LEVAX: An Input-Aware Learning-Based Error Model of Voltage-Scaled Functional Units

Abstract

As Moore's Law comes to an end and transistor scaling increasingly falls short in improving energy efficiency, alternative computing paradigms are direly needed. This need is further highlighted by the overwhelming increase in computing demand posed by emerging applications such as multimedia and data analysis. Fortunately, such driving workloads also present new opportunities since, thanks to their inherent error tolerance, they do not require completely accurate computations. Thus, by trading off accuracy for better performance or improved efficiency, approximate computing promises tremendous growth for future computing. Various approximation methods demonstrate the effectiveness of voltage scaling in functional units (FUs) for exploring this energy-error trade-off. Yet, while an accurate error model is critical for assessing the error behavior of voltagescaled FUs and its effects on application quality, existing error models of voltage-scaled FUs overlook the effects of input data and error rate disparity among different bits. To tackle this challenge, we propose LEVAX, an input-aware learning-based error model of voltage-scaled FUs that can predict the timing error rate (TER) for each output bit. This model is trained using random forest methods, with input features and output labels extracted from gate-level simulations. To validate its effectiveness and demonstrate its prediction accuracy, we use LEVAX on various FUs. Across all bit positions, voltage levels, and FUs, LEVAX achieves, on average, a relative error of 1.20%. LEVAX also achieves an average per-voltage Root Mean Square Error (RMSE) of 1.03% and per-bit RMSE of 1.17%. Exposing this error rate even up to the application level, LEVAX can estimate the quality of four image processing applications under voltage scaling with an average accuracy of 97.9%. To the best of our knowledge, LEVAX is the first voltage scaling error model of FUs that can incorporate the effects of input data.

Instruction-aware Learning-based Timing Error Models through Significance-driven Approximations

“…d) Training process: We utilize Random Forest (RF), a widely used supervised classification algorithm, using the scikit-learn framework of python, which is consistent with what have been reported in prior ML-based prediction studies [11], [14], [15]. We utilize a tuning technique (i.e., grid search) to fine-tune the hyperparameters of our model, to achieve better results.…”

“…Subsequent work [11], [15], [17], [31], [32], which studied the correlation between instruction history and errors, indi- cated that besides the currently executed instruction, only the instruction in the previous cycle affects timing errors, neglecting the influence of all the concurrently executed instructions in the pipeline. A later study [13] considers the full pipeline depth for predicting timing errors, however, it is operand agnostic, and thereby, cannot predict bit-level timing errors (i.e., the exact bit location where timing errors occur).…”

“…Such studies may have showcased the potential of using ML on error prediction, but have left a lot of room for improvement. Actually, recent studies have either neglected important microarchitecture features [11], [12], [15] or have left unexplored more critical operating regions [14]. Moreover, they have not yet exploited approximate computing techniques, that could enable trade-offs between accuracy and inference time (required prediction time per sample), which may prove useful in speeding up error injection campaigns and realizing effective run-time error-aware system power management schemes.…”