The energy efficiency of analog forms of computing makes it one of the most
promising candidates to deploy resource-hungry machine learning tasks on
resource-constrained system such as mobile or embedded devices. However, it is
well known that for analog computations the safety net of discretization is
missing, thus all analog computations are exposed to a variety of imperfections
of corresponding implementations. Examples include non-linearities, saturation
effect and various forms of noise. In this work, we observe that the ordering
of input operands of an analog operation also has an impact on the output
result, which essentially makes analog computations non-associative, even
though the underlying operation might be mathematically associative. We conduct
a simple test by creating a model of a real analog processor which captures
such ordering effects. With this model we assess the importance of ordering by
comparing the test accuracy of a neural network for keyword spotting, which is
trained based either on an ordered model, on a non-ordered variant, and on real
hardware. The results prove the existence of ordering effects as well as their
high impact, as neglecting ordering results in substantial accuracy drops.

电流计算在能效方面表现出色，然而由于缺乏离散化的安全网，存在多种实现上的缺陷，如非线性、饱和效应和各种噪声。本研究观察到模拟操作的输入操作数的顺序也对输出结果有影响，这使得模拟计算非关联，即使底层操作可能在数学上是关联的。通过创建一个捕捉顺序效应的实际模拟处理器模型，本文对此进行了简单测试，并通过比较关键词识别神经网络的测试精度来评估顺序的重要性，其中网络基于有序模型、无序变体或实际硬件进行训练。结果证明了顺序效应的存在以及其高影响，因为忽略顺序会导致显著的精度降低。