1. A system for implementing a neural network, the system comprising: a crosspoint array comprising a plurality of nodes, each node representing a weight assigned to a neuron of the neural network; a capacitor associated with a set of nodes from the plurality of nodes, wherein the capacitor is configured to store a current value corresponding to a sum of outputs from each respective node from the set of nodes; and a clocking circuit comprises a first clocking device, a second clocking device, a third clocking device, and a fourth clocking device, wherein the clocking circuit is configured to: initiate a forward pass to propagate the current value stored in the capacitor to a subsequent layer of the neural network by setting the second clocking device and the third clocking device; initiate a backward pass to propagate the current value stored in the capacitor to a preceding layer of the neural network by setting the first clocking device and the third clocking device; and initiate a weight-update pass to update the weights in the neural network by setting the second clocking device and the fourth clocking device.