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Soft errors in large VLSI circuits pose dramatic influence on computing- andmemory-intensive neural network (NN) processing. Understanding the influence ofsoft errors on NNs is critical to protect against soft errors for reliable NNprocessing. Prior work mainly rely on fault simulation to analyze the influenceof soft errors on NN processing. They are accurate but usually specific tolimited configurations of errors and NN models due to the prohibitively slowsimulation speed especially for large NN models and datasets. With theobservation that the influence of soft errors propagates across a large numberof neurons and accumulates as well, we propose to characterize the soft errorinduced data disturbance on each neuron with normal distribution modelaccording to central limit theorem and develop a series of statistical modelsto analyze the behavior of NN models under soft errors in general. Thestatistical models reveal not only the correlation between soft errors and NNmodel accuracy, but also how NN parameters such as quantization andarchitecture affect the reliability of NNs. The proposed models are comparedwith fault simulation and verified comprehensively. In addition, we observethat the statistical models that characterize the soft error influence can alsobe utilized to predict fault simulation results in many cases and we explorethe use of the proposed statistical models to accelerate fault simulations ofNNs. According to our experiments, the accelerated fault simulation showsalmost two orders of magnitude speedup with negligible simulation accuracy lossover the baseline fault simulations.

Statistical Modeling of Soft Error Influence on Neural Networks