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Homomorphism AutoEncoder — Learning Group Structured Representations from Observed Transitions


Keurti, Hamza; Pan, Hsiao-Ru; Besserve, Michel; Grewe, Benjamin; Schölkopf, Bernhard (2023). Homomorphism AutoEncoder — Learning Group Structured Representations from Observed Transitions. In: 40th International Conference on Machine Learning, Honolulu, Hawaii, USA, 23 July 2023 - 29 July 2023. MLResearch Press, 16190-16215.

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.

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.

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Additional indexing

Item Type:Conference or Workshop Item (Paper), not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Scopus Subject Areas:Physical Sciences > Artificial Intelligence
Physical Sciences > Software
Physical Sciences > Control and Systems Engineering
Physical Sciences > Statistics and Probability
Language:English
Event End Date:29 July 2023
Deposited On:30 Jan 2024 16:08
Last Modified:01 Feb 2024 11:40
Publisher:MLResearch Press
Series Name:Proceedings of Machine Learning Research (PMLR)
ISSN:2640-3498
OA Status:Green
Official URL:https://proceedings.mlr.press/v202/keurti23a.html
  • Content: Published Version
  • Language: English