Abstract: An artificial neural network (ANN), including processing layers which are each configured to process input quantities in accordance with trainable parameters of the ANN to form output quantities. At least one normalizer is inserted into at least one processing layer and/or between at least two processing layers. The normalizer includes a transformation element configured to transform input quantities directed into the normalizer into one or more input vectors, using a predefined transformation. The normalizer also includes a normalizing element configured to normalize the input vector(s) using a normalization function, to form one or more output vectors. The normalization function has at least two different regimes and changes between the regimes as a function of a norm of the input vector at a point and/or in a range, whose position is a function of a predefined parameter. The normalizer also includes an inverse transformation element.

Abstract: A method for training an artificial neural network (ANN), that includes a multiplicity of processing units. Parameters that characterize the behavior of the ANN are optimized with the goal that the ANN maps learning input variable values as well as possible onto associated learning output variable values as determined by a cost function. The output of at least one processing unit is multiplied by a random value x and subsequently supplied as input to at least one further processing unit. The random value x is drawn from a random variable with a probability density function containing an exponential function in |x?q| that decreases as |x?q| increases, where q is a freely selectable position parameter and |x?q| is contained in the argument of the exponential function in powers |x?q|k where k?1. A method for operating an ANN is also described.

Abstract: A method for providing an activation signal for activating an actuator. The activation signal is ascertained as a function of an output signal of a neural network. The neural network includes a scaling layer. The scaling layer maps an input signal present at the input of the scaling layer onto an output signal present at the output of the scaling layer in such a way that this mapping corresponds to a projection of the input signal onto a predefinable value range, parameters being predefinable, which characterize the mapping.

Abstract: A computer-implemented method for training a neural network, which, in particular, is configured to classify physical measuring variables, a fitting of parameters of the neural network occurring as a function of an output signal of the neural network, when the input signal is supplied, and as a function of an associated desired output signal, the fitting of the parameters occurs as a function of an ascertained gradient. The components of the ascertained gradient are scaled as a function of to which layer of the neural network the parameters corresponding to these components belong.

Abstract: A computer-implemented method for training a neural network, which, in particular, is configured to classify physical measuring variables. The neural network is trained with the aid of a training data set. Pairs including an input signal and an associated desired output signal are drawn from the training data set for training. An adaptation of parameters of the neural network occurs as a function of an output signal of the neural network, when the input signal is supplied, and as a function of the desired output signal. The drawing of pairs always takes place from the entire training data set.