Supervised learning in a spiking neural network

We introduce a method to train a bio-inspired neural network model, having the characteristics of spiking-timing-dependent interaction and learning, in a manner of supervised learning. We assume the spiking neural network model has the tendency to obey the charge conservation principle or the junction rule on a long (or the learning dynamics) time scale. The tendency makes the distribution of connectivities is determined depending on not only the incoming stimuli to input neurons but also the outgoing stimuli from output neurons as if a solution of the finite elementary method in a fluid system. We apply the learning method to several cases in simulations and find the adoption of the conservation principle exerts desired effects on the neural network learning. Finally, we discuss the significance and the drawbacks of the introduced method and compare it with the supervised learning method implemented by the artificial neural network model.