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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

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in Symmetry and Geometry in Neural Representations (NeurReps) »
Event URL: https://openreview.net/forum?id=Z1mlSfNrbnj »

It is crucial for agents, both biological and artificial, to acquire world models that veridically represent the external world and how it is modified by the agent's own actions. We consider the case where such modifications can be modelled as transformations from a group of symmetries structuring the world state space. We use tools from representation learning and group theory to learn latent representations that account for both sensory information and the actions that alters it during interactions. We introduce the Homomorphism AutoEncoder (HAE), an autoencoder equipped with a learned group representation linearly acting on its latent space trained on 2-step transitions to implicitly enforce the group homomorphism property on the action representation.Compared to existing work, our approach makes fewer assumptions on the group representation and on which transformations the agent can sample from. We motivate our method theoretically, and demonstrate empirically that it can learn the correct representation of the groups and the topology of the environment. We also compare its performance in trajectory prediction with previous methods.

Keywords: Unsupervised Learning · Representation Learning · group representation · Autoencoder · Disentanglement · Equivariant representation · Homomorphism · Sensorimotor · Interaction based Learning

Author Information

Hamza Keurti (MPI-IS --- ETH)
Hamza Keurti

I am a third year CLS PhD fellow working on learning structured representations from interaction. I am generally interested in how perception would emerge from observing transformations of the environment rather than from static stimuli, this touches on developmental psychology, group theory, category theory, and representation learning. I am co-supervised by Prof. Benjamin Grewe (ETHZ) and Prof. Bernhard Schölkopf (MPI-IS).

Hsiao-Ru Pan (Max Planck Institute for Intelligent Systems)
Michel Besserve (MPI for Intelligent Systems)
Benjamin F. Grewe (ETH Zurich)
Bernhard Schölkopf (MPI for Intelligent Systems, Tübingen)

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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