Working memory allows us to selectively remember and flexibly manipulate a limited amount of information. Importantly, once we learn a certain operation, it generalizes to any memory object, not just the objects it has been trained on. Here we propose a conceptual model for how this might be achieved on the neural network level. It relies on spatial computing, in which sensory information flows spatially within the network over time. As a result, information about, for instance, object order can be retrieved agnostically to the detailed synaptic connectivity responsible for encoding specific memory items. This spatial flow is reflected in low-dimensional brain activity complementing high-dimensional activity that accounts for storing the sensory information itself. By comparing the dimensionality of local field potentials and spiking activity from prefrontal cortex of rhesus macaques performing multi-item working memory tasks we verify predictions from this model. We discuss how spatial computing may be a principle to aid generalization and zero-shot learning by utilizing spatial dimensions as an additional information encoding dimension. The new model also helps explain several aspects of neurophysiological activity related to working memory control, including dimensionality, context-dependent selectivity as well as persistent and non-persistent delay activity.