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Homomorphism AutoEncoder --- Learning Group Structured Representations from Observed Transitions
Hamza Keurti · Hsiao-Ru Pan · Michel Besserve · Benjamin F. Grewe · Bernhard Schölkopf

Tue Jul 25 02:00 PM -- 04:30 PM (PDT) @ Exhibit Hall 1 #614

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.

Author Information

Hamza Keurti (MPI-IS)
Hsiao-Ru Pan (Max Planck Institute for Intelligent Systems)
Michel Besserve (MPI for Biological Cybernetics; MPI for Intelligent Sytems)
Benjamin F. Grewe (ETH Zurich)
Bernhard Schölkopf (MPI for Intelligent Systems Tübingen, Germany)

Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.

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