Meta-Precision under Finite Capacity: Spectral Governance in Hierarchical Inference

作者：Takashi Kubo · 发表于：Open MIND · 年份：2026 · DOI：10.5281/zenodo.18907539 · 被引用次数：6 · 研究领域：Ecosystem dynamics and resilience、Neural Networks and Reservoir Computing、Model Reduction and Neural Networks

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 i...