Figure 4
Imposing structural constraints with FTP. (a) Synaptic weight matrices \({\mathbf{W}}^{in}\) and \({\mathbf{W}}^{rec}\) of the network obtained through FTP before structural constraints were imposed. The network was constructed to solve the s-task for \(\tau = 4\) and \(f_{r} = 3\), with a target FR of 0.1 spikes/time step. (b) Loss function \({\mathcal{L}}\) as a function of the number of iterations of the PGD algorithm. The loss function falls below the criterium \(e_{1} = 10^{ - 3}\) at iteration 121. (c,d) Synaptic weight matrices \({\mathbf{W}}^{in}\) and \({\mathbf{W}}^{rec}\) for a network with the same stimulus–response mapping but after applying structural constraints: (c) no self-connections, Dale’s principle, with 40 excitatory and 10 inhibitory neurons, and sparsity \(sp = 40\%\); (d) no self-connections, Dale’s principle, with 26 excitatory and 24 inhibitory neurons, and sparsity \(sp = 23\%\). (e) Average number of attempts to obtain one network with successful structural fitting, as a function of the number of integration neurons, and for different \(\tau\). The number of attempts is high when the neuron number is low, but it decreases fast as the neuron number increases. From 60 neurons onwards, less than five attempts are needed, on average, to obtain one network with the desired structural constraints. Mean ± SD are shown. (f), total running time to obtain one network with successful structural fitting, as a function of the number of integration neurons, and for different \(\tau\) (color code as in (e)). Running time decreases and then increases for \(\tau = 3\) and \(\tau = 4\). The case of \(\tau = 6\) is the one with more neurons and equations to solve and present some of the highest running times, even when the number of neurons is high. Nevertheless, all average running times are in the order of tens of seconds.
