Soft errors in large VLSI circuits pose dramatic influence on computing- and memory-intensive neural network (NN) processing. Understanding the influence of soft errors on NNs is critical to protect against soft errors for reliable NN processing. Prior work mainly rely on fault simulation to analyze the influence of soft errors on NN processing. They are accurate but usually specific to limited configurations of errors and NN models due to the prohibitively slow simulation speed especially for large NN models and datasets. With the observation that the influence of soft errors propagates across a large number of neurons and accumulates as well, we propose to characterize the soft error induced data disturbance on each neuron with normal distribution model according to central limit theorem and develop a series of statistical models to analyze the behavior of NN models under soft errors in general. The statistical models reveal not only the correlation between soft errors and NN model accuracy, but also how NN parameters such as quantization and architecture affect the reliability of NNs. The proposed models are compared with fault simulation and verified comprehensively. In addition, we observe that the statistical models that characterize the soft error influence can also be utilized to predict fault simulation results in many cases and we explore the use of the proposed statistical models to accelerate fault simulations of NNs. According to our experiments, the accelerated fault simulation shows almost two orders of magnitude speedup with negligible simulation accuracy loss over the baseline fault simulations.
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