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 behavior of a system. We reevaluate 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 behavior of S and supervises a S-R closed loop mapping. Secondarily, we demonstrate how physical phenomena such as temporal criticality, non-normal denoising, and alternating procedural acquisition can recast behavior 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.