A method operates a hearing aid system having a hearing instrument. An electro-acoustic input transducer of the hearing instrument generates an input signal from an acoustic signal from the environment, and an output signal is generated from the input signal by a signal processor. An output acoustic signal is generated from the output signal by an electro-acoustic output transducer of the hearing instrument. For at least one sub-process of the signal processing an artificial neural network is used which is implemented in the hearing instrument. A topology of the artificial neural network is defined and/or weights between individual neurons of the artificial neural network are selected according to an operation to be performed in the sub-process and/or according to an ambient situation and/or according to a user input by a user of the hearing aid system.