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, SpikeProp, akin to traditional error-backpropagation. 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, the trained networks demonstrate that temporal coding is a viable code for fast neural information processing, and as such requires less neurons than instantaneous rate-coding. Furthermore, we find that reliable temporal computation in the spiking networks was only accomplished when using spike response functions with a time constant longer than the coding interval, as has been predicted by theoretical considerations.