  We describe an approximation to backpropagation algorithm for training deep
neural networks, which is designed to work with synapses implemented with
memristors. The key idea is to represent the values of both the input signal
and the backpropagated delta value with a series of pulses that trigger
multiple positive or negative updates of the synaptic weight, and to use the
min operation instead of the product of the two signals. In computational
simulations, we show that the proposed approximation to backpropagation is well
converged and may be suitable for memristor implementations of multilayer
neural networks.
