A Quaternionic Rate-Based Synaptic Learning Rule Derived from Spike-Timing Dependent Plasticity

Most of the differential Hebbian rules derived from Spike-Timing Dependent Plasticity (STDP) focus on the rates of change of post-synaptic activity that carries the information about the future and enables the neural network to predict. And the current model mainly consider three factors for the adjustment of synaptic weight, namely, the rate of pre- and post-synaptic activity and the rate of change of postsynaptic activity. We argue that the rate of change of pre-synaptic activity also plays an important role on the adjustment of synaptic weight. Hence, this paper proposes a quaternionic rate-based synaptic learning rule that depends on four elements, namely, the instantaneous firing rates of both pre- and post-synaptic neurons and their time derivatives.