Spike-Timing-Dependent Learning for Oscillatory Networks

We apply to oscillatory networks a class of learning rules in which synaptic weights change proportional to preand post-synaptic activity, with a kernel A(r) measuring the effect for a postsynaptic spike a time r after the presynaptic one. The resulting synaptic matrices have an outer-product form in which the oscillating patterns are represented as complex vectors. In a simple model, the even part of A(r) enhances the resonant response to learned stimulus by reducing the effective damping, while the odd part determines the frequency of oscillation. We relate our model to the olfactory cortex and hippocampus and their presumed roles in forming associative memories and input representations.