Cognitive activity emerges from large-scale neuronal dynamics that are constrained to a low-dimensional manifold. How this low-dimensional manifold scales with cognitive complexity, and which brain regions regulate this process, are not well understood. We addressed this issue by analyzing sub-second high-field fMRI data acquired during performance of a task that systematically varied the complexity of cognitive reasoning. We show that task performance reconfigures the low-dimensional manifold and that deviations from these patterns relate to performance errors. We further demonstrate that individual differences in thalamic activity relate to reconfigurations of the low-dimensional architecture during task engagement.