Spatial remapping in the subicular complex and entorhinal cortex follows low-dimensional geometric principles

Neurons in the hippocampal formation are part of the brain's cognitive map, representing the spatial structure of the environment through coordinated activity across place cells, grid cells, border cells, head-direction cells and others^1-5. Although remapping between environments has been extensively documented^6-9, it remains unknown whether transitions between maps reflect unconstrained reorganization or obey a systematic transformation principle. To address this question, we recorded large neuronal populations from the subicular complex and entorhinal cortex in awake, behaving mice navigating environments spanning a wide range of geometries. We asked whether spatial representations across rooms could be related through a shared class of coordinate transformations. Despite pronounced heterogeneity and apparent randomness in single-cell remapping, population-level decoding across environments demonstrated a consistent low-dimensional affine transformation of coordinates, comprising rotation, scaling, shear, reflection, and translation. Thus, what appears as complex remapping at the level of individual neurons reduces to a compact geometric rule at the level of neural assemblies. These results indicate that the hippocampal formation maintains a structured internal coordinate template that is flexibly tailored to environmental geometry. This may serve as the organism's internal model of space.