Output Error Estimation for Memristor-Based Deep Neural Networks

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Abstract—Memristors allow computing in memory, which maybe leveraged by deep neural network (DNN) accelerators toreduce energy footprint. However, such gains in energy efficiencycome at the cost of noise on the computation results due tothe analog nature of memristors. In this work, we introducea theoretical framework to estimate the mean squared error(MSE) of a memristor-based DNN. We propose an efficientsoftware implementation of this framework which is shown to beorders of magnitude faster than using Monte-Carlo simulations.Additionally, we study two different techniques for mappingconvolutional layers to memristors and compare their relativeimpact on the mean squared error and its computation time. Theaccuracy of the proposed analysis is first evaluated on a simpleregression problem, and then on a more complex classificationtask with a network capable of achieving high accuracy on theCIFAR-10 dataset, which shows that our method is efficient overpractical up-to-date DNNs. The proposed framework is thenused to perform a meta-heuristic optimization of the memristormaximal conductance value so as to minimize the energy usage.

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