Figure 3. Example of the dynamics and evolution of top-down weights in the integrate-and-fire model.

a. Snapshots showing the evolution of W (N) in the integrate-and-fire network simulations over time defined by the number of stimulus presentations (N). The format is the same as in Figure 2a . This model had 100 lower units and 100 higher units. The parameters used in this simulation are shown in the last column of Table 1 , with rSTDP and  = 1.2. b–c. Measures of weight stability. b. Standard deviation of the distribution of top-down weights as a function of the stimulus presentation number. The convergence criterion for the standard deviation was that the slope of this plot (calculated as with ΔN = 6000) be less than 10⁻⁵. The convergence criterion was met at the point indicated by the red asterisk. The dotted vertical lines correspond to the times of the five snapshots shown in part a. c. Blue line: Pearson correlation coefficient between the vectorized W (N) and W (N-ΔN), for ΔN = 3000 iterations. For comparison with Figure 2 , we also show the correlation coefficient between W(N) and the inverse of Q (green line). We note that in the integrate and fire simulations we do not expect W(N) to converge to the described in the text and Figure 2 . A simulation run was classified as ‘convergent’ when the correlation coefficient was greater than 0.99 and when the std criterion in part b was met. In this example, the simulation achieved the correlation criterion at T = 75000 (red asterisk). d. Measure of weight diversity: Distribution of the synaptic weights for the final snapshot. Bin size = 0.1. e. Measure of absence of strong loops: Average firing rate for lower-level neurons as a function of stimulus presentation number. The average firing rate almost immediately stabilizes to a constant value, and does not increase to pathological levels as occurs in the presence of strong excitatory loops.