How is a three dimensional cup mapped to a two dimensional grid cell array?
Have you seen this?
I think this poster is even more relevant.
There will also be a paper soon about how 2D grid cell modules can track N-dimensional variables.
Did you click on it for the higher resolution version?
Aha, it is a problem with my iPhone… it works in my laptop as you mentioned…Thanks
This is a major step. Using the 3D case it explains why a grid cell ARRAY representation, it is a SDR, it really is HTM.
I would go further and say the point of grid cell arrays is not to make a homunculus of the world. It is not the one fully overlapping point that is useful, it is the SDR that is used.
I have a few questions on the article “A framework for Intelligence and Cortical Function Based on Grid Cells”. The questions are not on the basic idea yet, but on the grid cell theory behind it. You say that every learned environment is associated with a set of unique locations. So suppose you have two identical rooms, except one is colored blue and the other is colored green. You release a rat in one room, it learns its surroundings, then you release it in the other room, and it learns to get around in that room too. So it seems that the grid cells that are active at the left back corner of the blue room should be the same as the grid cells that are active at the left back corner of the green room. But it seems you are saying this is not true. If it is not, then why not? You also say that on entering a learned environment, grid cell modules anchor differently. Anchor means which grid cells are selected. Do you have a diagram that would illustrate this? Finally, in the example of the cup with the logo, why do two spaces exist - logo space and cup space? Are they both represented by the same modules? If they are, I would think there would be danger of overlap, unless you switch in time from one to the other and back.
Thanks in advance
This is an area of great interest in grid cells studies.
Google “grid cells remapping” and find that as a critter enters and orients to a space the response of the ensemble of grid/place/border cells seems to be reshuffled.
I have yet to read a paper that is able to describe the principles of how it works - only that it does.
There are promising signs that someone will sort out how location is coded but these are still “early day.”
Here’s a super relevant experimental result: https://academic.oup.com/cercor/article/25/11/4619/2367613
In this experiment, the two rooms have the same shape and size. They have different colors and odors. Grid cells’ firing fields are different in the two rooms. Interestingly, the difference is purely translational.