Gradient learning in networks of smoothly spiking neurons

Abstract

A slightly simplified version of the Spike Response Model SRM0 of a spiking neuron is tailored to gradient learning. In particular, the evolution of spike trains along the weight and delay parameter trajectories is made perfectly smooth. For this model a back-propagation-like learning rule is derived which propagates the error also along the time axis. This approach overcomes the difficulties with the discontinuous-in-time nature of spiking neurons, which encounter previous gradient learning algorithms (e.g. SpikeProp). The new algorithm can naturally cope with multiple spikes and preliminary experiments confirm the smoothness of spike creation/deletion process. © 2009 Springer Berlin Heidelberg.