The molecular regulatory network underlying stem cell pluripotency has been intensively studied, and we now have a reliable ensemble model for the “average” pluripotent cell. However, evidence of significant cell-to-cell variability suggests that the activity of this network varies within individual stem cells, leading to differential processing of environmental signals and variability in cell fates. Here, we adapt a method originally designed for face recognition to infer regulatory network patterns within individual cells from single-cell expression data. Using this method we identify three distinct network configurations in cultured mouse embryonic stem cells—corresponding to naïve and formative pluripotent states and an early primitive endoderm state—and associate these configurations with particular combinations of regulatory network activity archetypes that govern different aspects of the cell's response to environmental stimuli, cell cycle status and core information processing circuitry. These results show how variability in cell identities arise naturally from alterations in underlying regulatory network dynamics and demonstrate how methods from machine learning may be used to better understand single cell biology, and the collective dynamics of cell communities.