Abstract: A computer-implemented method of training a machine learnable model for controlling and/or monitoring a computer-controlled system. The machine learnable model is configured to make inferences based on a probability distribution of sensor data of the computer-controlled system. The machine learnable model is configured to account for symmetries in the probability distribution imposed by the system and/or its environment. The training involves sampling multiple samples of the sensor data according to the probability distribution. Initial values are sampled from a source probability distribution invariant to the one or more symmetries. The samples are iteratively evolved according to a kernel function equivariant to the one or more symmetries. The evolution uses an attraction term and a repulsion term that are defined for a selected sample in terms of gradient directions of the probability distribution and of the kernel function for the multiple samples.

Abstract: A computer-implemented method of training a machine learnable model for controlling and/or monitoring a computer-controlled system. The machine learnable model is configured to make inferences based on a probability distribution of sensor data of the computer-controlled system. The machine learnable model is configured to account for symmetries in the probability distribution imposed by the system and/or its environment. The training involves sampling multiple samples of the sensor data according to the probability distribution. Initial values are sampled from a source probability distribution invariant to the one or more symmetries. The samples are iteratively evolved according to a kernel function equivariant to the one or more symmetries. The evolution uses an attraction term and a repulsion term that are defined for a selected sample in terms of gradient directions of the probability distribution and of the kernel function for the multiple samples.