A model cortical circuit of Markovian integrate-and-fire neurons produces gamma-band (30-90 Hz) rhythms through multiple-firing events: brief stochastic episodes in which recurrent excitation drives many neurons to fire nearly synchronously until accumulating inhibition shuts the episode down. Because the network alternates between this fast episode and a slow inter-event interval, the return map from one event onset to the next can be split in two: the slow branch is cheap to simulate directly by tau-leaping, while the fast branch is replaced by a trained feedforward network. This Idea covers what makes that fast map learnable at all - coarse-graining the full 3N-dimensional state down to binned voltage distributions plus pending-spike totals, and keeping only the lowest discrete-cosine modes to strip sampling noise - and how labelling training data with the synaptic coupling strengths turns a single trained map into a surrogate that generalizes across coupling space and across network size.
Gamma-band oscillations (30-90 Hz) in a model cortical circuit arise from multiple-firing events (MFEs): brief, stochastic episodes in which many neurons fire nearly synchronously, triggered by a cha…