Abstract: An invention based on learning a discrete recurrent neural network for a given signal domain is described. In one implementation to the domain of visual images, the method can be used to efficiently compress digital photographs and to devise a new perceptual distortion measure between images that well-matches data collected from a human psychophysics experiment. Other applications of the invention include unsupervised detection of recurrent patterns in high-dimensional data and Shannon-optimal error-correcting coding from few training examples.