A 'good' regulator may provide a world model for intelligent systems

One classic idea from the cybernetics literature is the Every Good Regulator Theorem (EGRT). The EGRT provides a means to identify good regulation, or the conditions under which an agent (regulator) can match the dynamical behaviour of a system. We re-evaluate and recast the EGRT in a modern context to provide insight into how intelligent autonomous learning systems might utilize a compressed global representation (world model). One-to-one mappings between a regulator (R) and the corresponding system (S) provide a reduced representation that preserves useful variety to match all possible outcomes of a system. The EGRT also extends to second-order cybernetics, where an internal model (M) observes the behaviour of S and supervises an S-R closed-loop mapping. Secondarily, we demonstrate how physical phenomena such as temporal criticality, non-normal denoising and alternating procedural acquisition can recast behaviour as statistical mechanics and yield regulatory relationships. These diverse physical systems challenge the notion of tightly coupled good regulation when applied to non-uniform and out-of-distribution phenomena. Overall, we aim to recast the EGRT as a potential approach for developing world models that adapt and respond to a wide range of task environments. This article is part of the theme issue 'World models in natural and artificial intelligence'.