Individual medial entorhinal cortex (mEC) ‘grid’ cells provide a representation of space that
appears to be essentially invariant across environments, modulo trivial transformations, in contrast to multiple, rapidly acquired hippocampal maps; it may therefore be established gradually, during rodent development. We explore with a simplified mathematical model the possibility that the self-organization of multiple grid fields into a triangular grid pattern may be a single-cell process, driven by firing rate adaptation and slowly varying spatial inputs. A simple analytical derivation indicates that triangular grids are favored asymptotic states of the self-organizing system, and computer simulations confirm that such states are indeed reached during a model learning process, provided it is sufficiently slow to effectively average out fluctuations. The interactions among local ensembles of grid units serve solely to stabilize a common grid orientation. Spatial information, in the real mEC network, may be provided by any combination of feedforward cortical afferents and feedback hippocampal projections from place cells, since either input alone is likely sufficient to yield grid fields.
This paper presents a promising computational model for grid cells. I hypothesize that the grid cell model described in this paper can be connected to an HTM with the effect of forming alocentric locations. The paper goes into some detail about the properties of the hippocampus place cells which serve as input to their model, and I think that the hippocampus input could be substituted for by the output layer of numenta’s sensory-motor integration model. This use of grid cells in the cortex would represent the space around and between the objects which the output layer is representing.
The grid cells can work with inputs which have the following properties:
- The input is a sparse distributed representation, ~2500 inputs with 2 - 12% density.
- The input represents specific locations, each cell can participate in representing many locations.
- The inputs change slowly. It is critical for this model that the locations which the inputs represent are large enough that motions across them take some time. The output layer of the two layer HTM also has this property because it contains stable represents of objects which persist across multiple sensations.