COSAIM: Counter-based Stochastic-behaving Approximate Integer Multiplier for Deep Neural Networks
COSAIM: Counter-based Stochastic-behaving Approximate Integer Multiplier for Deep Neural Networks
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COSAIM：深度神经网络的基于计数器的随机行为近似整数乘法器
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发表时间：
2021
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通讯作者：
S. Tan
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作者：
Shuyuan Yu;Yibo Liu;S. Tan
在这项工作中，我们针对许多新兴的容错应用程序工作负载（例如深度神经网络）提出了一种新的基于计数器的随机行为近似整数无符号乘法器，称为 COSAIM。与基于某些确定性临时方法或数学公式的现有近似乘法器不同，新设计是改进的随机乘法器，它以确定性方式对乘法运算执行改进的顺序计数。在这项工作中，我们通过引入近似方案来进一步提高计数效率，显着加快计数过程，从而显着减少时钟周期而不损失精度。 COSAIM 具有随机计算的所有优点，例如用于渐进性能与精度权衡的内置可配置性。同时，它表现出非常小的延迟和高能效。我们的评估表明，具有误差改进操作的 COSAIM 可以实现非常低的误差偏差 (0.06%)，以及较低的平均误差 (0.30% 至 3.49%) 和低峰值误差 (约 1.81%)，方差为 1. $47 imes 10^{-4}$ %。 Xilinx ISE 的实验结果表明，与 8 位精确乘法器基线相比，COSAIM 在面积、功耗、能源和产品面积方面最多可节省 53.95%、32.84%、52.24%、21.05%。分别为 1/吞吐量。此外，通过共享并行设计，COSAIM 可以进一步导致面积、功率和能耗比基线分别减少 60.44%、53.33% 和 68.54%。我们还在卷积神经网络 (CNN) 中实现 COSAIM，并在 CIFAR10 数据集上进行测试，发现使用 COSAIM 的 CNN 与某些最先进的近似乘法器相比可提供相似的推理精度。
In this work, we propose a new counter-based stochastic-behaving approximate integer unsigned multiplier, called COSAIM, for many emerging error tolerant application workloads such as deep neural networks. Unlike existing approximate multipliers, which are based on some deterministic ad-hoc methods or mathematical formula, the new design is an improved stochastic multiplier, which performs improved sequential counting for multiplication operation in a deterministic way. In this work, we further improve the counting efficiency by introducing approximate schemes to significantly speed up the counting process, which leads to significant clock cycle reduction with no accuracy loss. COSAIM bears all the advantages of stochastic computing such as built-in configurability for progressive performance-accuracy trade-off. At the same time, it shows very small latency and high energy efficiency. Our evaluation shows that the COSAIM with error improvement operation can achieve very low error bias (0.06%), along with lower mean error (0.30% to 3.49%), and low peak errors (around 1.81%) with variance of 1. $47 imes 10^{-4}$ %. Experimental results obtained from Xilinx ISE show that compared with the 8-bit exact multiplier baseline, COSAIM can save up to 53.95%, 32.84%, 52.24%, 21.05% in area, power, energy and the product Area. 1/Throughput, respectively. Furthermore, by doing shared parallel design, COSAIM can further lead to improvements in area, power and energy reduction by 60.44%, 53.33% and 68.54%, respectively compared to the baseline. We also implement COSAIM in a Convolution Neural Network (CNN) and test it on CIFAR10 dataset and find that CNN with COSAIM delivers similar inference accuracy compared to some state of art approximate multipliers.