Computing with inter-spike interval codes in networks of integrate and fire neurons

Information encoding in spikes and computations performed by spiking neurons are two sides of the same coin and should be consistent with each other. This study uses this consistency requirement to derive some new results for inter-spike interval (ISI) coding in networks of integrate and fire (IF) neurons. Our analysis shows that such a model can carry out useful computations and that it does also account for variability in spike timing as observed in cortical neurons. Our general result is that IF type neurons, though highly non-linear, perform a simple linear weighted sum operation of ISI coded quantities. Further, we derive bounds on the variation of ISIs that occur in the model although the neurons are deterministic. We also derive useful estimates of the maximum processing speed in a hierarchical network.