Why a hexagonal grid. If we have several overlaying grids of different orientation and scale how do they know which grids to activate?
If the mechanism is bottom up, we are at point A and point A has an overlap with the active part of grid X and likewise for several grids. This is backwards the specific to a large unspecific grid how can that help? It makes more sense to have some top down global signal to trigger grids but how could this work?
In this post I describe how a combination of mutual reciprocal excitation and local inhibition acts as a voting mechanism where the cells in a neighborhood act to select the strongest response to a previously learned pattern. Weaker responses are suppressed. This hex-grid response extends over however much area is responding to the learned pattern.
I will have read it in detail and walk through the math before saying anything.
I did a quick pass through and I was trying to see how the pattern formed conveys spatial information - this did not jump out at me.
I will be looking for this key detail. I will edit into this answer if I have anything to add.
Thats exciting! I have not read the details but this appears to be further evidence for the Kroff & Treves 2008 grid cell model. It is a promising model of grid cells and it is highly compatible with HTM theory. I have implemented it as a simple extension of the SpatialPooler model, and Im currently working to contribute it to the community fork of nupic. Thanks for posting this.