Figure 3
Imposing activity constraints with FTP. (a) FR measured in networks constructed to solve the s-task, as a function of the target FR. The FR of networks constructed with the FTP algorithm is close to the target FR (blue line). There is a tendency to obtain lower firing rates for target FR values above 0.5 spikes/time step, and higher firing rates for target FR values below 0.5 spikes/time step (the gray line is the identity function). The same networks with their synaptic weights shuffled (red line) show a similar relationship between target FR and measured FR, albeit with a lower slope. A total of 30 networks were generated for each target FR. Weights in \({\mathbf{W}}^{in}\) and \({\mathbf{W}}^{rec}\) were shuffled separately. Mean ± SD are shown. (b) Correlation between pairs of integration neurons as a function of the scaling factor fcc. Pairwise correlation, computed over all time steps, increases with fcc until it saturates at CC = 0.48 for \(f_{cc} \ge 5\) (blue line). Networks with their afferent synaptic weights shuffled (red line) show low correlation, invariant to fcc. A total of 30 networks were constructed for each fcc value, with target FR set to 0.1 spikes/time step. Mean ± SD are shown. (c) Pairwise correlation computed separately for \(s_{1}\) and \(s_{2}\) (noise correlation). The correlation coefficient increases with fcc, similarly for both stimuli and closely following correlation values in (b). Mean ± SD are shown, n = 30. (d) Measured FR as a function of pairwise correlation. Each blue dot shows the FR and CC of one network constructed to solve the s-task with desired FR and CC imposed through \({\mathbf{U}}_{base}\) initialization. Values for 2700 networks are shown. Points form stripes pointing towards FR = 0.5 spikes/time step, each stripe corresponding to networks with the same target FR. As correlation increases, the measured FR tends to 0.5 spikes/time step. Black dots show FR and CC of 4 networks for which desired FR and CC were imposed by evolution of a population of \({\mathbf{U}}_{base}\) matrices.
