Figure 4.

Schematic showing the construction of the generative model for birdsongs. This comprises two Lorenz attractors where the higher attractor delivers two control parameters (gray circles in the corresponding equations of motion) to a lower level attractor, which, in turn, delivers two control parameters to a synthetic syrinx to produce amplitude and frequency modulated stimuli. These control parameters correspond to hidden causes that have to be inferred, given the stimulus. This stimulus is represented as a sonogram (lower left panel). The upper equations represent the hierarchical dynamic model in the form of Eq. 2; while the lower equations summarize the recognition or Bayesian filtering scheme in the form of (a simplified version of) Eq. 3. The lower right panels show the sensory predictions of this Bayesian filtering scheme in terms of the predicted sonogram based upon posterior expectations (left) and the precision-weighted prediction errors driving these expectations (right).