The free energy principle. The schematic shows the probabilistic dependencies (arrows) among the quantities that define free energy. These include the internal states of the brain

and quantities describing its exchange with the environment. These are the generalized sensory states

and action

*a*(

*t*). The environment is described by equations of motion, which specify the trajectory of its hidden states and a mapping to sensory states. The quantities

causing sensory states comprise hidden states and parameters. The hidden parameters control the equations (

**f**,

**g**) and precision (inverse variance) of random fluctuations (

*ω*_{x}(

*t*),

*ω*_{s}(

*t*)) on hidden and sensory states. Internal brain states and action minimize free energy

, which is a function of sensory states and a probabilistic representation

of their causes. This representation is called the recognition density and is encoded by internal states that play the role of sufficient statistics. The free energy depends on two probability densities; the recognition density,

, and one that generates sensory samples and their causes,

. The latter represents a probabilistic generative model (denoted by

*m*), whose form is entailed by the agent. The lower panels provide alternative expressions for the free energy to show what its minimization entails. Action can only reduce free energy by increasing accuracy (i.e., selectively sampling sensory states that are predicted). Conversely, optimizing internal states makes the representation an approximate conditional density on the causes of sensory states. This enables action to avoid surprising sensory encounters. See main text for further details.

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