Abstract
This paper describes a free energy principle that tries to explain the ability of biological systems to resist a natural tendency to disorder. It appeals to circular causality of the sort found in synergetic formulations of self-organization (e.g., the slaving principle) and models of coupled dynamical systems, using nonlinear Fokker Planck equations. Here, circular causality is induced by separating the states of a random dynamical system into external and internal states, where external states are subject to random fluctuations and internal states are not. This reduces the problem to finding some (deterministic) dynamics of the internal states that ensure the system visits a limited number of external states; in other words, the measure of its (random) attracting set, or the Shannon entropy of the external states is small. We motivate a solution using a principle of least action based on variational free energy (from statistical physics) and establish the conditions under which it is formally equivalent to the information bottleneck method. This approach has proved useful in understanding the functional architecture of the brain. The generality of variational free energy minimisation and corresponding information theoretic formulations may speak to interesting applications beyond the neurosciences; e.g., in molecular or evolutionary biology.
Highlights
What are the basic principles that underwrite the self-organisation or self-assembly of biological systems like cells, plants and brains? This paper tries to address this question by asking how a biological system, exposed to random and unpredictable fluctuations in its external milieu, can restrict itself to occupying a limited number of states, and survive in some recognisable form
We presume that this characterizes open biological systems that exhibit homoeostasis – in other words, systems that maintain their states within certain bounds [17,25,26,27,28,29,30] Using minimal assumptions, we show that this sort of behaviour can be cast in terms of Bayesian modelling of causal structure in the environment; in a way that is consistent with both the good regulator theorem
This paper describes a general, if somewhat abstract, motivation for a variational free energy principle that has a wide explanatory scope in neurobiology and has construct validity in relation to important information theoretic treatments, in particular, the information bottleneck method [58]
Summary
We motivate the free energy principle in general (and abstract) terms―using random dynamical systems and information theory, starting with the premise that biological agents resist a dispersion of their states in the face of fluctuations in the environment We presume that this characterizes open biological systems that exhibit homoeostasis (from Greek: μοιος, hómoios, similar and στάσις, stásis, standing still) – in other words, systems that maintain their states within certain bounds [17,25,26,27,28,29,30] Using minimal assumptions, we show that this sort of behaviour can be cast in terms of Bayesian modelling of causal structure in the environment; in a way that is consistent with both the good regulator theorem (every Good Regulator of a system must be a model of that system [31]) and Jaynesian perspectives on statistical physics [32]. This example focuses on perception in the brain, to show how it informs the functional architecture of brain circuits
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