Numenta Research Meeting, Nov 25, 2019

I am not certain this is happening yet, but I am making room for it.

Topic is GAMMA BURSTS, speaker will likely be Florian.

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I will be boarding a plane then - another backlogged meeting to catch-up on!

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Live now.

Thanks for the presentation!

I would like to come back on a figure that Florian showed in the middle of the video (at 39:33):

I found the figure within its context in Florian’s thesis (p84):

I guess that @Bitking would be interested by this theory, closely related to his hex-grid theory presented on this forum. In short and from my comprehension, those two theories share lots of similitudes except that the connections between the hypercolumns don’t necessarily need to form regular hexagons. Moreover, Florian has explored potential mechanisms involving L2/3 pyramidal and basket cells inter-hypercolumn and intra-hypercolumn interactions to explain this pattern.

It is the first time I am seeing this kind of figure for the cortex, and it reminded me the following picture from a great 2018 paper about grid cells (I was also extrapolating in my head a similar cortical L2/3 organization). We can see the same patterns inside grid cell modules in layer 2 cells.

Source: *A Map-like Micro-Organization of Grid Cells in the Medial Entorhinal Cortex, Yi Gu, Sam Lewallen, Amina A. Kinkhabwala, Jeffrey L. Gauthier, Ila R. Fiete, David W. Tank, 2018:

Note that a module seems to be composed of only half a dozen hypercolumns. Like an intermediate structure between an hypercolumn (=macrocolumn) and a map (in @Bitking’s terminology).

The entorhinal cortex and its grid cells appears to be an excellent way to reverse-engineer the neocortex!


Yes, these are better drawings of what I was trying to convey in the hex-grid post starting with this drawing:

Through to this drawing:
Florian’s description is easier to understand.

Ignoring the regular vs the irregular array difference - I see that there is nothing that constrains a (hyper) column to a fixed location. Considering the irregular column this is even more important. The span of a column is based on the winner of the local competition and could move around with no real center.
In the early sensory cortex the column location is attached to the sensory fibers which are relatively sparse in comparison to the cortical cells. As you move of the hierarchy this is no longer an anchor to hyper-column formation.

The inhibitory cells are a continuous fabric with no column preference. The inhibition is a roughly circular zone of action around a given basket cell.

I strongly agree that the column competition runs at the gamma rate.

I would very much like to hear @FFiebig comments on my hex-grid post.


@Falco: in the case of responsiveness to specific edge orientations, we have that kind of topological map all over V1:

a pinwheel in that context is any of those particular spots where you have a central point surrounded by each possible color… and when he said the abstract schema of a circular arrangement surrounding an inhibitor was inspired by those, that triggered Jeff to look for it in the subsequent slides…

not all places are pinwheels, yet they are found with relative regularity. It seems to me it is quite “natural” that they do so in that topological context… but surely some tricky local inhibition has to be pervasive for arranging those beautiful color patches just the way they are.

not sure it was worth arguing about pinwheels specifically, though.

@CollinsEM : constraint on SDR yes.
but I believe there’s still much encoding space to mess around…


Could you expand on why you see this as a constraint on SDR? I think I feel the answer but I find it hard to describe clearly.

The discussion at 40 minutes - @FFiebig should have pointed out that the TB Theory anticipates that input sampling a global pattern will learn to fire together with the lateral voting.

This is actually the core of TBT addition to standard TM.

At 59 minutes, Q: why is there a smooth response continuum? Going back to the original Mountcastle papers that get referenced at Numenta many times - Mountcastle severed the monkey nerves to tease apart the wiring to isolate the individual response fields. The normal wiring when the axons innervate the sheets on their own maintain topology; this was the bit that Montcastle disrupted; see figure 7 in this classic paper:

The smooth progression of sensory input is something that biology wires when it establishes the wiring between senses and cortex.

While you are reading this paper, see figure 10 for an nice illustration of an actual mapped pinwheel. At the risk of beating a dead horse - this is what the axon innervation of the senses chose to do when they land in the cortex after the long strange trip from the eye to the cortex. The classic ice-cube proposal was made by plotting the RF using a needle passing in a single line through these pinwheels.

The number of distinct encodings for k-active bits out of m total bits is, of course, m-choose-k. This value get’s very large, even for modest values of m (e.g. m>100) and values of k corresponding to appropriately small fractions of m (for sparsity).

By further imposing a grid-cell-like structure on what would be considered valid SDR encodings would dramatically cut down on that number. If this grid-cell-structure constraint must be manifested in the 2D topology of the cortical sheet (what I meant by moving in recognizable groups) then the number of allowable combinations of k-active cells is dramatically reduced, and the number of allowable transitions between them reduced further as well.

For sufficiently large values of m, the number of allowed representations might still be sufficient to represent positions, movements, and/or orientations in a 3D space. However, when considering the potential applicability of grid-cell like behavior to more conceptual spaces, it may be necessary to take advantage of the much greater representational power afforded by not constraining the topology of the grid-cells to the physical adjacency of the 2D cortical sheet.


Maybe it reduces the dimensions of representational space… but it could be beneficial in other ways. Assuming large areas of these “constrained” codes are sampled, you still have lots of distinct encodings to play with. And that visible organization in V1, constraining each position spaced about 0.5mm apart to fine-tune against specificities of its particular input space, could very well, for all we know, be a core ingredient for our quest of “intelligence”. Biology seems to have chosen for this particular balance between the two, in lots of brain areas.

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