Manifolds for the neural representation of 3D spatial experience

The precision with which animals navigate and interact with objects depends in part on how their brains represent position and orientation in three dimensions. A central challenge is to explain within a common framework how neural systems ranging from insects to primates represent three-dimensional (3D) pose. Here we develop a framework based on the hypothesis that neural representations of pose lie on manifolds derived from the Special Euclidean Group, SE(3), which describes the full space of rigid-body positions and orientations in three dimensions. The framework shows how movement constraints, object geometry, and visual features jointly determine the topology of the resulting pose manifold, yielding a taxonomy that guides experimental tests. We apply the framework to derive low-dimensional manifolds for neural representations of 3D object orientation in macaque parietal cortex and head direction in the limbic systems of fruit bats, mice, and monkeys. This analysis also guides the construction of neuronal tuning functions that respect the topology determined by experimental conditions. Together, these results provide a common approach for linking the geometry of 3D pose to neural coding across species and brain systems.