Fig 7. Robustness of the learning rules to missing connections, noise, and synaptic delays.

All simulations are based on EI networks receiving two-dimensional, random input signals. Network size is given as number of inhibitory neurons. The pool of excitatory neurons is twice as large in all cases. A. Performance (mean-square error between input signal and signal estimate) of the learnt network as a function of (inhibitory) network size. Trained network (blue) and equivalent Poisson rate network (black), given by neurons whose firing follows Poisson processes with identical average rates. B. Performance of the learnt network as a function of connection sparsity. Here, we randomly deleted some percentage of the connections in the network, and then trained the remaining connections with the same learning rule as before. We adjusted the variance of the input signals to achieve the same mean firing rate in each neuron (r = 5 Hz in excitatory, r = 10 Hz in inhibitory neurons). Black lines denote the performance of an equivalent (and unconnected) population of Poisson-spiking neurons. C. Network performance as a function of synaptic noise and synaptic delay. Here, we injected random white-noise currents into each neuron. The size of the noise was defined as the standard deviation of the injected currents, divided by the time constant and firing threshold. Roughly, this measure corresponds to the firing rate cause by the synaptic noise alone, in the absence of connections or input signals. As in B, the input variance was scaled to get the same mean firing rate in each neuron (r = 5 Hz in excitatory, r = 10 Hz in inhibitory neurons). Different colors show curves for different synaptic delays (see panel D). D. Temporal profile of EPSCs and IPSCs (injected currents each time a spike is received) in the delayed networks, plotted as a function of the synaptic delay d. We rescaled the time axis to get the different delays used in panel C.