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. 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, where it is also known as active inference. 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. 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, where it is also known as active inference. The free energy principle is that systems—those that are defined by their enclosure in a Markov blanket—try to minimize the difference between their model of the world and their sense and associated perception. This difference can be described as 'surprise' and is minimized by continuous correction of the world model of the system. As such, the principle is based on the Bayesian idea of the brain as an “inference engine.” Friston added a second way to minimization: action. By actively changing the world into the expected state, systems can also minimize the free energy of the system. Friston assumes this to be the principle of all biological reaction. Psychiatrist Friston believes his principle applies to mental disorders as well as to artificial intelligence. AI implementations based on the active inference principle have shown advantages over other methods. 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 and subsequent treatments in psychology and machine learning. Variational free energy is a function 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. 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. Active inference is closely related to the good regulator theorem and related accounts of self-organisation, such as self-assembly, pattern formation, autopoiesis and practopoiesis. It addresses the themes considered in cybernetics, synergetics and embodied cognition. Because free energy can be expressed as the expected energy (of outcomes) under the variational density minus its entropy, it is also related to the maximum entropy principle. Finally, because the time average of energy is action, the principle of minimum variational free energy is a principle of least action. Definition (continuous formulation): Active inference rests on the tuple ( Ω , Ψ , S , A , R , q , p ) {displaystyle (Omega ,Psi ,S,A,R,q,p)} , The objective is to maximise model evidence p ( s ∣ m ) {displaystyle p(smid m)} or minimise surprise − log ⁡ p ( s ∣ m ) {displaystyle -log p(smid m)} . This generally involves an intractable marginalisation over hidden states, so surprise is replaced with an upper variational free energy bound. However, this means that internal states must also minimise free energy, because free energy is a function of sensory and internal states: