Evaluation of Application-Independent Unbiased Approximate Multipliers on Quantized Convolutional Neural Networks

Unbiasedness is considered an important property when applying approximate multipliers in applications that involve consecutive multiplication operations, and mean error (ME) is an application-independent error metric that can demonstrate the unbiasedness of an approximate multiplier. A few prior works have claimed that application-independent error metrics cannot guarantee reliable performance for real deep learning applications, but the effectiveness of ME on such applications has not been fully explored. This paper aims to fill this gap by providing Zero-ME 8-bit approximate multipliers based on the proposed double-carry 4-2 approximate compressor and evaluating the application-independent error metrics, including ME, and the classification accuracy of quantized convolutional neural networks (CNNs). The experimental results suggest that the proposed Zero-ME 8-7 multiplier has the potential as a low-power circuit for CNNs based on approximate multiplication. However, the results also indicate that evaluating the effect of bias in approximate multipliers for CNN applications using ME is insufficient, and it is expected to develop a new application-specific method for designing unbiased multipliers and a corresponding error metric.