The Structural Origin of Prediction Error: Evaluation Dynamics and the Free Energy Principle

This paper reinterprets prediction error minimization in the free energy principle within a more general framework of difference-attribution dynamics. In existing formulations of the free energy principle, uncertainty minimization is assumed as a fundamental principle of cognitive systems, but the structural conditions from which this minimization arises are not clearly specified. To address this issue, the analysis begins from the phenomenon of difference concentration that arises when an operational system has multiple generative paths leading to the same result. When difference concentration holds, an observed difference cannot be determined solely from the generative structure as either a difference in results or a difference in generative paths. Consequently, an evaluative structure that determines the attribution of differences becomes unavoidable. This paper formalizes this structure as evaluation, understood as a decision structure for difference attribution, and defines its operational state in terms of evaluation entropy. The evaluation process can be interpreted as a search over possible difference attributions whose temporal evolution takes the form of entropy decay. On this basis, the paper formulates evaluation dynamics and interprets active inference as a special case of entropy reduction in difference-attribution search. Within this framework, the free energy principle is understood not as a fundamental principle specific to cognitive systems but as a particular implementation of difference-attribution dynamics. The result is a theoretical framework of evaluation dynamics that specifies the structural conditions under which the free energy principle arises.