Common concepts in agent groups, symmetries, and conformity in a simple environment

We analyze representations of the world attained through an
infomax principle by agents acting in a simple environment.
The representations obtained by different agents in general
differ to some extent from each other in different instances.
This gives rise to ambiguities in how the environment is
represented by the different agents. We now develop an
information-theoretic formalism able to extract a "common
conceptualization" of the world for a group of agents. It turns
out that the common conceptualization intuitively seems to
capture much higher regularities or symmetries of the environment
than the individual representations.
We formalize the notion of identifying symmetries in the environment
- with respect to "extrinsic" operations on the environment
as well as with respect to "intrinsic" operations,
i.e. the reconfiguration of the agent’s embodiment. In particular,
using the latter formalism, we can re-wire an agent
to conform to the highly symmetric common conceptualization
to a much higher degree than an unrefined agent; and
that without having to re-optimize the agent from scratch. In
other words, we can "re-educate" an agent to conform to the
de-individualized "concept" of the agent group with comparatively
little effort.