Brain maps (e.g. retinotopy, somatotopy) vary across individuals. This is thought to reflect underlying computational differences. However, artificial neural networks (ANNs) show that similar performance and internal representations can coexist with diverse circuit layouts. Consequently, we tested the presumption that spatial diversity reflects representational diversity in the brain, but found this presumption often breaks down. Using task and resting-state fMRI data we compared regional functional topographies and representational geometries-the within-individual dissimilarities among activity patterns. Across individuals ( n = 414), representations converged in higher-order cortex despite substantial topographic diversity, indicating that similar information was encoded by different, individual-specific activity patterns. Topography only tracked representational differences in sensory-motor cortices and regions under strong architectural constraints, such as myelination or laminar differentiation. We show this parallels ANNs: architectural permissiveness allows idiosyncratic layouts to arise from random initializations rather than learned representations. To test whether topographies and representations show analogous developmental origins, we examined twins ( n = 394), and found topographies were more heritable than representations. This shows that representational convergence occurs across idiosyncratic layouts in both artificial and biological systems, but is moderated by architectural constraints on implementation flexibility. Accordingly, the relevance of localization- and representation-based paradigms of brain function depends on neural architecture.