Oscillatory Hebbian Rule (OHR): An adaption of the Hebbian rule to Oscillatory Neural Networks

Hebbian rule plays an important role in training of artificial neural networks. According to this rule, a synaptic weight between two neurons is increased or decreased depending on the activity of the presynaptic and postsynaptic neurons. In this paper, an oscillatory version of the Hebbian rule is proposed for ONNs and is called Oscillatory Hebbian Rule (OHR). OHR simply expresses the weight change as a function of the phase difference between the presynaptic and postsynaptic neurons. Similar to STDP that weight change is an exponential function of the time difference between the presynaptic and postsynaptic spikes, OHR relates weight change to the phase difference between the presynaptic and postsynaptic neurons using exponential functions. Specifically, when two neurons are in-phase, the weight between them is increased while a weight between two anti-phase neurons is decreased. Simulation results show the capability of OHR for both supervised and unsupervised learning. In supervised learning, a basic block of feedforward architectures is trained as a classifier. When the basic block is used in unsupervised mode, it is capable to learn patterns while the output phase is converged to a specific phase.