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arXiv · 2502.12654

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

Peter R Williams·Zhan Chen
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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.

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Peter R Williams, Zhan Chen. 2025-02-18. Free Energy and Network Structure: Breaking Scale-Free Behaviour Through Information Processing Constraints. https://arxiv.org/abs/2502.12654

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