Abstract: A hierarchical network as a simple model of the visual system is presented and trained with an algorithm for unsupervised learning of invariances. The input layer is a one-dimensional retinal layer with 65 units. Stimulus patterns are derived from sections of low-pass filtered Gaussian white noise. When the network is trained with patterns that vary with respect to a certain aspect (location, size, contrast, rotation (cyclic shift), or illumination), it learns a representation that is largely invariant to that aspect and can be used for pattern recognition. The results support the view that invariances can be learned in the visual system based on visual experience.