Abstract: A computer-implemented method for training a normalizing flow. The normalizing flow is configured to determine a first output signal characterizing a likelihood or a log-likelihood of an input signal. The normalizing flow includes at least one first layer which includes trainable parameters. A layer input to the first layer is based on the input signal and the first output signal is based on a layer output of the first layer. The training includes: determining at least one training input signal; determining a training output signal for each training input signal using the normalizing flow; determining a first loss value which is based on a likelihood or a log-likelihood of the at least one determined training output signal with respect to a predefined probability distribution; determining an approximation of a gradient of the trainable parameters; updating the trainable parameters of the first layer based on the approximation of the gradient.

Abstract: A computer-implemented method of training an image generation model. The image generation model comprises an argmax transformation configured to compute a discrete index feature indicating an index of a feature of the continuous feature vector with an extreme value. The image generation model is trained using a log-likelihood optimization. This involves obtaining a value of the index feature for the training image, sampling values of the continuous feature vector given the value of the index feature according to a stochastic inverse transformation of the argmax transformation, and determining a likelihood contribution of the argmax transformation for the log-likelihood based on a probability that the stochastic inverse transformation generates the values of the continuous feature vector given the value of the index feature.

Abstract: A lossy data compressor for physical measurement data, comprising a parametrized mapping network hat, when applied to a measurement data point x in a space X, produces a point z in a lower-dimensional manifold Z, and configured to provide a point z on manifold Z as output in response to receiving a data point x as input, wherein the manifold Z is a continuous hypersurface that only admits fully continuous paths between any two points on the hypersurface; and the parameters ? of the mapping network are trainable or trained towards an objective that comprises minimizing, on the manifold Z, a distance between a given prior distribution PZ and a distribution PQ induced on manifold Z by mapping a given set PD of physical measurement data from X onto Z using the mapping network, according to a given distance measure.

Abstract: A lossy data compressor for physical measurement data, comprising a parametrized mapping network hat, when applied to a measurement data point x in a space X, produces a point z in a lower-dimensional manifold Z, and configured to provide a point z on manifold Z as output in response to receiving a data point x as input, wherein the manifold Z is a continuous hypersurface that only admits fully continuous paths between any two points on the hypersurface; and the parameters ? of the mapping network are trainable or trained towards an objective that comprises minimizing, on the manifold Z, a distance between a given prior distribution PZ and a distribution PQ induced on manifold Z by mapping a given set PD of physical measurement data from X onto Z using the mapping network, according to a given distance measure.