Biological constraint of grid cells

[Bitking]

@Falco
You said:
For some reason the angles of the triangles in the grid are constant (60°) but the edges are not. Also, the orientation varies, but we don’t know by how much. And I have seen papers where grid cells physically located nearby, code for grids with close orientation. There must be a physiological reason for this. (I suspect that axion lengths and therefore signal transmission speeds must play a role).

In the post referenced below (scattered throughout the text) I describe how the lateral axonal connections of layer 2/3 reinforce each other. The shortest distance for three cells to interact forms a triangle. This is the key feature for forming Calvin Tile hex-grid coding. As you can see, these horizontal axonal projections can be in any direction so the resulting triangles do not have to be aligned on any particular axis. The vary in length over a limited range, allowing some variation in the spacing between the mini-column nodes. I see this as the underlying mechanism of the three signalling modes of scaling, orientation, and phase.
This drawing sums up this relationship, the light lines and shaded zones are the rising axonal connections and zones that they can influence, skipping about 15 “in-between” mini columns, the heavy lines are the lateral axonal connections for this trio of cells:

HTM Mini-Columns into Hexagonal Grids!

Or at least some wild conjectures to provoke thought! This post assumes that you are familiar with basic HTM theory and are conversant with the concepts of SDRs and HTM minicolumns. May I be so bold: [HTM%20and%20GRIDS] First - let’s be clear what I am and am not talking about. This is about cells that work by forming regular hexagonal grid structures and are not necessarily the same thing as the “grid cells” that are coding some spatial aspect of the surrounding environment. These grid-fo…

This construction forms the low-level hex-grid units. When hex-grids signaling from two or more maps interact (through projections to a distant map) this underlying hex grid pattern interacts to form the macro Moser grid pattern as described in this post:

SDRClassifier in javascript

Yes, something like this. I happen to have one approach that I am working on that may work as a classifier (hex-grid coding) but there are certainly other ways that HTM cells can group together work as classifiers. There is something at work to form the cluster of features that we can identify as a grid cell being active when certain inputs are present. I think that in time Numenta will show how the TBT builds up to doing this. I think that the Calvin tiles method (hex-grid coding) shows grea…

This is one of the key differences between what I am doing and what Numenta has been working on in the research meeting I have seen - I put the Moser grids as a larger scale emergent property of Calvin tile coding on the mini-column level and Numenta is asserting the grid modules are somehow a direct property of the macro-column module.