Schema of ideal precision settings, at the first and second levels of a module, for learning and recognition under noise.
The precision of a population at each level is indicated by the line thickness around the symbols, and the influence of a population over another is indicated by arrow strength. A) During learning, the precision ratio at the first level (precision of the sensory states, i.e., causal states, over precision of the internal (hidden) dynamics) should be high. Consequently, the internal dynamics at the first level are dominated by the dynamics of the sensory input. At the second level, a very high precision makes sure that the module is forced to explain the sensory input as sequential dynamics by updating (learning) the connections between first and second levels (the I's in the first line of Equation 2). B) Under noisy conditions, the sensory input is not reliable and recognition performance is best if the precision at the sensory level is low compared to the precision of the internal dynamics at both levels (low sensory/internal precision ratio). This allows the module to rely on its (previously learned) internal dynamics, but less-so on the noisy sensory input. For the exact values of the precision settings in each scenario, see Text S1.