HESSPROP: Mitigating Memristive DNN Weight Mapping Errors with Hessian Backpropagation

A universal objective function to minimize mem-ristive crossbar deep neural network weight mapping errors through Hessian backpropagation (HessProp) is presented. Hes-sProp minimizes the
$L_{2}$
norm of the neural network gradient to achieve a flat minima in a neural network's weight space. We hypothesize that this leads to robustness against small perturbations of weights. The stochastic weight mapping phe-nomenon on memristor crossbars is simulated, and the proposed method was evaluated on image classification tasks using the MNIST dataset. The result demonstrates on average 40.81% and 41.45% groundbreaking accuracy increase for distilled and large memristive convolutional neural networks in worst-case scenarios.