HTM layers, cortex layers, and degrees of freedom


#1

Back when there were only 2 white papers and a few videos I became interested in the HTM and saw a video of a 2D helicopter being detected and wondered about the relation between the layers they used and the ability to recognize objects. I remembered 6 equations with 6 unknowns (the degrees of freedom) are required to solve the dynamics of 3D rotation and translation. The layers of the helicopter HTM matched with what it was able to detect if they were unknowingly being used in a subtle 2-equations and 2 unknowns methodology. Of course this begs the question “Are the 6 layers in the cortex required to see the 3D world?” Numenta’s view of the cortical column implies that the 6 layers have nothing to do with this but I would like to question that view. Jeff has also warned against pursuing the reverse black hole question no one has ever escaped: “Is the 3D world the result of a 6-layered brain?” But an understanding of the relation between mass and space-time prevents me from abandoning the reverse question. More importantly, physics has an elephant in the room that is rarely acknowledged and questioned: the only integers that appear in physics are the result of 3D spacetime and Feynman states no fundamental aspect of QED requires an extension beyond 1D. QED is sort of the core of all physics except for gravity and nuclear stuff. An expert in the area informed me that spin is what creates 3D space, so my line of questioning is suspect. But my view is that we may have invented spin to maintain the view that objects are independent of our perceptions. I admit I am immediately deep in a recursive black hole: the 6 layers is a mass of neurons that I’m proposing we can see only because we have the 6 layers. BTW, if we had 10 layers to support the perception of 4D objects in 4D space then I believe all velocities would be static positions and all accelerations would be velocities. instead of E + mc^2 = 0 we would have E+mc^3=0 (now really getting side-tracked on the physics: by keeping relativity units correct there is a missing negative in some equations. Another example is F+ma=0 where the “F” is more correctly defined as the reactive force of the object which is in the opposite direction of the “a”. This comes from meters=i*c*seconds which comes from Einstein’s “Relativity” appendix 2 which he stated allows use of Euclidean instead of Minkowski space-time which is in keeping with the Occam’s razor requirement.)

What I’m suggesting is falsifiable. Others posting here will know if it takes 6 layers to fully recognized objects in 4D space time. The degrees of freedom is N translational plus N(N-1)/2 rotational. I tried testing the theory via observation and thought of ants. It seems to be supported there: their eyes that need to detect only 2D “shadows and light” without rotation have roughly two layers. And yet their feelers and front legs, having to deal with 3D objects in 3D space, have 6 layers. There’s a great extension to this observation: wasps are the closest cousins to the ants and have 6 layers for their eyes.

I posted this question nearly a decade ago in the old forum, but I’ll ask again. Is a 6 layer HTM required for fully characterizing 3D objects in 4D space-time?


#2

If you have enough memory you can simply recall with a single layer nonlinear network every possible input, output combination you want. Or at least you can do that to some approximation. A problem with that is you get even sampling of the input space, where actually you want the sampling to be highly detailed say with regard to human faces but very approximate with say background scenery. i guess there are a number of ways around that including deeper networks.


#3

I think a single layer would require a lot more new training on every object. For example, it sees a circle moving about and learns its behavior. Then it turns sideways and turns out to be a cylinder, and then it starts rotating, so training has to start over. I don’t think it could conceive very well “this is the same object” and/or generalize the lessons learned on past objects to future objects. It just seems like it would have difficulty understanding objects like we do. I believe 6 layers would be able to perceive the laws of dynamics but 1 layer would not. These six layers are not an HTM but the foundation of a single cortical column. Each CLA layer of the HTM would require the 6 layers. So the CLA would need to be redone if you want it to think like mammals and see like wasps. The motor control of layer (5th layer of cortex) may serve may also serve part of this “inherent object modelling”, not just motor control. The motor control part might be crucial to developing the concept of inertia (mass). Mass is another variable (“dimension”) which implies 7 layers should be present. To get out of that mathematical corner, I have to conjecture mass is something special in the modelling like “the higher dimensions that 6 layers can’t model and that have permanence”.

I do not mean to say that 6 layers is necessarily inherently needed in A.I. to be superior to humans even in the realm of understanding physics, but that it is needed to think more directly like animals. But if 6 layers per HTM layer is actaully needed for a higher intelligence, then 10 layers to do 4D space should be even more powerful. 15 layers are needed for 5D. I do not accept the conjecture that objective reality, if there is one, depends on a specific integer of spatial dimensions like “3”.

The visual cortex by itself with its 6 layers does not seem to have any concept of objects, but I think the 6 layers are still needed for encoding the information so that the concept of the objects is still extractable by the higher levels in the “HTM” of the brain (e.g. frontal lobes). But the concept of an object seems to be possible in the 6 layers just “behind” the eyes of flying insects: wasps certainly have a better concept of the object nature of people than ants, judging by the way they identify and attack. Ants are virtually blind to what people are, except for detecting skin and biting.


#4

Okay, I get your point. To simulate a 3D system efficiently with neural networks you need 6 layers.


#5

I think it’s a bit too “convenient” for each layer to represent a dimension in the way you describe. I think we’ll end up discovering (and the current thinking agrees with this) that each layer is performing an auto-encoding/predictive/pooling function with its particular effect defined by its inputs and outputs, and works on whichever input modality or dimension(s) you feed to it.


#6

That’s actually what I’m saying, assuming by “dimension” you mean a mathematical “dimension” that represents a dynamics “degree of freedom”. As I said, it’s one layer per degree of freedom based on physical spatial dimensions. Also, the 6 layers should mostly be interconnected in order for it to function like 6 equations solving 6 unknowns in order to perceive objects in 4D space-time. The original inputs of observation should be smaller in number than the interconnections.


#7

There was this easy to understand paper on Arxiv today:
https://arxiv.org/pdf/1707.02617.pdf
I don’t think anyone has proven the rationality of deep neural networks. I mean no one has shown that you could not do the same things by more efficient means. If you think of the layers of a deep network as being associative memory then decision tree/forest like behavior can be envisioned. You could train deep networks according to that viewpoint hoping to gain efficiency by better fitting in with the actual capabilities of the network. Or you could take things more literally and have a decision tree/forest where the splitting decisions were made by simple single layer networks. A gain there would be you would not lose information prematurely due to filtering effects as in when data moves through a conventional deep net.
There is a universe of possibilities you can try on your digital computer at home. How do you sift through a universe again?