Noise is conventionally viewed as a severe problem in diverse fields, e.g., engineering, learning systems. However, this paper aims to investigate whether the conventional proposition always holds. It begins with the definition of task entropy, which extends from the information entropy and measures the complexity of the task. After introducing the task entropy, the noise can be classified into two kinds, Positive-incentive noise (Pi-noise or $\pi$-noise) and pure noise, according to whether the noise can reduce the complexity of the task. Interestingly, as shown theoretically and empirically, even the simple random noise can be the $\pi$-noise that simplifies the task. $\pi$-noise offers new explanations for some models and provides a new principle for some fields, such as multi-task learning, adversarial training, etc. Moreover, it reminds us to rethink the investigation of noises.

翻译：通常,噪音被视为不同领域(例如工程、学习系统)的一个严重问题。然而,本文旨在调查传统主张是否始终有效。它从任务变异的定义开始,它从信息变异和任务复杂性的测量中延伸而来。在引入任务变异后,噪音可以分为两类:积极激励噪音(Pi-noise 或$-pi-noise)和纯噪音,取决于噪音是否能降低任务的复杂性。有趣的是,正如理论和经验所显示的那样,即使是简单的随机噪音也可以是简化任务的$\pi$-noise。$\pi$-noise为某些模型提供了新的解释,并为一些领域(如多任务学习、对抗训练等)提供了新的原则。此外,它提醒我们重新考虑对噪音的调查。