A universal objective function to minimize memristive crossbar deep neural network weight mapping errors through Hessian backpropagation (HessProp) is presented. HessProp minimizes the L2 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. Stochastic weight mapping phenomenon on memristor crossbar 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.