Mixing Low-Precision Formats in Multiply-Accumulate Units for DNN Training

Mariko Tatsumi, Silviu-Ioan Filip, Caroline White, Olivier Sentieys, Guy Lemieux
Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, Canada
hal-03885471, (December 5, 2022)


   title={Mixing Low-Precision Formats in Multiply-Accumulate Units for DNN Training},

   author={Tatsumi, Mariko and Filip, Silviu-Ioan and White, Caroline and Sentieys, Olivier and Lemieux, Guy},

   booktitle={IEEE International Conference on Field Programmable Technology (FPT)},



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The most compute-intensive stage of deep neural network (DNN) training is matrix multiplication where the multiply-accumulate (MAC) operator is key. To reduce training costs, we consider using low-precision arithmetic for MAC operations. While low-precision training has been investigated in prior work, the focus has been on reducing the number of bits in weights or activations without compromising accuracy. In contrast, the focus in this paper is on implementation details beyond weight or activation width that affect area and accuracy. In particular, we investigate the impact of fixed-versus floating-point representations, multiplier rounding, and floatingpoint exceptional value support. Results suggest that (1) lowprecision floating-point is more area-effective than fixed-point for multiplication, (2) standard IEEE-754 rules for subnormals, NaNs, and intermediate rounding serve little to no value in terms of accuracy but contribute significantly to area, (3) lowprecision MACs require an adaptive loss-scaling step during training to compensate for limited representation range, and (4) fixed-point is more area-effective for accumulation, but the cost of format conversion and downstream logic can swamp the savings. Finally, we note that future work should investigate accumulation structures beyond the MAC level to achieve further gains.
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