A synaptic plasticity rule providing a unified approach to supervised and unsupervised learning

At the early stages of their exploration, spiking neural networks were considered mainly as plausible models of biological neuronal ensembles, but then it became clear that they can solve many of the same problems as the traditional neural networks - classification and clustering using various supervised and unsupervised learning methods. The majority of synaptic weight adjustment algorithms proposed for these two kinds of learning are based on different principles - Hebbian learning (STDP etc.) for unsupervised learning and gradient methods similar to error backpropagation - for supervised learning. Since the biological plausibility of gradient descent algorithms is doubtful, it would be desirable to find a purely Hebbian mechanism for the both kinds of learning. The appropriate synaptic plasticity law (though different from STDP) is considered in this paper. It is called 2TP (Two Threshold Plasticity) rule because it includes 2 thresholds for membrane potential - one for firing, leading to synapse potentiation, and one for synaptic depression. It is demonstrated that this rule can serve as a basis for efficient unsupervised and supervised learning algorithms called L2TP/U and L2TP/S, respectively.