Hex Grids & 1000 Brains Theory

The blue lines are axonal outputs.

No - I am not showing any of the inhibitory cells - this is all pyramidal cells at this point.

Yes, it is an attractor model.

Just checking because in my model of how a continuous attractor model works to generate a grid is through inhibitory neurons. Pyramidal grid cells don’t connect directly to each other from what we have seen in entorhinal cortex.

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Agreed - the inhibitory interneurons are very important.
These are already VERY busy diagrams.
I was not sure how to work inhibition in for the first presentation.

The inhibitory inter-neurons are evenly distributed and are being activated by that huge output arbor.
It takes a strong resonant interconnection to counter this and continue to activate.
Like you suggest - a top %10 or %20 maybe.

I have been reading about neurology for 20 years and had a pretty good idea what to expect.
HTM just filled in some blanks and gave me a new way to frame my understanding - I was ready to unlearn a few things and plug this theory in.

The part I was missing was the temporal part - how to go from one state to another. As soon I I saw the predictive mechanism it was not a big leap to see how it fit in and explained many of the questions I had.

There are a bunch of things related to hierarchy that I have worked out before I every saw HTM and the bit I am trying to get across here is the extension needed to fill those holes.

If this really does work this way then lots of things are explained.

I cannot stress enough how important it is to solve the basic problem of how the eye puts sequential saccades together into an object. This model does that.

I am trying to make drawings like these to get this concept across. Once you see how it works and how neatly it dovetails into the basic HTM theory you may wonder why it did not occur to you first. It’s that basic.


This is interesting, but I don’t see it in your other public posts anywhere.

You mean roughly like this, right? http://mrcslws.com/blocks/2017/04/16/grid-cells-CAN-model-visualized.html

The thing I’m struggling with is where are the grid cells? Are all the pyramidal neurons in a minicolumn grid cells? Do we consider the minicolumn itself the grid cell? Is “grid cell” just some behavior we arbitrarily attached to a neuron when it is actually expressed in a local group of neurons?

Emergent behavior of mixing HTM with lateral connections…

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It is prominent in my notes at home but it has not come up much here.

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Is it fair to say that each minicolumn has griddiness as if it were a grid cell in grid cell module?

minicolumn is to grid cell
hex grid is to grid cell module

Would you say hex grids span across cortical columns? or that they define cortical columns?

BTW I know you are at work. I’m not meeting with Marcus until tomorrow afternoon, so no rush to answer right away, I’ll keep reading and asking more questions.

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Mini-columns are the hubs of the grids. Any mini-column could be part of a grid.

The hex-grid pattern is just the state of the instantaneous collection of mutually interacting mini-columns across some part of a map. The “griddyness” part is the map of these reinforcing links.

It does NOT explain the repeating nature of cells vs location. I am hoping that the work numenta is doing will show how that code ends up being repeated as it is in the hippocampus. I have been trying to extend what I have read of the Numenta work in that direction and so far - no success.

Hex-grids: It could be as little as three mini-columns or across the entire map if it is a well learned pattern. When a grid is fully formed it also served as the sparsification step of HTM at about 5% sparsity if I remember my calculations correctly. A single grid hex serves the same function as a macro-column does.

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I’m going to ask a couple of basic questions again just to be sure:

I’m trying really hard to relate this this to how I understand grid cell modules to work. I think you are describing minicolumns as behaving exactly as grid cells behave inside a grid cell module. You’re hesitating to say that a hex grid is acting like grid cell module. Why? Am I missing something?

This feeds into the larger question of how a hex-grid is learned and how the learning extends.

As I see it a learning starts with some random best-fit on a single mini-column.

As others learn some pattern at the same time they riff off each other and reinforce when they see their part of a common pattern.

Over time this patch grows as a patch learns this pattern together. Once is it established it adds details around the edges and learns to discriminate between two similar patterns. The yellow in the picture below is a loose group - say 50 hexes. As the pattern is refined more hexes are recruited and by the time we get to the green it might be 500 hexes.

Look at this process in action: The two patterns start out the same but as details are added in the two patterns start to diverge and I would expect that the phase or scale shifts between the two patterns.

oh… thank you I have to think about this now… so the atomic computation unit we see physiologically localized in sensory cortex is distributed in other parts of cortex… right?

So the cortical column is distributed into a learned hex grid in higher areas of cortex, each hex grid behaves like a grid cell module, bumps within the module are minicolumns firing / echoing from some recognized sensory input (or something else). Am I still on the right track?

Yes, with the key difference being that in the early stages we are anchored to the sensory feed - the location have to be fixed as the sense fibers are fixed.

As we move up the hierarchy the hex-grids are free to form at any mini-column location and shift (phase/spacing/rotation) to collecting the sensory information into hex-grid coding of objects.

Then go back and look at the video you made on grid signalling and plug this in. I think you will see that it is describing the same thing from the bottom up.

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when you say “hexes” you mean hex grids working together yes? So I could also say cortical columns here.

Yes - same thing - different terminology.

The curse of working in the AI field.

Please keep in mind that Calvin defined this a long time before HTM was offered as a thing. I have been thinking this way since the 90’s.


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Hexagonal topography has been around along time. Biology finds interesting ways to use maths.

I think I understand what you mean by “well shuffled” now. Well shuffled up the hierarchy.

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Yes - the “dendrites have thousands of synapses” but they have to have something to sample and they really don’t reach very far.

If we are going to extend this reach we have two mechanisms:

  • Bring more mixed input to the dendrite to sample
  • Harness them together across some expanse with a system like hex-grids.

I was ready to see SDRs as the best input coding scheme; it has much to offer.

btw, do you mind if I update your post to say “minicolumns” where it should instead of “columns”? HTM Columns into Hexagonal Grids!

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Go ahead - it’s really the right thing to say.

gmirey pointed out that I was very sloppy with my terminology and that it was very confusing for him.

If I ever get everything down that I am thinking I will end up collecting this up into book-length material and publishing it in some form. Editing to get everything to match up will be a large task.

So much left to get down.

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I like the idea that different CAN parameters can be used to extract different hex grids from a set of activated minicolumns. I don’t think we are considering representation at this level. We are only using overlap score with input within columnar boundaries.

I have yet to talk to Marcus about it (this afternoon), but the idea of doing a hex-grid search across a set of activated minicolumns with proper topology, getting a ranked list of grids and inspecting what that means is quite interesting.

I talked to Jeff about it this morning and he still thinks that the lateral voting as defined in the Columns+ paper does the same thing. I was directed to read and understand our voting mechanism better. Admittedly, this is not something I’ve done a video on yet so I don’t fully understand it.

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