How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional knowledge, we study this problem using tools from representation learning and group theory. We propose methods enabling an agent acting upon the world to learn internal representations of sensory information that are consistent with actions that modify it. We use an autoencoder equipped with a group representation acting on its latent space, trained using an equivariance-derived loss in order to enforce a suitable homomorphism property on the group representation. In contrast to existing work, our approach does not require prior knowledge of the group and does not restrict the set of actions the agent can perform. We motivate our method theoretically, and show empirically that it can learn a group representation of the actions, thereby capturing the structure of the set of transformations applied to the environment. We further show that this allows agents to predict the effect of sequences of future actions with improved accuracy.} }
Endnote
%0 Conference Paper %T Homomorphism AutoEncoder -- Learning Group Structured Representations from Observed Transitions %A Hamza Keurti %A Hsiao-Ru Pan %A Michel Besserve %A Benjamin F Grewe %A Bernhard Schölkopf %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-keurti23a %I PMLR %P 16190--16215 %U https://proceedings.mlr.press/v202/keurti23a.html %V 202 %X How can agents learn internal models that veridically represent interactions with the real world is a largely open question. As machine learning is moving towards representations containing not just observational but also interventional knowledge, we study this problem using tools from representation learning and group theory. We propose methods enabling an agent acting upon the world to learn internal representations of sensory information that are consistent with actions that modify it. We use an autoencoder equipped with a group representation acting on its latent space, trained using an equivariance-derived loss in order to enforce a suitable homomorphism property on the group representation. In contrast to existing work, our approach does not require prior knowledge of the group and does not restrict the set of actions the agent can perform. We motivate our method theoretically, and show empirically that it can learn a group representation of the actions, thereby capturing the structure of the set of transformations applied to the environment. We further show that this allows agents to predict the effect of sequences of future actions with improved accuracy.
APA
Keurti, H., Pan, H., Besserve, M., Grewe, B.F. & Schölkopf, B.. (2023). Homomorphism AutoEncoder -- Learning Group Structured Representations from Observed Transitions. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:16190-16215 Available from https://proceedings.mlr.press/v202/keurti23a.html.

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