Error-backpropagation in temporally encoded networks of spiking neurons

For a network of spiking neurons that encodes information in the timing of individual spike-times, we derive a supervised learning rule, emph{SpikeProp, akin to traditional error-backpropagation and show how to overcome the discontinuities introduced by thresholding. With this algorithm, we demonstrate how networks of spiking neurons with biologically reasonable action potentials can perform complex non-linear classification in fast temporal coding just as well as rate-coded networks. We perform experiments for the classical XOR-problem, when posed in a temporal setting, as well as for a number of other benchmark datasets. Comparing the (implicit) number of spiking neurons required for the encoding of the interpolated XOR problem, it is demonstrated that temporal coding requires significantly less neurons than instantaneous rate-coding.