Adaptive systems operating under finite inferential capacity must redistribute precisionacross hierarchical levels, and such redistribution can generate structural instabilities as domi-nant modes approach criticality. Previous work established that bounded global precision givesrise to redistribution eigenmodes and local structural phase transitions in hierarchical inference.This paper advances that framework by introducing meta-precision, a higher-order control vari-able that regulates the rate of precision redistribution in response to the local spectral state ofthe constrained dynamics.We formalize this idea on a finite-capacity manifold as a coupled slow–fast system: precisionredistribution evolves on a fast timescale, whereas meta-precision evolves more slowly throughfeedback from a regularized spectral proxy of the dominant redistribution mode. Since meta-precision acts multiplicatively on the fast flow, it does not directly change the constrainedequilibrium set. Its function is instead to govern the temporal organization of redistributionand the system’s residence relative to the local stability boundary.Under standard smoothness, boundedness, and time-scale separation assumptions, we showthat the coupled dynamics admit locally stable equilibria satisfying a compatibility relationbetween the target spectral boundary and the regulated meta-precision level. As a consequence,thejointequilibriumismaintainedonthestablesideofthelocalstabilityboundary,orarbitrarilyclose to it when the target is chosen near zero. Meta-precision therefore supports locally stablenear-critical operation while avoiding generic instability.More broadly, the framework proposes a higher-order principle of adaptive regulation: underfinite capacity, intelligent systems may not merely allocate precision across levels, but alsoregulate how close those redistribution dynamics remain to structural instability. In this way,meta-precision provides a formal link between predictive processing, bounded rationality, andthe controlled maintenance of responsiveness near critical regimes.
Takashi Kubo (Sun,) studied this question.