this invention pertains to compact synaptic circuits and networks comprising compact synaptic circuits that exhibit functional characteristics of biological synapses and networks of synapses including , but not limited to , spike timing dependent plasticity . temporal coincidence of pre - and post - synaptic action potentials across the synapses of the present invention induces proportional hebbian synaptic weight updates . networks of the synapses of the present invention operated according to the methods of this invention are designed to implement biological learning functions , such as stdp .