From the delicate clasp of two binding proteins, to the symbiotic connections between different cells, to the neurons and tangled synapses inside a brain, to the web of friendships that weave our social world—it's networks all the way down... and up. Not only are these many complex systems best represented by networks, but the networks themselves often have similar structural or dynamical properties, as if they are driven by a common process or otherwise shared a similar set of goals. We will develop a theoretical and computational framework for understanding this apparent goal-directed, purposeful, teleological behavior that is often observed in the structure and dynamics of complex networks. To do this, we make an explicit connection between Network Science and the Free Energy Principle (FEP), a mathematical framework that describes the behavior of any system that does not dissipate into its environment (Friston, 2010; 2019). Our proposal builds upon recent work on causal emergence (Klein & Hoel, 2019) along with the theoretical scaffolding of the FEP to develop a framework that 1) describes the optimal scale to model the structure, dynamics, and goals of a system, 2) defines a set of underlying processes that can bring about commonalities observed in networks across different systems, and 3) advances a perspective that adopts teleological descriptions of networks in order to maximize the information gained from modeling our world. This work will also generate several technical advances, providing more accurate ways to describe dynamics, growth, adaptation, robustness, and control in networks. We illustrate the utility of this approach in experimental settings by quantifying the difference in information gained from experiments designed under teleological models vs. classical models. Lastly, an understanding of purposefulness in networks can further our understanding of the environments that networks are embedded in, rather than simply the network itself.
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