Skip to main content
. 2020 Oct 28;3:509354. doi: 10.3389/frai.2020.509354

Figure 8.

Figure 8

C's and D's. Prior beliefs over observations and hidden states for both hierarchical levels. Note that superscripts here index the hierarchical level, and separate modalities/factors for the C and D matrices are indicated by stacked circles. At the highest level (Level 2), prior beliefs about second-modality outcomes (C(2),2) encode the agent's beliefs about receiving correct and avoiding incorrect feedback. Prior beliefs over the other outcome modalities (C(2),1 and C(2),3) are all trivially zero. These beliefs are stationary over time and affect saccade selection at Level 2 via the expected free energy of policies G. Prior beliefs about hidden states D(2) at this level encode the agent's initial beliefs about the scene identity and the location of their eyes. This prior over hidden states can be manipulated to put the agent's beliefs about the world at odds with the actual hidden state of the world. At Level 1, the agent's preferences about being in the “Break-sampling” state increases over time and is encoded in the preferences about second modality outcomes (C(1),2), which corresponds to the agents umambiguous perception of its own sampling state. Finally, the prior beliefs about initial states at Level 1 (D1) correspond to the motion direction hidden state (the RDM identity) as well as which sampling-state the agent is in. Crucially, the first factor of these prior beliefs D(1),1 is initialized as the “expected observations” from Level 2: the expected motion direction (first modality). These expected observations are generated by passing the variational beliefs about the scene at Level 2 through the modality-specific likelihood mapping: Q(o(2),1|s(2),1) = P(o(2),1|s(2),1)Q(s(2),1). The prior over hidden states at Level 1 is thus called an empirical prior as it is inherited from Level 2. The red arrow indicates the relationship between the expected observation from Level 2 and the empirical prior over (first-factor) hidden states at Level 1.