As a potential alternative for implementing the large number of multiplications in convolutional neural networks (CNNs), approximate multipliers (AMs) promise both high hardware efficiency and accuracy. However, the characterization of accuracy and design of appropriate AMs are critical to an AM-based CNN (AM-CNN). In this work, the generation and propagation of errors in an AM-CNN are analyzed by considering the CNN architecture. Based on this analysis, a novel AM error metric is proposed to evaluate the accuracy degradation of an AM-CNN, denoted as the architectural mean error (AME). The effectiveness of the AME is assessed in VGG and ResNet on CIFAR-10, CIFAR-100, and ImageNet datasets. Experimental results show that AME exhibits a strong correlation with the accuracy of AM-CNNs, outperforming the other AM error metrics. To predict the accuracy of AM-CNNs, quadratic regression models are constructed based on the AME; the predictions show an average of 3% deviation from the ground-truth values. Compared with a GPU-based simulation, the AME-based prediction is about $10^{6}\times$ faster.

翻译：作为实现卷积神经网络（CNN）中大量乘法运算的潜在替代方案，近似乘法器（AM）在硬件效率和精度方面均展现出良好前景。然而，精度表征与合适AM的设计对于基于AM的CNN（AM-CNN）至关重要。本工作通过考虑CNN架构，分析了AM-CNN中误差的产生与传播机制。基于此分析，我们提出了一种新颖的AM误差度量方法，用以评估AM-CNN的精度衰减，称为架构平均误差（AME）。在CIFAR-10、CIFAR-100和ImageNet数据集上，通过VGG和ResNet网络评估了AME的有效性。实验结果表明，AME与AM-CNN的精度表现出强相关性，其性能优于其他AM误差度量方法。为预测AM-CNN的精度，我们基于AME构建了二次回归模型；预测值与真实值的平均偏差约为3%。与基于GPU的模拟方法相比，基于AME的预测速度提升了约$10^{6}\times$。