Positive-incentive Noise

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 $π$-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 $π$-noise that simplifies the task. $π$-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.