Generator-Filter Theory (GFT) as a Dynamic Extension of the Free Energy Principle (FEP)

The Free Energy Principle (FEP), proposed by Karl Friston, states that any self-organizing system minimizes its long-term average surprise by minimizing a proxy known as Variational Free Energy (F). This memo introduces Generator-Filter Theory (GFT) as a metavariational extension of FEP, wherein not only the internal model (Generator) but also the prior constraints (Filter) co-evolve. We establish a formal mathematical identity between GFTs Informational Action and negative FEP, and show how joint variation over both components enables modeling of meta-learning, morphogenesis, and adaptive physical laws. Note: Part of:A Meta-Variational Principle: The Generator-Filter Theory (GFT) as a Unifying Framework for Dynamical and Informational Systems — https://zenodo.org/records/17438530