Fig. 5.

Bayesian mechanics and active inference. This graphic summarises the belief updating scheme in the minimisation of variational free energy and expected free energy [38], [45], [93]. In the first step (circles on the left), discrete actions solicit a sensory outcome (i.e., in the parlance of the SIF, a solicitation) used to form approximate posterior beliefs about states of the world. This belief updating involves the minimisation of free energy under a set of plausible policies (blue panel – Perceptual inference). Note that free energy F(π,s) includes Markovian dependencies among hidden states. This reflects the fact that the generative model is a Markov decision process. In the second step (green panel – Policy selection), the approximate posterior beliefs from the first step are used to evaluate expected free energy F(π,τ) and subsequent beliefs about action. These beliefs correspond to the epistemic and pragmatic affordances that underwrite policy selection. Note that the free energy per se is a function of sensory states, given a policy. In contrast, the expected free energy is a function of the policy. The construct of affordance in active inference corresponds to inferences about action on the environment, which are selected in terms of competing policies via the minimisation of expected free energy. The variables in this figure correspond to those in Fig. 1. Here, a policy π comprises a sequence of actions; the expression Q(η|π) denotes beliefs about hidden states given a particular policy; and Q(π) denotes posterior beliefs about the policy that is currently being pursued by the agent. Free energy is the difference between complexity and accuracy, while expected free energy can be decomposed into expected complexity (i.e., complexity cost or risk) and expected inaccuracy (i.e., ambiguity). Risk can be regarded as the (KL) divergence (D) between beliefs about future states under a particular policy and prior preferences about states. Ambiguity denotes the loss of a definitive mapping between external states and observed sensory states (quantified as entropy, H). Alternatively, expected free energy can be decomposed into epistemic and pragmatic affordance. Posterior beliefs about policies depend on their expected free energy. Crucially, these posterior beliefs include the free energy evaluated during perceptual inference. This has several interesting consequences from our perspective. This construction means that the agent has to infer the policy that it is currently pursuing and verify its predictions in light of sensory evidence. This is possible because the beliefs about actions that are encoded by internal states are distinct from the active states of the agent's MB. Free energy per se provides evidence that a particular policy is being pursued. In this scheme, agents (will appear to) entertain beliefs about their own behaviour, endowing them with what is defined as intentionality of goal directed behaviour under active inference. In effect, this enables agents to author their own sensorium in a fashion that has close connections with niche construction: see main text and [48]. See [94] for technical discussion. Figure from [95].