Mutual-Information-Dependent Nonlinear Threshold Response Model Linked to the Free Energy Principle

Abstract

Biological systems not only infer states of the external world from sensory input but also vary the expression of their responses according to the information they have acquired. Here, without altering the standard inferential and policy-evaluation schemes of the Free Energy Principle (FEP) and active inference, we propose a minimal dynamics that links the mutual information formed between an external state and an internal representation through inference to a response-expression variable distinct from policy selection. In this formulation, established information is positioned as a state signal that modulates response expression. The model introduces a piecewise nonlinear term in which response activation is driven only when mutual information exceeds an information threshold. Monte Carlo simulations using a two-state Markov environment showed that increasing observation accuracy increased the mutual information between the external state and the internal representation and, in turn, increased response activation. By contrast, in a control condition without information-response coupling, the response remained at its baseline level. The basic pattern of response activation was preserved when observation accuracy, the information-response coupling coefficient, the information threshold, and the closed-loop coefficient linking response to sensory sampling were varied. These results show that coupling information formed by FEP-consistent inference to an independent response-expression dynamics can generate a nonlinear response that depends on an information threshold.