Check out Matt Taylor’s superb Grid cells presentation in the HTM school!
Matt points out that thinking of grid cells as maps of a room vastly underestimates the general potential of mentally mapping any arbitrary 2D space.
Matt demonstrates the relationship between SDR representation and grid coding. I outline multiple methods of using HTM to form grids in this post. There are some pieces to put together but this combination represents a potential tool to code a reasonably intelligent agent. So much to do to tie this all together.
He also introduces the concept that grid cells might be used in the neocortex to represent all objects in the brain, not just locations relative to an agent’s body. The papers below show how general mental cognition may well rest on this ability to mentally represent and manipulate space.
Here are the links referenced in the video comments:
2014 Nobel Prize Lecture:
Referenced papers:
The representation of space in the brain (Roddy M. Grieves, Kate J. Jeffrey):
https://www.researchgate.net/publication/311915392_The_representation_of_space_in_the_brain
Network Mechanisms of Grid Cells (Edvard Moser, May-Britt Moser, Yasser Roudi): http://rstb.royalsocietypublishing.org/content/369/1635/20120511
Computational Models of Grid Cells (Lisa M. Giocomo, May-Britt Moser, Edvard Moser):
http://www.cell.com/neuron/abstract/S0896-6273(11)00650-7
Evidence for grid cells in a human memory network (Christian F. Doeller, Caswell Barry, Neil Burgess): Evidence for grid cells in a human memory network - PMC
Mapping of a non-spatial dimension by the hippocampal-entorhinal circuit (Dmitriy Aronov, Rhino Nevers, David W. Tank):
Organizing conceptual knowledge in humans with a gridlike code (Alexandra O. Constantinescu, Jill X. O’Reilly, Timothy E. J. Behrens):
http://science.sciencemag.org/content/352/6292/1464
Organizing Conceptual Knowledge in Humans with a Grid-like Code
Alexandra O. Constantinescu1, Jill X. O’Reilly, Timothy E. J. Behrens
It has been hypothesized that the brain organizes concepts into a mental map, allowing conceptual relationships to be navigated in a similar fashion to space. Grid cells use a hexagonally-symmetric code to organize spatial representations and are the likely source of a precise hexagonal symmetry in the functional magnetic resonance imaging signal. Humans navigating conceptual two-dimensional knowledge showed the same hexagonal signal in a strikingly similar set of brain regions to those activated during spatial navigation. This grid-like signal is consistent across sessions acquired hours and more than a week apart. Our findings suggest that global relational codes may be used to organize non-spatial conceptual representations and that these codes may have hexagonal grid-like pattern when conceptual knowledge is laid out in two continuous dimensions.