Abstract: A method and apparatus are disclosed for implementing a neural network having a sleep mode during which capacitively stored synaptic connectivity weights are refreshed. Each neuron outputs an analog activity level, represented in a preferred embodiment by the frequency of digital pulses. Feed-forward synaptic connection circuits couple the activity level outputs of first level neurons to inputs of second level neurons, and feed-back synaptic connection circuits couple outputs of second level neurons to inputs of first level neurons, the coupling being weighted according to connectivity weights stored on respective storage capacitors in each synaptic connection circuit.