On the Non-Associativity of Analog Computations
This addresses a critical reliability issue for deploying energy-efficient analog computing in resource-constrained systems like mobile devices, though it is incremental in highlighting a specific imperfection.
The paper demonstrates that analog computations are non-associative due to operand ordering effects, leading to substantial accuracy drops in neural networks for keyword spotting when these effects are neglected.
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.