  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.
