A Machine Learning-based Error Model for Quality Control of Functional Approximate Computing

Approximate computing (AC) is a prominent computing standard, which is used in some applications that could tolerate accuracy for enhanced design efficiency. AC demonstrates the effectiveness of functional approximation in digital circuits, e.g., adders, subtractors, dividers and multipliers, in order to reduce the accuracy of the final results for energy saving. An accurate model of the approximation error is considered signifi-cant for estimating the error behavior, especially for functionally approximated arithmetic units and its impact on the final quality of applications. However, current error models are unable to address the impacts of input data and the deviation of output quality among different inputs. In order to address this hurdle, we propose a decision tree-based error model of approximated arithmetic circuits that is able to forecast the error magnitude for each input. The proposed model is trained using a decision tree (DT) algorithm with two input features and one output labels, which are based on functional simulation. As a case study, we built the models and evaluate their accuracy for 20 different designs of 8-bit approximate array multipliers. Across the 20 circuits, their error models achieve an average accuracy of 94.5%. To evaluate their effectiveness at the application level, we used image processing applications. Accordingly, the proposed model can estimate the quality of image processing under functional approximation with a medium accuracy of 97.5% for image blending, and 94% for image Gaussian filtering.