Homeostatic plasticity is a stabilizing mechanism that allows neural systems to maintain their activity around a functional operating point. This is an extremely useful mechanism for neuromorphic computing systems, as it can be used to compensate for chronic shifts, for example due to changes in the network structure. However, it is important that this plasticity mechanism operates on time scales that are much longer than conventional synaptic plasticity ones, in order to not interfere with the learning process. In this paper we present a novel ultra-low leakage cell and an automatic gain control scheme that can adapt the gain of analog log-domain synapse circuits over extremely long time scales. To validate the proposed scheme, we implemented the ultra-low leakage cell in a standard 180 nm Complementary Metal-Oxide-Semiconductor (CMOS) process, and integrated it in an array of dynamic synapses connected to an adaptive integrate and fire neuron. We describe the circuit and demonstrate how it can be configured to scale the gain of all synapses afferent to the silicon neuron in a way to keep the neurons average firing rate constant around a set operating point. The circuit occupies a silicon area of 84 {mu}m x 22 {mu}m and consumes approximately 10.8 nW with a 1.8 V supply voltage. It exhibits time constants of up to 25 kilo-seconds, thanks to a controllable leakage current that can be scaled down to 1.2 atto-Amps (7.5 electrons/s).
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