S3M: Static Semi-Segmented Multipliers for Energy-Efficient DNN Inference Accelerators

Approximate multipliers offer an efficient approach to reduce power consumption in compute-intensive applications, such as Deep Neural Networks (DNNs). However, current 8-bit approximate multipliers struggle to maintain high accuracy across various DNN applications. In this paper, we highlight challenges in 8-bit multiplier designs with body approximation strategies and evaluate the effectiveness of input approximation methods. Recognizing that exact multipliers with quantization bit-widths below 8 bits have demonstrated superior performance, we aim to explore whether alternative input approximation methods can provide an even better tradeoff between accuracy and energy consumption. To this end, by exploiting the fact that weight operand values are smaller than activations and prepared offline in DNNs, we simplify a static segmented multiplier (SSM) into a static semi-segmented multiplier <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mathbf{S}^{3}\mathbf{M})$</tex>, achieving a 31.58% reduction in power-delay product (PDP) compared to the original SSM, with similar classification accuracy. Additionally, we propose Coded <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{S}^{3}\mathbf{M}$</tex> with optimized memory usage and im-plement various multipliers on a systolic array-based accelerator. Experimental results show that the proposed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{S}^{3}\mathbf{M}$</tex> and Coded <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{S}^{3}\mathbf{M}$</tex> outperform existing 8-bit approximate multipliers in DNN applications, effectively bridging the PDP and inference accuracy tradeoff observed across exact commercial IP multipliers of varied bit-widths without requiring time-consuming retraining. Consequently, the proposed multiplier designs provide enhanced computational solutions for energy-efficient DNN inference ac-celerators.