Free Energy and Network Structure: Breaking Scale-Free Behaviour Through Information Processing Constraints

TL;DR

This work addresses why real-world networks deviate from pure scale-free behaviour by linking network formation to information processing under the Free Energy Principle. It develops a minimal Active Inference model in a one-dimensional setting, deriving a Gaussian-based closed-form updating scheme for the agent's belief and a mechanistic attachment kernel that translates detection, belief, and movement into network links. The core contribution is the identification of three regimes—noise-dominated, optimal detection, and saturation—that collectively generate knee-shaped degree distributions and explain deviations from preferential attachment as signatures of cognitive constraints. The framework offers testable predictions for how information processing limits sculpt network topology across biological, social, and artificial systems, with implications for network design and AI agent connectivity. Its significance lies in unifying cognitive information-processing principles with macroscopic network structure, providing a mechanistic, testable alternative to purely phenomenological growth models.

Abstract

In this paper we show how The Free Energy Principle (FEP) can provide an explanation for why real-world networks deviate from scale-free behaviour, and how these characteristic deviations can emerge from constraints on information processing. We propose a minimal FEP model for node behaviour reveals three distinct regimes: when detection noise dominates, agents seek better information, reducing isolated agents compared to expectations from classical preferential attachment. In the optimal detection regime, super-linear growth emerges from compounded improvements in detection, belief, and action, which produce a preferred cluster scale. Finally, saturation effects occur as limits on the agent's information processing capabilities prevent indefinite cluster growth. These regimes produce the knee-shaped degree distributions observed in real networks, explaining them as signatures of agents with optimal information processing under constraints. We show that agents evolving under FEP principles provides a mechanism for preferential attachment, connecting agent psychology with the macroscopic network features that underpin the structure of real-world networks.