Phi fluctuates with surprisal: An empirical pre-study for the synthesis of the free energy principle and integrated information theory

The Free Energy Principle (FEP) and Integrated Information Theory (IIT) are two ambitious theoretical approaches. The first aims to make a formal framework for describing self-organizing and life-like systems in general, and the second attempts a mathematical theory of conscious experience based on the intrinsic properties of a system. They are each concerned with complementary aspects of the properties of systems, one with life and behavior, the other with meaning and experience, so combining them has potential for scientific value. In this paper, we take a first step towards such a synthesis by expanding on the results of an earlier published evolutionary simulation study, which show a relationship between IIT-measures and fitness in differing complexities of tasks. We relate a basic information theoretic measure from the FEP, surprisal, to this result, finding that the surprisal of simulated agents’ observations is inversely related to the general increase in fitness and integration over evolutionary time. Moreover, surprisal fluctuates together with IIT-based consciousness measures in within-trial time. This suggests that the consciousness measures used in IIT indirectly depend on the relation between the agent and the external world, and that it should therefore be possible to relate them to the theoretical concepts used in the FEP. Lastly, we suggest a future approach for investigating this relationship empirically.Author summary: Two influential theoretical frameworks in cognitive science, neuroscience and computational biology, are the Free Energy Principle and Integrated Information Theory. The first is a formal approach to self-organization and adaptive behavior ‐ in short, life ‐ based on first principles from statistical physics. The second is an attempt at formally describing the intrinsic experience of a given system, that is, how it feels to be that system. In this way, these two theories provide tools for understanding two complementary aspects of a given organism; namely, how it acts in a goal-directed manner based on statistical beliefs about the world, and how it feels to be that system in that process. In this paper, we provide an initial numerical investigation of the potential relation of these theoretical frameworks. We simulate agents that undergo evolution, and show that as their level of integration (Φ, a measure from Integrated Information Theory) increases, information theoretic surprisal (a quantity used in the Free Energy Principle) decreases. We also see that Φ and surprisal fluctuate together, and that these fluctuations depend on sensory input. Finally we provide considerations for future simulation work, and how to bring these two theoretical frameworks closer together.