Recent evidence suggests that neural information is encoded in packets and may be flexibly routed from region to region. We have hypothesized that neural circuits are split into sub-circuits where one sub-circuit controls information propagation via pulse gating and a second sub-circuit processes graded information under the control of the first sub-circuit. Using an explicit pulse-gating mechanism, we have been able to show how information may be processed by such pulse-controlled circuits and also how, by allowing the information processing circuit to interact with the gating circuit, decisions can be made. Here, we demonstrate how Hebbian plasticity may be used to supplement our pulse-gated information processing framework by implementing a machine learning algorithm. The resulting neural circuit has a number of structures that are similar to biological neural systems, including a layered structure and information propagation driven by oscillatory gating with a complex frequency spectrum.