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.