A method for training an artificial neural network, in particular a Bayesian neural network, by way of training data sets, having a step of adapting the parameters of the artificial neural network depending on a loss function, the loss function encompassing a first term that represents an estimate of a lower bound of the distances between the classifications of the training data sets by the artificial neural network and the expected classifications of the training data sets. The loss function further encompasses a second term that is configured in such a way that differences in the aleatoric uncertainty in the training data sets over different samples of the artificial neural network are regulated.