  Perception of artificial agents is one the grand challenges of AI research.
Deep Learning and data-driven approaches are successful on constrained problems
where perception can be learned using supervision, but do not scale to
open-worlds. In such case, for autonomous embodied agents with first-person
sensors, perception can be learned end-to-end to solve particular tasks.
However, literature shows that perception is not a purely passive compression
mechanism, and that actions play an important role in the formulation of
abstract representations. We propose to study perception for these embodied
agents, under the mathematical formalism of group theory in order to make the
link between perception and action. In particular, we consider the commutative
properties of continuous action sequences with respect to sensory information
perceived by such an embodied agent. We introduce the Sensory Commutativity
Probability (SCP) criterion which measures how much an agent's degree of
freedom affects the environment in embodied scenarios. We show how to compute
this criterion in different environments, including realistic robotic setups.
We empirically illustrate how SCP and the commutative properties of action
sequences can be used to learn about objects in the environment and improve
sample-efficiency in Reinforcement Learning.
