The invention specifies a method for operating a hearing system (1) with a hearing instrument (2), wherein an input signal (16) is generated from a sound signal (14) of the environment by at least one electroacoustic input converter (12) of the hearing instrument (2), wherein an output signal (20) is generated from the input signal (16) by means of signal processing, and an output sound signal (24) is generated from the output signal (20) by an electroacoustic output converter (22) of the hearing instrument (2), wherein for at least one sub-process the An artificial neural network (30) is used for signal processing, which is implemented in the hearing system (1), depending on an operation to be carried out in the sub-process and/or depending on an environmental situation and/or depending on a user input by a user of the hearing system (1) a topology of the artificial neural network (30) is defined and/or weights (42) between individual ones Neurons (32) of the artificial neural network (30) are selected. The invention also mentions a corresponding hearing system (1) with a hearing instrument (2).
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