  Memristors enable the computation of matrix-vector multiplications (MVM) in
memory and, therefore, show great potential in highly increasing the energy
efficiency of deep neural network (DNN) inference accelerators. However,
computations in memristors suffer from hardware non-idealities and are subject
to different sources of noise that may negatively impact system performance. In
this work, we theoretically analyze the mean squared error of DNNs that use
memristor crossbars to compute MVM. We take into account both the quantization
noise, due to the necessity of reducing the DNN model size, and the programming
noise, stemming from the variability during the programming of the memristance
value. Simulations on pre-trained DNN models showcase the accuracy of the
analytical prediction. Furthermore the proposed method is almost two order of
magnitude faster than Monte-Carlo simulation, thus making it possible to
optimize the implementation parameters to achieve minimal error for a given
power constraint.
