A theory of geometry representations for spatial navigation

The geometric information of space, such as environment boundaries, is represented heterogeneously across brain regions. The computational mechanisms of encoding the spatial layout of environments remain to be determined. Here, we postulate a conjunctive encoding theory to illustrate the construct of cognitive maps from geometric perception. The theory naturally describes a spectrum of cell types including experimentally observed boundary vector cells, border cells, "annulus" and "bulls-eye" cells as special examples. In a similar way, inspired by the integration of egocentric and allocentric information as found in the postrhinal cortex, the theory also predicts a new cell type, named geometry cell. Geometry cells encode the geometric layout of the local space relative to the environment center, independent of the animal's positions and headings within the local space. The predicted geometry cell provides pure allocentric high-level representations of local scenes to support the quick formation of cognitive map representations capturing the spatial layout of complex environments. The theory sheds new light on the neural mechanisms of spatial cognition and brain-inspired autonomous intelligent systems.