A proper account of the neural computations involved in visual cognition must address, among other things, structure and similarity. In this work we present a set of behavioral experiments that investigate the effect of hierarchic structures in visual cognition, and suggest that learning the correct category of visual stimuli is easier when their underlying generative distributions are organized more hierarchically. We then go on to discuss the implications of the Reproducing Kernel Hilbert Space theory for measurements of similarity in neural settings, and discuss a number of empirical findings that suggest the brain in fact relies on kernel-like computations at various stages of processing.