Learning Spike Train to Spike Train Transformations in Multilayer Feedforward Neuronal Networks

We address the problem of learning temporally precise spike train to spike train transformations in multilayer feedforward networks of spiking neurons. We pursue a framework based strictly on spike timing, that is, one that avoids invoking concepts pertaining to spike rates. The proposed error functional compares the spike train emitted by the output neuron of the network to the desired spike train by way of their putative impact on a virtual postsynaptic neuron. This formulation sidesteps the need for spike alignment, which in turn leads to closed form solutions for all quantities of interest. Next, through a perturbation analysis of individual spike times and synaptic weights of the output as well as the intermediate neurons in the network, we derive the gradients of the error functional with respect to the said entities. Learning proceeds via a gradient descent mechanism that leverages these quantities. Simulation experiments demonstrate the efficacy of the proposed