Novel hybrid probabilistic–statistical error metrics for approximate adders

Approximate computing (AxC) has emerged as a promising approach for improving error-tolerant applications’ performance and energy efficiency. The approximate adder designs provide disproportionate energy and performance gains at the cost of a bounded loss in precision. The existing error metrics provide limited insights into error generation and propagation and correlate poorly with end-application quality-of-result (QoR). In this paper, we propose four novel error metrics for approximate adders that bring together the best of statistical and probabilistic approaches. These metrics are based on the probabilistic adder-dependent error-generation vector ($\overrightarrow{AGV},$) and the input-dependent error-propagation vector ($\overrightarrow{IPV}$). Our proposed metrics decouple error generation from propagation and model the impact of both adder characteristics and (application-dependent) input distribution. Extensive evaluation with 28 approximate adders over three real-world applications (Gaussian Smoothing, Support Vector Machine, and Neural Network evaluated on datasets such as MNIST, CIFAR-10, and ImageNet) shows that our metrics are more strongly correlated with application QoR than conventional metrics such as mean relative error distance (MRED), worst-case error (WCE) or error-rate (ER). Our metrics also help identify suitable adder designs for different applications. We will open-source our code.