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.

Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as the commonly employed softmax is capable of representing any categorical distribution. In regression, however, restrictive assumptions on the type of continuous distribution to be realized are typically placed, like the dominant choice of training via mean-squared error and its underlying Gaussianity assumption. Recently, modelling advances allow to be agnostic to the type of continuous distribution to be modelled, granting regression the flexibility of classification models. While past studies stress the benefit of such flexible regression models in terms of performance, here we study the effect of the model choice on uncertainty estimation. We highlight that under model misspecification, aleatoric uncertainty is not properly captured, and that a Bayesian treatment of a misspecified model leads to unreliable epistemic uncertainty estimates. Overall, our study provides an overview on how modelling choices in regression may influence uncertainty estimation and thus any downstream decision making process.