Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions

Humans acquire such internal models by interacting with the world, but the learning principles allowing it How can agents learn internal models that veridically remain elusive. We investigate how Machine Learning (ML) represent interactions with the real world can shed light on this question, as it moves towards representations is a largely open question. As machine learning that carry more than just observational information is moving towards representations containing not (Sutton & Barto, 2015; Schölkopf et al., 2021) and develops just observational but also interventional knowledge, tools for interactive and geometric structure learning (Cohen we study this problem using tools from representation & Welling, 2016; Eslami et al., 2018), learning and group theory. We propose methods enabling an agent acting upon the Our setting is inspired by neuroscientific evidence that, as world to learn internal representations of sensory animals use their motor apparatus to act, efference copies of information that are consistent with actions that motor signals are sent to the brain's sensory system where modify it. We use an autoencoder equipped with they are integrated with incoming sensory observations to a group representation acting on its latent space, predict future sensory inputs (Keller et al., 2012). We argue trained using an equivariance-derived loss in order that such efference copies can be useful for learning to enforce a suitable homomorphism property on structured latent representations of sensory observations the group representation. In contrast to existing and for disentangling the key latent factors of behavioral work, our approach does not require prior knowledge relevance. This view is also in line with hypotheses formulated of the group and does not restrict the set of by developmental psychology (Piaget, 1964), stating actions the agent can perform.