An Architectural Error Metric for CNN-Oriented Approximate Multipliers

TL;DR

The paper tackles the challenge of predicting AM-CNN accuracy for CNN accelerators using approximate multipliers by proposing the architectural mean error (AME), a metric that fuses CNN architectural information with AM error characteristics. It builds a linear error-generation and propagation model, deriving AME as a Frobenius inner product between architectural matrices and AM error matrices, capturing how errors accumulate through convolutional, nonlinear, batch normalization, and residual layers. Empirical results across VGG-16 and ResNet variants on CIFAR-10/100 and ImageNet show AME correlates strongly with accuracy and enables 3% deviation in accuracy predictions via quadratic regression, with speedups around 10^6× compared to GPU-based simulations. The approach is demonstrated to effectively accelerate AM selection and design, including Pareto optimization over AM libraries like EvoApprox8b, while enabling scalable automated design for CNN-oriented approximate computing.

Abstract

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.

Figures (10)

• Figure 1: Scatterplot of AM-based convolutional layers, where the abscissa is the ${\rm E}(e)$ estimated by using (\ref{['eq:E_estimate']}), and the ordinate is the $\mu(e)$ measured by using (\ref{['eq:ME_layer']}).
• Figure 2: The proposed linear error propagation model.
• Figure 3: $\alpha$ values for four AM-based approximate convolutional layers and a max pooling layer in VGG-16 on CIFAR-10.
• Figure 4: Example of error estimation.
• Figure 5: Overview of the experiments.