Neurophysiology studies propose that predictive coding is implemented via alpha/beta (8-30 Hz) rhythms preparing specific pathways to process predicted inputs. This leads to a state of relative inhibition, reducing feedforward gamma (40-90 Hz) rhythms and spiking for predictable inputs. This is called predictive routing model. It is unclear which circuit mechanisms implement this push-pull interaction between alpha/beta and gamma rhythms. To explore how predictive routing is implemented, we developed a self-supervised learning algorithm we call generalized Stochastic Delta Rule (gSDR). Development of this algorithm was necessary because manual tuning of parameters (frequently used in computational modeling) is inefficient to search through a non-linear parameter space that leads to emergence of neuronal rhythms. We used gSDR to train biophysical neural circuits and validated the algorithm on simple objectives. Then we applied gSDR to model observed neurophysiology. We asked the model to reproduce a shift from baseline oscillatory dynamics (~<
20Hz) to stimulus induced gamma (~40-90Hz) dynamics recorded in the macaque visual cortex. This gamma oscillation during stimulation emerged by self-modulation of synaptic weights via gSDR. We further showed that the gamma-beta push-pull interactions implied by predictive routing could emerge via stochastic modulation of the local circuitry as well as top-down modulatory inputs to a network. To summarize, gSDR succeeded in training biophysical neural circuits to satisfy a series of neuronal objectives. This revealed the inhibitory neuron mechanisms underlying the gamma-beta push-pull dynamics that are observed during predictive processing tasks in systems and cognitive neuroscience.