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Free energy principle
The free energy principle tries to explain how (biological) systems maintain their order (non-equilibrium steady-state) by restricting themselves to a limited number of states.〔Ashby, W. R. (1962). (Principles of the self-organizing system ).in Principles of Self-Organization: Transactions of the University of Illinois Symposium, H. Von Foerster and G. W. Zopf, Jr. (eds.), Pergamon Press: London, UK, pp. 255–278.〕 It says that biological systems minimise a free energy functional of their internal states, which entail beliefs about hidden states in their environment. The implicit minimisation of variational free energy is formally related to variational Bayesian methods and was originally introduced by Karl Friston as an explanation for embodied perception in neuroscience,〔Friston, K., Kilner, J., & Harrison, L. (2006). (A free energy principle for the brain ). J Physiol Paris. , 100 (1–3), 70–87.〕 where it is also known as active inference.
== Background ==
The notion that self-organising biological systems – like a cell or brain – can be understood as minimising variational free energy is based upon Helmholtz’s observations on unconscious inference〔Helmholtz, H. (1866/1962). Concerning the perceptions in general. In Treatise on physiological optics (J. Southall, Trans., 3rd ed., Vol. III). New York: Dover.〕 and subsequent treatments in psychology 〔Gregory, R. L. (1980). (Perceptions as hypotheses ). Phil Trans R Soc Lond B. , 290, 181–197.〕 and machine learning.〔Dayan, P., Hinton, G. E., & Neal, R. (1995). (The Helmholtz machine ). Neural Computation , 7, 889–904.〕 Variational free energy is a functional of some outcomes and a probability density over their (hidden) causes. This variational density is defined in relation to a probabilistic model that generates outcomes from causes. In this setting, free energy provides an (upper bound) approximation to Bayesian model evidence.〔Beal, M. J. (2003). (Variational Algorithms for Approximate Bayesian Inference ). PhD. Thesis, University College London.〕 Its minimisation can therefore be used to explain Bayesian inference and learning. When a system actively samples outcomes to minimise free energy, it implicitly performs active inference and maximises the evidence for its (generative) model.
However, free energy is also an upper bound on the self-information (or surprise) of outcomes, where the long-term average of surprise is entropy. This means that if a system acts to minimise free energy, it will implicitly place an upper bound on the entropy of the outcomes – or sensory states – it samples.〔Friston, K. (2012). (A Free Energy Principle for Biological Systems ). Entropy , 14, 2100–2121.〕
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