The paper studies principles behind structured, especially symmetric, representations through enforced inter-agent conformity. For this, we consider agents in a simple environment who extract individual representations of this environment through an information maximization principle. The representations obtained by different agents differ in general to some extent from each other. This gives rise to ambiguities in how the environment is represented by the different agents. Using a variant of the information bottleneck principle, we extract a 'common conceptualization' of the world for this group of agents. It turns out that the common conceptualization appears to capture much higher regularities or symmetries of the environment than the individual representations. We further formalize the notion of identifying symmetries in the environment both with respect to 'extrinsic' (birds-eye) operations on the environment as well as with respect to 'intrinsic' operations, i.e. subjective operations corresponding to the reconfiguration of the agent's embodiment. Remarkably, using the latter formalism, one 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, one can 're-educate' an agent to conform to the de-individualized 'concept' of the agent group with comparatively little effort.
Keywords: collective concepts; embodied agents; information bottleneck; information theory; symmetries.
© 2023 The Authors.