  To make progress in science, we often build abstract representations of
physical systems that meaningfully encode information about the systems. The
representations learnt by most current machine learning techniques reflect
statistical structure present in the training data; however, these methods do
not allow us to specify explicit and operationally meaningful requirements on
the representation. Here, we present a neural network architecture based on the
notion that agents dealing with different aspects of a physical system should
be able to communicate relevant information as efficiently as possible to one
another. This produces representations that separate different parameters which
are useful for making statements about the physical system in different
experimental settings. We present examples involving both classical and quantum
physics. For instance, our architecture finds a compact representation of an
arbitrary two-qubit system that separates local parameters from parameters
describing quantum correlations. We further show that this method can be
combined with reinforcement learning to enable representation learning within
interactive scenarios where agents need to explore experimental settings to
identify relevant variables.
