Methods, hearing systems and neural networks for audio signal processing are described. A hearing system comprises a neural network. An input audio signal is processed into an output audio signal at least partially by means of a processing unit of the hearing system. The audio signal processing of the input audio signal includes executing audio signal processing by the neural network for performing a step of the audio signal processing, determining a confidence parameter resembling the reliability of the audio signal processing by the neural network and steering the audio signal processing in dependence of the confidence parameter. A particularly suitable neural network is configured to solve a regression-based acoustic processing task and additionally determining the confidence parameter.