Learning parsimonious dynamics for state abstraction and navigation

Cognitive maps associate complex, high-dimensional stimuli, such as visual percepts, with abstract
latent variables, such as spatial locations. It has been argued that animals use these abstract spatial
features to navigate and infer novel shortcuts in their environments. Employing information theory, we
present a simple computational account of how such abstract spatial representations may emerge
from interactions with high-dimensional stimuli: We show that learning world models in which the
dynamics are parsimonious and apply (approximately) independently of the state in an abstract state
space give rise to spatial concepts, improved performance in navigation tasks and neural
representations of space found in humans and rodents. Specifically, we show that artificial agents
equipped with such world models i) outperform agents with non-parsimonious world models in
planning tasks where they need to extrapolate about the dynamics of novel parts of the environment,
and ii) learn latent state spaces that afford faster policy learning. By constructing latent spaces in
which a small set of dynamical laws hold independently of where the agent may be in this space, our
model uses a simple computational principle to explain how geometric representations of high-
dimensional worlds emerge. Additionally, these parsimonious world models allow for systematic
generalization about transition dynamics in a way reminiscent of those of animals, and provide an
information-theoretic account of the emergence of the neural representations associated with these
abilities.