分析近似乘法器如何影响深度神经网络精度，提出快速评估方案。
Approximate Multiplier Induced Error Propagation in Deep Neural Networks
- 建立近似乘法器误差与矩阵运算误差的数学关联模型。
- 发现误差主要由乘法器均值偏差主导，且预测与实测结果高度一致。
- 适合芯片设计者快速评估硬件近似计算对模型性能的影响。
深度神经网络（DNN）依赖密集的算术运算，促使使用近似乘法器（AxMs）以降低硬件加速器的能耗。然而，关于AxM误差分布如何影响DNN准确率的严谨数学表征仍不充分。本文提出一种分析框架，将AxM的统计误差矩与通用矩阵乘法（GEMM）中的误差失真相联系。通过误差矩阵的Frobenius范数，推导出适用于实际DNN规模的闭式表达式，表明失真主要由乘法器均值误差（偏置）决定。为在真实场景中验证该模型，我们在GEMM和卷积层中引入可控误差注入，并考察其对ImageNet规模网络的影响。预测失真与观察到的精度下降高度相关，基于FPGA实现的可配置误差AxM案例研究进一步验证了分析趋势。该框架为行为级或硬件级仿真提供了轻量级替代方案，可快速估算AxM对DNN推理质量的影响。
原文摘要 · Abstract (English)
Deep Neural Networks (DNNs) rely heavily on dense arithmetic operations, motivating the use of Approximate Multipliers (AxMs) to reduce energy consumption in hardware accelerators. However, a rigorous mathematical characterization of how AxMs error distributions influence DNN accuracy remains underdeveloped. This work presents an analytical framework that connects the statistical error moments of an AxM to the induced distortion in General Matrix Multiplication (GEMM). Using the Frobenius norm of the resulting error matrix, we derive a closed form expression for practical DNN dimensions that demonstrates the distortion is predominantly governed by the multiplier mean error (bias). To evaluate this model in realistic settings, we incorporate controlled error injection into GEMM and convolution layers and examine its effect on ImageNet scale networks. The predicted distortion correlates strongly with the observed accuracy degradation, and an error configurable AxM case study implemented on an FPGA further confirms the analytical trends. By providing a lightweight alternative to behavioral or hardware level simulations, this framework enables rapid estimation of AxM impact on DNN inference quality.
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