The Free Energy Principle (FEP) for the Brain

The FEP is a general theoretical principle that has been proposed to provide a unified account of brain functioning (Friston, 2010). This principle originates in the observation that adaptive agents such as embodied brains seek to minimize surprise – the difference between a brain’s current and predicted states – in order to maintain a systemic homeostasis in the face of destabilizing influences in the environment (Friston, 2010; Pio-Lopez et al., 2016). One way the brain achieves this is by organizing itself in a manner that reflects the causal and structural regularities of its environment so as to predict and oppose environmental changes that disrupt homeostasis (Friston, 2010, 2012). That is, the brain’s organization represents a generative model m of its environment that it uses to generate data or observations o from hidden environmental variables ν that generate or cause the observations but are not directly evident from the pattern of observations. These hidden states are inferred by the brain and are represented via internal neural states in a manner that minimizes an upper bound on surprise called free energy – a higher-order probabilistic function of the brain’s observed states and its internal representation of the causes of observations, given the brain’s generative model; see Figure 1. Free energy may be expressed as a higher-order function of observations and causes as (Friston, 2010; Friston et al., 2014):

where P(o,ν| M) is the generative model distribution describing the joint probability of observations and their causes given the brain’s theoretically best possible (i.e., “correct” or “true”) encoding of this information, an optimum generative model denoted by M. The distribution Q(ν|μ,m) is called the recognition distribution and reflects a probabilistic neural representation of the causes of observations conditional on a distribution parameter represented within the brain by internal neural states μ.

The free energy bound on surprise arises by treating the brain as a Bayesian agent that transforms prior beliefs into posterior beliefs according to a posterior distribution P(ν|o,m) described by Bayes’ rule, an approach called the Bayesian brain hypothesis (Lee and Mumford, 2003; Knill and Pouget, 2004; Doya et al., 2007). In many situations, a direct computation of the true posterior P(ν|o,M) is computationally intractable because the causes of observations are hidden variables and the number of possible causes of observations can be very large (Dayan et al., 1995; Pio-Lopez et al., 2016). The FEP approach circumvents this by assuming that the brain embodied as an agent minimizes its free energy by performing approximate Bayesian inference, which may be carried out in two ways. First, the brain may optimize its representations about the causes of its observations by optimizing the recognition distribution Q(ν|μ,m) to be as close as possible to P(ν|o,M); see Figure 1. Given that this internal representation is in part constrained by the brain’s organization, such an optimization may also involve the brain changing its organization in order to encode a better approximation of the optimum generative model m. Second, an embodied brain agent may minimize its free energy by acting on the world in order to change observations in accordance with its (sub-optimal) predictions, where such actions “[enforce] a sampling of [observed] data that is consistent with the current representation … [in order to] minimize prediction error” (Friston, 2010, p. 128); see Figure 1. In this case, actions influence observations, o = o(a), and free energy may be expressed as (following Friston et al., 2015; Pio-Lopez et al., 2016; Gershman, 2019),

Minimization of free energy with respect to actions is called active inference (Friston et al., 2015; Pio-Lopez et al., 2016; Gershman, 2019).

In the present study, the free energy F(o,ν) of global states of the human brain were quantified during the perception of simple visual categories. In the original formulation of the FEP, sensations are the observations about which the brain seeks to minimize its free energy estimate of surprise, and the relevant hidden variables reflect different physical features of an object (e.g., orientation of line segments, spatial frequency, etc.). However, causes can also be categorical in nature (Friston, 2005). In the present study, the observations under consideration were category perceptions, in which perceptual objects are perceived to be members of discrete categories and/or referents of concepts – abstract mental representations of the general properties and structure of object classes that may also serve to structure and influence perceptions (Goldstone and Kersten, 2003; Rips et al., 2012). In some Bayesian approaches to categorization (e.g., Shi et al., 2010), hidden variables reflect the concepts that refer to different categories (where concepts are operationalized as the assignment of semantic labels to the categories); in this case the posterior distribution P(ν|o,m) indexes the probability that a category label describes an object, given the object’s perceptual characteristics. Thus the theoretical FEP framework can also be used to describe how the brain approximates this posterior distribution of category labels via free energy minimization of surprise. In this case, the surprise to be minimized reflects the difference between the predicted and correct or “true” category label of an object. These are quantities for which probability distributions can be estimated from the a priori knowledge of the stimulus category on each trial and probabilistic estimates of the brain’s representations of its category perceptions to yield an empirical measure of free energy (see section “Analytical Methods, Global Brain Free Energy Difference Quantification”).