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In this paper, the sensitivity of the neural network (NN) outputs to device parameter uncertainties (non-idealities) in inverter-based memristor (IM) crossbar neuromorphic circuits is mathematically modeled and verified using exhaustive circuit and system-level simulations. The NN sensitivity is obtained by modeling the sensitivity of the IM neuron output to the non-idealities of its circuit elements. The analysis reveals a higher sensitivity of the output voltage of the IM neuron to the non-idealities of the inverters compared to the conductance variation of the memristors. Among the inverter non-idealities, horizontal shift of the inverters voltage transfer characteristic (VTC) shows the highest impact on the output voltage of the neuron. To reduce the accuracy loss due to the variations, a training approach which includes a sensitivity term in the cost function of the training phase, is suggested. The achievable improvements through the said NN training approach are evaluated. In the evaluation, the California Housing, MNIST, and Fashion MNIST datasets are employed. The results show up to 50% reduction in the NN output variations in the presence of circuit elements’ non-idealities. [ABSTRACT FROM AUTHOR]