A neural network is implemented as a memristive neuromorphic circuit that includes a neuron circuit and a memristive device connected to the neuron circuit. An input voltage is sensed at a first terminal of a memristive device during a feedforward operation of the neural network. An error voltage is sensed at a second terminal of the memristive device during an error backpropagation operation of the neural network. In accordance with a training rule, a desired conductance change for the memristive device is computed based on the sensed input voltage and the sensed error voltage. Then a training voltage is applied to the memristive device. Here, the training voltage is proportional to a logarithmic value of the desired conductance change.