  Humans perceive and interact with hundreds of objects every day. In doing so,
they need to employ mental models of these objects and often exploit symmetries
in the object's shape and appearance in order to learn generalizable and
transferable skills. Active inference is a first principles approach to
understanding and modeling sentient agents. It states that agents entertain a
generative model of their environment, and learn and act by minimizing an upper
bound on their surprisal, i.e. their Free Energy. The Free Energy decomposes
into an accuracy and complexity term, meaning that agents favor the least
complex model, that can accurately explain their sensory observations. In this
paper, we investigate how inherent symmetries of particular objects also emerge
as symmetries in the latent state space of the generative model learnt under
deep active inference. In particular, we focus on object-centric
representations, which are trained from pixels to predict novel object views as
the agent moves its viewpoint. First, we investigate the relation between model
complexity and symmetry exploitation in the state space. Second, we do a
principal component analysis to demonstrate how the model encodes the principal
axis of symmetry of the object in the latent space. Finally, we also
demonstrate how more symmetrical representations can be exploited for better
generalization in the context of manipulation.
