Grid Cells, Modules, and Hexagonal Tiling of Space
Grid cells in medial entorhinal cortex provide a periodic, hexagonally tiled spatial coordinate system that complements hippocampal place cells in representing an animal’s location.
Torus-Shaped Neural Manifolds of Grid Cell Populations
Recent Nature work from the Moser lab shows that the joint activity of grid cells within a single module lies on a torus-shaped low-dimensional manifold, providing a geometric view of population dynamics.
Continuous Attractor Networks and Intrinsic Grid Dynamics
The torus manifold of grid-cell activity is interpreted as a continuous attractor: a low-dimensional set of stable states defined by recurrent connectivity, largely independent of specific sensory inputs.
Environment Invariance and Generalization of Grid Manifolds
The toroidal manifold of grid-cell activity is remarkably invariant across different environments and even across brain states, suggesting a generalizable internal coordinate system.
Geometric Insight from Manifolds for Understanding Brain Computation
The torus example serves as a broader illustration of how geometric manifolds can provide intuitive, low-dimensional views of seemingly noisy, high-dimensional neural activity.