This article analyzes the effects of approximate multiplication when performing inferences on deep convolutional neural networks (CNNs). The approximate multiplication can reduce the cost of the underlying circuits so that CNN inferences can be performed more efficiently in hardware accelerators. The study identifies the critical factors in the convolution, fully-connected, and batch normalization layers that allow more accurate CNN predictions despite the errors from approximate multiplication. The same factors also provide an arithmetic explanation of why bfloat16 multiplication performs well on CNNs. The experiments are performed with recognized network architectures to show that the approximate multipliers can produce predictions that are nearly as accurate as the FP32 references, without additional training. For example, the ResNet and Inception-v4 models with Mitch-$w$w6 multiplication produces Top-5 errors that are within 0.2 percent compared to the FP32 references. A brief cost comparison of Mitch-$w$w6 against bfloat16 is presented where a MAC operation saves up to 80 percent of energy compared to the bfloat16 arithmetic. The most far-reaching contribution of this article is the analytical justification that multiplications can be approximated while additions need to be exact in CNN MAC operations.

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近似乘法对卷积神经网络的影响

本文分析了在对深度卷积神经网络 (CNN) 进行推理时近似乘法的影响。近似乘法可以降低底层电路的成本，从而可以在硬件加速器中更高效地执行 CNN 推理。该研究确定了卷积层、全连接层和批量归一化层中的关键因素，这些因素允许更准确的 CNN 预测，尽管存在近似乘法的误差。同样的因素也提供了为什么 bfloat16 乘法在 CNN 上表现良好的算术解释。实验是使用公认的网络架构进行的，以表明近似乘数可以产生几乎与 FP32 参考一样准确的预测，而无需额外的训练。例如，$w$w与 FP32 参考相比，6 乘法产生的 Top-5 误差在 0.2% 以内。Mitch的简要成本比较-$w$w6 与 bfloat16 相比，MAC 运算与 bfloat16 算法相比可节省高达 80% 的能量。本文最深远的贡献是在 CNN MAC 操作中乘法可以近似而加法需要精确的分析证明。