Neural networks include neuron layers arranged in order from an input neuron layer to an output neuron layer, with at least one hidden layer between them. Weight arrays between respective pairs of neuron layers each include controllable resistance elements and AND gates configured to control addressing of the plurality of controllable resistance elements. Each controllable resistance element includes a junction field effect transistor configured to provide a resistance on a signal line and a first pass transistor configured to apply a charge increment or decrement to the junction field effect transistor responsive to a control pulse, such that the resistance on the signal line changes. The control pulse is only passed to a controllable resistance element when a respective AND gate is triggered. A training module is configured to train the neural network by adjusting resistances of the plurality of controllable resistance elements in each of the weight arrays.