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From YouTube: Tutorial and Discussion on Cortical Column Voting Mechanisms Developed by Numenta - 5 April, 2022

Description

Subutai Ahmad gives a tutorial on the voting mechanisms in cortical columns developed by Numenta and answers questions from the team.

Whiteboard photo: https://tinyurl.com/5apr-whiteboard
Columns paper "A Theory of How Columns in the Neocortex Enable Learning the Structure of the World": https://www.frontiersin.org/articles/10.3389/fncir.2017.00081/full
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A

I think ben's questions came about because uh he's thinking of actually starting to implement some of this stuff and the team is starting to implement some of this stuff. So it's a little more real now, and so I talked with him a little bit on friday afternoon already so I don't mind getting started without him, um but what I'll do is go through kind of very mechanistically. What's going on with voting, mostly from the point of view of a single neuron, everything is pretty much happening once you understand what a single neuron is doing.

A

Everything else is just an emergent uh from from that um which, I think is actually a really nice property of the algorithm, um so I'll go through step by step, how we learn uh how cells learn to associate with other str's and then how voting happens and how that kind of maps to our neuron model- um and this is somewhat of a repeat of stuff I did before anyway- um so it's- uh it might be a bit repetitive um and then thanks for all the other questions that came on the on slack as well, so we can deal with that.

A

uh Let me go through kind of ben's question. First, um we'll go through step by step, and then we can address some of these. Some of these other questions like feedback and noise determinism and things like that. As long as we don't talk about consciousness,.

B

A

And I might end up using all four colors, so hopefully you can see that all right. So what I've drawn here is three columns, um basically using the columns paper as the outline, so I'm not really planning on talking much about grid cells or or anything else, um just really focusing on the output of the building here, amen.

A

And if you remember from the columns paper, we had the outlook layer, we what we call the output layer, which is sort of you know. Our map will be l23 in the oracle column and then the input layer, which is where sensory input comes in layer four. So mostly I'm going to be talking about the output layer, but this is just for the full picture and the basic idea is that each particle column is censoring.

A

Some subset of the full sensory space, and this is moving over over time and what at any point in time, the input layer contains a very unique sdr that corresponds to the particular sensory input at a particular location. So this is the location signal, and this is.

C

C

A

And so this is changing very fast as we move um and at any point in time the current sensory input is going to be consistent with a bunch of other possible objects and the output layer is going to contain essentially the set of objects that are consistent with all of the sensory inputs. Seen up to this point, that's kind of the most generic and it's consistent not just with what it sees, but with what everyone else is seeing. So there's information transfer from other portable columns, as well as uh over time within the vertical column,.

A

Okay, uh so I guess what I'll do is I'll focus on the column two, because it's in the middle um and then we'll sort of walk through step by step here. Any questions so far high level comments.

B

Somehow I feel like I'm a professor right now.

D

I think that means for today we have to call you a doctor. Is that right.

E

Okay, can we vote on the correct answer? Just keep one answer.

A

Yeah sometimes voting is not the right way to do good things. Sometimes it's a dictator approach, I'm gonna be a dictator, um okay, um and what I find really cool about, like I kind of alluded to like the entire voting thing, can be understood if you just understand what a single neuron is doing and how the behavior of a single neuron depends how it learns and how it dendrites work. Once you understand a single neuron and alpha layer, you can kind of from.

A

There derive all of the voting properties which I really like, um okay, so um yeah, maybe I'll switch to. So this is a neuron in one of these output layers. It looks a lot like neurons in our temporal memory and then the dendrites paper that we just published so there's sensory input coming in here and there's contextual input, that's coming laterally and the way this neuron works is slightly different from the temporal memory neuron um in that, if it has, you know, first of all,.

E

If it has, if it has, it has to have sufficient sensory input.

A

In order uh well, actually let me take that basically, the way this neuron works is, if you have contextual input coming in, it's going to bias this cell to win um and the neurons, which are which have the highest bias from from contextual, because those are the ones that are going to be active.

A

What we did in the conductor is we enforce more stability in the output layer. We just said these: these cells are going to be more stable um and so, during learning, what we said is there's. We just assume there's a signal that says: okay, we're going to now learn a new object and everything we're going to see from this point on. Is this new object? So we enforce these kind of boundaries?

A

We didn't really have a continual seminary with that sense, so we said: okay, we're going to now learn the next object and do while it's learning these cells are just.

A

We pick a random sdr at each column that represents that object and we enforce those cells to stay on so basically in column, one, um maybe I'll just call it o. This is the output representation for object, one in column, one this one will have a this column will have an sdr in column, two for the same object and in column three.

A

uh It's going to have an for the same object, so these are going to be three different sdrs for the subscripts yeah. So this is like um object id, and this will be that column. You can see that a little so the subscript is the object id and the superstring is the column id. So this is all for one object: you're going to get this for the next object. You get another one.

F

So when you're looking at a new object and uh is there any similarity between similar objects.

A

No there's no similarity they're completely random, so this.

B

Is one of the potential downsides that we.

A

Did in the column paper every.

E

A

Is treated as a completely separate uh random object.

F

Okay- and you tell it now- you look at a new object, so it should be a new activation yeah.

G

A

Yeah, so during learning what we say: okay, we're now learning the next object. So we pick a random sdr here, and these are, uh I think, in the paper 40 out of 4096, something like that. It's pretty sparse, like one percent and it's pretty high dimensional uh 4096 and um there's actually some evidence. I think that their two three cells are.

F

A

Than lower level cells uh lower layers and they actually are more stable than lower layers, I think we cited some of those papers.

D

Layer, two, especially because this is why you never see any reports of activity in layer two, because are there any cells active.

E

A

So I think that that matches the biology. um So the interesting thing is that column one might have a completely different scr from column two and completely different sdr and column. Three, even though it's the exact same object. So what these cells have to do in order to vote is to be focused on column. Two.

A

These cells have to learn the associations to the sdrs and the neighboring columns in order for voting to work, there's no assumption that they're the same, and in fact I think the way we did it there doesn't have to be a one-to-one relationship. I was talking about this with ben on on friday. Suppose this is a. This is a say. Column is a somatosensory one column two is a visual column. This whole thing could still work um like.

A

Imagine, like you, have a coffee mug with a lumento logo that might be a specific object where you have another coffee, mug, that's identical shape, but it has the box logo on it right.

A

The touch sensors wouldn't be able to tell them apart, so they might have the same sdr for those two objects, whereas the visual column would have two different sdrs, because then we can tell them apart. So this whole thing should still work in that context, there's no assumption of exactly one-to-one mapping throughout and that's something in monty. I think we need to be careful about.

A

So that's one of the reasons like if you just use object ids uh that one's not gonna work. If you need to have as many too many.

F

Kind of mapping yeah, I mean yes for two- for, for example, the touch column to have the same representation for the cup with one logo and the other logo. Would this automatically happen just from the sensory input being the same, or would you have to tell it okay? This is the same shape. Basically during training yeah.

A

It's a good question. um You know we have to solve the problem of when it's. How does it know when it's a new object and when it's not- and I think you talked about some possible ways of doing that- we didn't really address that piece in the comments paper, we discussed it internally a little bit. You know, there's going to be a lot of bursting and a lot of activity if it's an unknown object, and so that could be the trigger for a new signal, potentially.

B

Not for the touch sensor with different logos.

A

A

So during learning, um let me walk through the learning process, so we let's say we're learning object, one. um We invoke an sdr in each of those columns. They're, completely random um and and those cells are going to stay stable during the process of learning. So what's going to happen here, is um you get a you? You go to some location on the object and you've got a unique sdr here.

A

You've got a unique sdr here. You guys are there for that single point and these cells that are active they will automatically just through heavy and learning up synapses. Their feed forward synapses are going to learn connections to that unique sdr, so that will just be straightforward. Heavy learning.

A

In addition, we're going to learn connections on the dendritic segments that correspond to um activity of the neighboring columns, so the the other, the next big difference we said in the columns vapor is, we said each dendritic segment is going to have synapses from different columns.

A

So what will end up happening here is if you look at a cell. Let's say this is a column two cell.

A

This is a cell in column. Two, this cell is active for object. One, it's gonna, learn, let's say on this dendritic segment: it's going to learn, object, 1-1, the sdr for column, one for object, one here it might learn its own okay. This is an extent.

A

And so it's going to learn those three as contextual signals on three different dendritic segments. Once you.

B

Learn those sdrs I mean it'll, respond very strongly to if that sdr is active in the.

A

Input yeah, it's just gonna, uh because we learned by adding and dropping connections. It's gonna make form connections to these.

A

So after in this setting after this cell after you've learned object, one they're going to be three different dendritic segments that have sdrs to the three different columns so notice that it also has connections to itself so the columns internally.

A

By itself I mean uh to other cells in the same column, okay, because this whole thing works even with only one column, and so the learning rule is again very heavy and like as because the cell is active, we're enforcing stability here as long as it's active, it's going to learn, connections to whatever axons are active that are nearby, so this sort of learning will happen just through pure heavy learning, but we're ensuring that they're on three different generic segments here- and there is some biological justification for that.

A

uh It would be kind of interesting to see if that's actually what happens or not, but um okay, so is that. Is that clear?

A

You should still object.

B

To your first one about object, one this is all object. One right now, yeah you wrote two.

B

I did write two but not object. Two.

A

So this is a column. This is a sound they're, always those oh one, two yeah, so this is the subscript is the object id and the superscript.

B

A

Okay, I write my ones like this.

B

uh Okay, let me fix that. That's fine.

A

Okay, um now, let's say we're learning object, two we're again going to pick a random set of cells in each column. It's actually possible for the same cell to participate in multiple object, ids right so.

F

A

Same cell could become active for column for object, two as well.

D

Wouldn't it be, it's almost certain it would right if it's a one percent sparsity, then one out of a hundred patterns, that's solid participating right. So it's like a one percent change as we learn more and more objects.

A

Every cell is going to participate in multiple objects, so in general, but the chance of a high overlap is really small and- and we know the math for that- but in general a particular cell can be involved in.

C

More than one object, so we can say: okay, this cell is involved in object, two as well just to be just to be honoring, so I just wanna double check the entire output. The entire sdr from one column is being received on a single dendrite of one of these cells. So if there are 47 all 40 synapses, all 40 cells have a synaptic connection to this. One.

A

uh No okay, so the question is, you know there are 40 cells active here. Do all 40 cells make connections here here now in general, our our learning rule always subsamples from the input. So um and as long as you have enough synapses, the whole thing works with very, very high probability. So that's.

E

A

Covered in the strms so.

E

If there's 40 cells active.

A

We might have, let's say: 20 or 30 synapses might sub sample from there. Okay.

C

Yeah, because we put a tilde over up here,.

A

This is why the numbers really matter- um and someone asked about noise robustness- I think in the in slack, but it's important to get the noise. The numbers correct for the noise stuff to all work out and also to get the capacity.

D

High enough, can I make an additional comment over there after that, I think. Imagine you had a thousand columns, not three we're not going to have a thousand dendritic segments. What's important for a dendritic segment. Is it has some minimum threshold of synapses to say 20 to create a dendritic spike and I've said this many times, but when it's not actually essential that a dendritic branch, a segment is always with one sampling from one column, another dendritic branch sampling for another column.

D

What does it matter? If I have a thousand columns? It turns out that you could. You could pick 20, synapses or 30 synapses from some subset of the thousand columns and if they're all trying to represent the same thing, it's still going to work. I could get one synapse in column, one one synapse from column. 47 one can option 300 to whatever.

D

So this is the way you've laid it out. Subtitle is a nice way of thinking about it, but it doesn't have to be strict like this.

A

That yeah, I think we can relax this quite a bit, maybe yeah all the way to one dinner excitement.

D

Well, or or it's just that it doesn't want to- I mean when people think like well, we have to have 20 synapses from one column or once in a dendrite another one another that would work and that's a good way of thinking about it, but really what matters is that you're the way to think about this?

D

If you have a thousand columns that are all participating, then you just have to do a sub sample across all those thousand columns, because that that sdr, that larger str across thousand columns is still an sdr for the object, so you're just sub sampling from that larger sdr, um it all work so nothing! I I don't think you have to redraw what you've shown here. I just want to clear that it's not strict like this at all yeah yeah, I'm just strictly describing what's in the columns.

A

Favor, but this would actually be a really nice extension- is to show that we don't need to do this exactly. Someone else asked also in slack whether if you have lots and lots of columns are they all. Is this column getting input from all other columns or how does that work? So that also is not necessary, and I can address that later as well, that one we did test.

A

One of our interns actually read some relations on that we tested that.

D

There I forgot that what they just said: we're not going to get any input from these columns and see what happens.

A

Yeah, well suppose you have to apology. uh You can make sure that each column is connected to its neighboring columns, but oh yeah, yeah yeah.

D

You don't have to so, but the information still travels pretty fast, yeah yeah I mean it. I don't wanna get off the tangent here, but when they look at these long range connections across the you know, from the left side of the brain to the right side of the brain, an individual axon may make you know a thousand synapses over there, but they're all over the place. They're not in any one location.

D

It almost seems like they're, random and all that would work. um You don't need to sample every column and you don't need to have it. You know it's just as long as you got 20 synapses from the ensemble you're good.

E

D

It's pretty amazing.

A

Yeah- and I think I want to stress again all this sdr math becomes super critical and it shows under what regimes. This whole thing is going to work um works pretty nicely in terms of number synapses on the generated segment. The answer is always like 20 to 30.. It doesn't matter how many columns, how many objects, how many, whatever it's always 20 to 30 and the threshold is like 10 to 15 right. Those are all good numbers that should work with.

A

So there's like there's like a floor, there 20 to 31 synapses, and it just always works out. It's kind of magical.

A

Okay, where was that going? Okay? So let's say this cell is active also for object two, um so I think you can now we'll realize that this thing is going to learn all of those.

A

Synapses on here.

B

um Yeah, so these generic segments are are going.

A

To get filled up with stuff, um okay, so this basically this is this: is it from a single cell standpoint that is the full learning algorithm um as long as it's and the it's basically ibm styling as long as it's active, it's going to form connections to all of the feed forward inputs that are active and it's going to form connections laterally to the way I described, but as long as this is active, it's going to form this connection. So it's a heavy and style uh learning rule, and so that's completely unsupervised.

A

This cell doesn't know anything about. It actually doesn't know about other cortical columns. It doesn't know about, um like. I said it's forced to segment it out this way, but that may not be necessary, but it doesn't really know anything about voting or other stuff. It just knows to form connections, and I should mention the bottom up stuff at for a given object, we're going to send multiple sensory inputs, multiple features as we move along each one of those is going to correspond to some very sparse sdr coming up here.

A

So this thing is going to learn a union of a bunch of synapses coming from below. So it's going to learn for feature 1, the sparse, a subset of again a subset of the sparse sdr coming up from below for feature. One is gonna form connections there and then, when you go to feature two there'll be another sparse sdr, so we're gonna run another subset of connections here and so on.

A

So it's going to learn a union of those, so you can see this it's starting to learn more and more synapses, so we are pretty worried about the capacity of issues and how many synapses- and we can talk about that- we tested that quite a bit- yeah. Okay, I just also.

C

Want to clarify the learning. Actually, I think I, if I remember correctly, it happens on one dendritic segment and with synapses local to the synapses that were active, so it's like if that dendritic segment turns on and then the neuron those dendrites are attached to fires. The update is specific to.

E

C

That was on and specific to those synapses that we're active on right, yeah.

A

Okay, just wanted to clarify that and in this particular algorithm everything is kind of deterministic and discrete- and you know, there's no noise in the output. So it's just it's just going to form connections with the synapses. It's the permanences that are increasing permanences are increased, yeah.

A

um Okay, any questions on the learning.

G

That's basically it well one. One quick question um is there's somatically anything interesting going on with the fact that dendrites branch other than the fact that that provides more opportunities for axons to connect with them? Is there any sense of you know? uh You know more or less forks having a effect on what the results are going to be.

A

um The more dendritic segments we have the more capacity to learn all of these lateral connections. So that's there, it doesn't actually have to be tied to the forks and the branches you can have local look physically local segments that are on the same branch can be isolated from one another. That's.

G

Okay, okay, so it's strictly, it provides for more connectivity. There's there's nothing about a higher fork or lower fork being dominated one over the other or something.

A

Yeah, the forks forks, I think of it- is just as a way physically to allow the dendrites to cover more space. It doesn't have any algorithmic, it is not strictly it's not true. In neuroscience, there are some impact, but at a high level, there's really no nothing important about the branching factor or anything like that.

D

Yeah, that's why we modeled it, but you know kevin's good point, because it's which I just mentioned there is some. There is some evidence. It's not very clear that you know um there is a sort of a an ordering to a branch, that's above above a fork and a branch that's below a fork, and some people have tried to make arguments about. The sequential activation should occur along from the from the extreme end of the dendrite towards the soma, but.

F

D

Evidence is not clear and we just didn't try to incorporate anything like that, but it may. It may be true that there's some computational thing going on, but uh it's not clear and we didn't model it.

A

Yeah, I think, from what I understand once you have a dendritic spike that is so large that it swamps out all these other effects.

D

Now, there's some people who some people have taken the neurosciences have taken. This idea that you know branching is critical because, because the way they used to model dendrites the models, don't work at the branches, and so so, there's on pointing out in the literature you'll see some people speculating about the walls of the branches. But as soon as I pointed out, we didn't see a need for it.

D

Yeah. You can definitely measure you know, measure things that are different depending on branching factors,.

G

The question is: does it have any real functional impact.

G

A

So we think that second, third or fourth order.

D

Yeah one more little point of this: if you just like depolarize the dendrite to a small amount. Well that did the polarization gets totally screwed up once you go through a branch, um but if you have as soon as I just said, if you have a dendritic spike, it goes right through it and the evidence is it continues on to gets in the salmon. So um that's just one little more piece of data on that.

G

Okay, thanks for saying where our state of knowledge is on that.

B

So if one then try, then genetically segment fires, that's sufficient corresponds to the sensor.

A

One dendritic segment is sufficient to prime.

B

Because they wouldn't know what it's doing.

A

Yeah, they don't know anything about objects. It's just learning patterns right. It just happens to learn this one is the pattern for object, one from column one. um This is the pattern for object, one from its own column uh and connections, to object, one from column, three sdrs. This is object. Two column, one object, two, so the column one happens to connect to two separate sequence: yeah and that's totally fine in this particular cell, uh I'm assuming the cell.

A

This cell is active both for object, one and object two in um but very small number of cells here will be active for both object, one and object two. In fact, there will be a really small chance of that happening, but in general, a given cell will definitely participate in multiple objects.

B

As you get to high capacity, so how many of those multiple branches do you have for each column for one well, this is very cell for this cell yeah. How many connections have two one of the cards? How many branches?

B

A

B

In this example,.

A

They're two in this example they're two, so it will end up depending on how many objects this cell becomes active form. So if it's object, if it's active for 10 different objects, then it'll have 10 different connections to column, 1 and 10 different collections or the threads variable during yeah. It's just random chance, the number of sequences it's the number of segments is related to how often that cell gets chosen for different objects, if it just by random chance, happens to get chosen for lots of objects, it's going to end up with more connections again.

A

None of this I'm describing a very strict version of the algorithm as implemented like jeff said this can be loosened up dramatically and you don't need to have so many connections and so on, but that would be kind of a nice.

B

Exercise for some of you.

F

Oh, can one and oh sorry.

E

F

Can one dendritic segment participate in multiple objects, for example, if it's the same sensory input.

A

Wait, you say: can the same dendritic segment participate from multiple objects.

F

Yeah like if one of those shorter lines would have multiple o's written on it,.

F

A

Example, it can in general, in the in the paper we enforced it, so it didn't, but you could have segments that are overloaded. um That are just again. We didn't implement that, but in general this can be very loose. You could potentially have multiple a given segment could have connections from multiple at different times, just by random chance, so it could be overloaded. It just gives you a question of what the capacity is and how many synapses you allow perpendicular excitement and kind of randomness.

D

Another way to think about this is this is an idealized version of a real neuron. What suitable is showing is every dendritic segment is recognizing a single pattern, so that would be like 30 synapses in our example here, but real dendritic segments are much longer than that. They might have hundreds of synapses on them, but only a 40, micron area of that dendritic segment is is, can can recognize a pattern, so you can think of a that in a real neuron.

D

A bunch of these segments of subatire's drawn them can actually be sequentially aligned along a dendritic branch, a real neuron.

G

D

So a real darn literally may have 400 or 500 synapses along a dendritic segment, but any 40 micron segment acts as a twin sense detector. So there's going to be a whole bunch of these coincidence, detectors aligned along the dendrite. It doesn't make any difference the way subut has drawn. It is just it's functionally equivalent, um but if you're thinking about real neurons, it wouldn't be like this.

A

Yeah, basically with real neurons, the answer to almost every question is yes, it's just very, but.

E

You just have to make sure.

A

That, on average, if things work out and yeah, um the extremely they're tolerant to so many different variations like this yeah.

B

It's also more like a tree on the roots right.

A

D

But it's not as branch, it's not as branchy, as you think. That's my point on many neurons. These segments are really long and again they can have four or 500 sentences on them. So we don't it's functionally equivalent to just saying give make each 40 micron segment and call it a segment and- and that's what subita has drawn here um again. I think you have to be careful when we mix like the model versus the real neurons yeah.

G

uh Question was that in any given 40 synapse connection, we say: 20 is enough to excite it well, uh a separate object. Could excite say the other another set of 20 on there, in which case there wouldn't be that overlap uh explicitly not requiring any kind of sequentiality at all.

D

Right would that still work just fine.

A

That's what I was calling these overloaded segments that would.

F

Work, I I actually meant, um since I am interpreting those as kind of pattern detectors, what if a different object, comes with the same pattern like with the coffee cup, with two different logos on it. There are two distinct objects, but on a touch column, it's two times the same pattern. So the same, the dendritic segment that encodes this pattern of the cup morphology, it will be activated, but it's two different objects. Yeah.

A

Yeah the way the learning algorithm works there is. If, if there is sufficient activity on a segment, then it would pick that segment to learn automatically anyway, because that segment. So in this case, if you've already learned an sdr for a cup from the somatosensory column, and you get that same thing again for a new object that same dendritic segment would still be active and it would still learn that so um yeah. I thought you meant two completely different objects on the same generic segment. So that's uh but yeah.

A

If it's the same sdr, it would pick the same multiple point. Well, no, the the in the.

B

Somatosensory case it would.

A

B

D

A

Object but it's actually a different object.

B

That would be the same.

D

From the semantic sensor.

A

Yeah yeah the same segment would become active and the same segment would learn in the temporal memory. Rules, in fact, don't find a matching segment that you start to ignore things.

D

So the way I feel is, if you have, if you have two cups, that look different but feel the same on the columns that represent touch there'd only be one representation, it would be the morphological feeling cup and on the visual columns. You'd have two representations, and so the the representation in the touch columns would uh could would be would would basically be associated with two different objects in the visual column. So, if I I would say, oh, I know what this is from a field, but I can't be certain which of the two objects.

D

It is from a visual point of view, but so there's a one-to-many mapping from one modality to another and that's all consistent uh with how this would work. Although we didn't model that um that would be consistent, so the touch columns wouldn't know the difference between a a memento company, non-dometico.

A

It's another thing: someone could sort of play with and see what the issues are. uh Let me talk about inference what happens in inference. So hopefully you have a good sense of learning. uh Do you have another? Very, very brief: it's just what are the biological constraints for how long those horizontal predictions can be? So if it's two, if there's maybe like 500 columns, can column 2 still reach um 500 yeah? Well, some connections are really long.

A

Like jeff was saying in general, like in the visual system, you might see that it goes several cortical columns on both sides- maybe half a dozen or something like that, but in but there are axons which go like all the way from one side of the brain to the other. Okay, um so I think jeff's brought up that you know. Sometimes the cortical columns for your left fingertip connect to cortical columns from your right fingertip, which are completely in the other hemisphere in your in your brain, because quite often you're using two hands to follow.

A

I mean once you think about voting. It makes total sense that it would be that way, but um it's a very, very long range.

B

Is it known to how many columns one column connects.

A

It um it varies a lot so there I can show you one image that I was showing then on friday. That shows us three to six on each side uh in the visual system of this particular animal. But I think that's that can vary quite a bit by level of the hierarchy of sensory modality.

D

I think it almost doesn't.

A

D

Yeah and even those when the neuroscientists look at this, so there's an accident coming out of the bottom of the neuron and they try to follow where that axon goes well. If they look locally they'll see, oh, it goes as the next column over the next column and so on.

D

But one of the definitions of pyramidal cells is that a branch of their axon, a branch always exit the bottom of the neocortex that by definition always happens, so they often will ignore that like well well, that branch goes all over the place, so some neuroscientists will look at the local projections and say: oh it goes so. These are a couple millimeters this way and several millimeters that way, but that cell is guaranteed to leave the cortex and go across the white matter and enter someplace else.

D

But one way to think about it like how many columns can an individual call it. The cell attached to well individual cells, have up to about 10 000 synapses, um maybe five to ten. The number is very difficult to find a good answer for that, um so that limits how many different that essentially limits. How many different columns an individual cell could get connections to so? This is why I could go back to earlier.

D

When you make long-range projections, it really doesn't have to connect to every column. It could connect to a very small set of columns and it'll work. Just fine as long as all the neurons are doing the same. So um as I think subasic said it's, it's kind of a red herring to think about it too. Much just assume that you're going to make enough connections um sufficient to meet the rules of sdr matching and uh and in this model, we're showing here is a very a very constrained model that illustrates.

A

All the points yeah it's essentially, if you need to make, if you need to do voting across two different columns, uh it doesn't matter what the distance is. um That probably will be something but or the possibility for something I.

F

Think if we're designing a.

A

System we may want to put some of that bias in, like the axon, going from one side of my finger to the other finger or my left hand to the right. That's probably genetically determined. It's not gonna happen by random chance, just through learning. So that's those are kinds of biases. We may want to build into a system that could depend a lot on the situation and stuff, so that could be an area of exploration.

A

It's kind of almost like how do you initialize the weight matrix you want to put some sort of biases in and that will determine what can build what kind but locally. um I think this can just happen as a function of learning.

C

So maybe you'll cover this when you talk about inference, but if we're trying to design a system do we know anything about what's optimal, so we definitely need enough voting connections to be useful. On the other hand, can you have too many voting connections? What, if it's all to all, is that actually less optimal than some slightly less connected immediately slower it'll be a lot slower.

D

Okay and take a lot more memory, yeah.

E

A lot of energy.

D

Yeah, you kind of want the smallest.

A

Number of connections, but no less than that, but is there an information to paraphrase einstein? That's okay! So.

C

That yeah, the energy, the energy and speed are important components. Is there an information component, though, to have that's bad about having too many connections? I could imagine a case where this might show up. So that's kind of my next thing.

C

I have to think about it. I can't.

A

D

I think you have to ask that question with asking about the threshold of a dendritic segment. If the threshold of a dementor segment is 20, synapses being active.

D

Well, if you now put, you know, 10 000 synapses on that dendrite, not you can, but in software you did that, and you only have a threshold of 20 but you're increasing you're, increasing your chances of having false positives. I'm not sure I don't know if that would actually be a problem or not. But my point is it's certainly not you're not gaining anything from it.

D

um You only need 20 to be active. Why do I give me 10 000., you know um it's you're trying to detect a single pattern and- and if you sampling 10, you know- I don't know it doesn't seem like it's in it only. It can only be the downside, there's no upside to it.

E

A

Yeah yeah other than computational efficiency just standing here, I can't think of a.

C

Downside to it, but also I mean one possibility- would be false positives.

A

No, I mean with these learning rules you shouldn't get false positives.

C

Really, even if you have ten thousands, I mean you're.

A

Not gonna make runs, I mean I'm assuming you're, still not going to make incorrect connections right, you're still going to connect to uh the same. You know, object, ids and sdrs and write columns and so on. It's just that. Instead of subsampling, you.

C

Have all of them right? That's your connection! That's your question.

C

Okay, a brief question on that, uh when you said it would be slower, is that because the software is going to be slower or is it because if I have more connections and I'm taking the union in of all these other sdrs, I'm going to get this big fat union.

A

No, the unions wouldn't be any debts. No, the unions wouldn't be any bigger. In that case, it's just union is just still the union of objects that are consistent with uh sensory, so.

D

I assume slower, did you mean by slower super tight that you just have to go and and look at all those synapses, so you have to somehow sequentially go through them. I.

A

Guess slower, I'm assuming a sparse computer.

A

If it's a gpu, that's always doing everything to everything. I guess it's not any slower, but um I'm assuming it's yeah. It's somehow it's dependent on the number of non-zeros, so um you'll have to compute max with a lot more synapses and it's going to be using up more energy, certainly in the biology it's going to use up way more energy and you just physically couldn't fit all the connections.

D

It's been argued that that synapses, the number of synapses is the determining factor in energy usage in the brain. That's not necessarily true in software, but in the brain and so the brain really, even though it has existing synapses, it really wants to reduce them uh and its method for doing that is to rely completely on sparsity for everything and consumitized on the math on this, and it works out beautifully so um yeah. Just it's another little biological data point that synapses are our energy.

D

F

D

Individual synapse doesn't take much energy, but they are active processes and they need to. They do active. They consume energy. When you, if you you start putting, you know, you know, 500, you know billions of synapses some place. It comes be a lot of energy.

A

E

Let's talk about inference.

A

um The inference rule for this cell is is pretty straightforward. um First, it needs to get sufficient amount of bottom up inputs in order to become active.

A

But hold on to that thought later, but it needs to get sufficient input from bottom up to become active.

A

But that's not enough, it also has to win in the winner, take all competition, and so what happens is within a column, uh we're gonna take the cells which have the most number of dendritic segments active and those will be the winner.

A

So if you have some cell that has three dendritic segments active and enough bottom up input, another cell has four dendritic segments active and enough deported, but the ones with four segments active are the width, the more segments you have um uh either any segments on a single neuron or in different ones on that on this neuron. So, in order for this guy to win, it has to have enough bottom-up input, and it's in the number of segments that are on has to be in the in the top right range.

A

So in your diagram, what you have six of these horizontal lines? That's not considered one! Second, that's just uh these are six segments yeah, so this is different from what we did in the continuous learning paper there. If you had even one, you would just pick one segment and that would bias the that means. Multiple segments are learning the same object.

A

Well, in this way, so these three segments are learning three different sdrs for the same object.

A

um So that's basically it that's the rule and so the way this would actually the phenomena that would happen would be. You get some bottom-up input and, let's say.

A

We look at column two here's time, and so you get some input such that the input is consistent with two different objects in here: um object: one and object: two, those two sdrs will be active and in column three.

A

Let's say the input is only consistent with object one, and so you get the sdr for object. One will become active. So at this point in time all the cells.

A

Yeah, so the cells that represent object, one are going to get lateral support locally from the other cells that represent object. One and the cells here that represent so in in these cells. They're going to be two dendritic segments active in the object, two cells, it's only going to get support internally, so it's only going to have one digit excitement active. So what will happen is that this will basically the object. One cells will be the ones that went out so it's.

A

This is what we mean by voting um so object. One cells are going to get two votes, one internally, one from the neighboring column, and then this one's only going to get one go to it. Only the one with the one spot swings okay. So this is the simplest.

B

B

Yeah, could we extend it to a case where that's a column? One is very, very confident. It's got to be this object and maybe column three is not as confident.

A

Yeah, that could be another extension. We didn't really model confidence uh in here or noise.

F

You have the strength of the synapse right. If the, if the weight that was learned with heavy and learning is stronger, then the voters waited a bit more right.

A

uh No, the way we did it is the the strength is just a permanence, so it's either determines whether it's connected or not, but the impact is binary, so we didn't have a weight learning biologically.

C

Speaking, there are two sources of input strength here would be the strength of the synapses and also the firing rate of the cells, so cells in layer, two three and one column- could just be firing faster than in another column, which would lead to possibly more activity.

A

Yeah yeah, we sort of waved our hands um this cell. If it has, the more dendritic segments are active, the quicker it would fire and that could be enough to win in the local winner, tickle or it could be like you're saying, maybe it just fires more more often or something, but anyway, that's the rule is it's just whichever cells have the most gendered segments act and those are the ones that end up with um another.

A

Because, here we can look at column one we can make this a little more complicated I'll just do abc. Instead of.

A

Let's say this is consistent with objects: a and b. This is consistent with object, b and c, and this is consistent with object c and a what would happen in this case.

A

I'm confused you're confused. That's! What's.

D

Going to happen.

A

Oh okay, okay, now I know I've been, I was trying to make a joke yeah, but you shouldn't have questions.

A

You're, like the ta today.

D

I'm sorry, I'm scared I'll mute myself.

A

What which cells would stay active, so you need to mold them right because there's a lot of supports for every single object. What do you mean? So if a yeah for a I have support in my column, but also in column, three b is important in my column, but also com2 and c. Saying: okay, two and three: each one has an equal amount of support, which means I have a union of all of them and I am confused yeah yeah. Exactly so that's exactly correct.

A

So each each cell would exact have exactly two votes, uh two sets of votes, and so there's no. You can't tell the difference at all. So then just keep them all all this union they will all become active. So maybe 80 cells acted here. Maybe 79 cells active here, because one cell is shared 80 cells active here or something like that, so it would be just a large union will be there.

F

So if we would assume we cut the connection between column, two and column, three so they're not connected, but the rest of the connection stays within object, b, win so say that again, so if these are not connected, yeah.

A

um Well, b would win here, but cna would still be active here.

F

Okay, so it doesn't matter if, if two columns already agree on one object, it's still the same way. If it, it's still just one vote. If it comes.

A

I mean that would be. That would be a weird situation, though it's like you're getting you're getting input, that's consistent with b here, but it's not consistent with b here. So then, what are you actually sensing? Are you actually are you actually sensing two different objects.

B

If there's no communication between two and three then b would then encounter a would win in column three, and then we serve a b and column. One.

A

Well, there's no connection from column three to these guys, both just two and three. Oh.

B

But three is still connected to one. Yes, just two and three is missing, so you think it still works. We lose the c support.

B

D

You know in some sense it doesn't, if you say, columns.

A

Do not actually be. This may not actually be possible.

D

So can I can I comment, or should I be complaining and no problem? um First of all, remember what I said earlier: we're thinking about lots of columns, in fact that two and three aren't connected really doesn't matter.

D

It's the entire network, we're just trying to set them, so you don't need a directional connection between any two columns as long as all the columns somehow reach each other, indirectly or indirectly, and- and in this case there is no answer, this would be something that you'd find very puzzling you'd, be sitting there scratching your head, saying this doesn't make any sense at all.

A

Yeah yeah, so maybe it is not a good. You.

D

Know what I think it's interesting, I think we should just.

A

F

Yeah- and I was just trying to figure out if the connectivity plays any role in in there.

A

It does, but in general, when we modeled it, um these things still settle pretty fast. um We, the question, is.

A

You know how much uh could you ever.

D

Yeah, I think this- I think this actually relates to the task of identifying objects tossed into a box, um because he had multiple objects and they are, you know, they're butting up against one another and they're not complete, and so what I would imagine would be happening in scenario.

D

This is true if you look at actually the columns in a particular region of the cortex they're, more heavily connected to nearby columns and the further and further the way you go, the sparser the connections are, and so there would be a bias towards a local group reaching a consensus that, even if that local group is inconsistent with some distant columns, so imagine you're. Looking at a partial object in the box that the get was in there, some yellow cereal box or something I know what it was.

D

I can't remember um some of these columns could say locally.

D

You know what we're all together here in some local region of the cortex, and we all agree that we're seeing you know, object a but there's some other people over there who aren't and they're not as heavily connected to us and they think they're seeing object b, it's quite possible that you know the system will say well, let's focus on one of these at a time a and then move over there we'll focus another one b, but the distant connections could be ignored uh because they're fewer so that I think that's something like that's likely happening.

D

um They're, not all connections between all columns aren't equal they're. There are sparser the further away you get, so you could lead to wrong. This example doesn't show it, but you couldn't reach a local consensus.

D

That says well at least the the center of the visual field or the tips of my five fingers and my right hand are all agreeing on something, even if some other columns further away are not agreeing with us.

A

Yeah yeah um and we didn't really model we didn't model or test out that scenario. I think the way to think about it is there's, at least from the columns. Favorite perspective is there's. Some true object that you're sensing and everything is going to be consistent with that object. So we can. We should make sure there's like a the true object, is let's say it's equal to b here, so everything's, going to always be consistent with b you're, never going to sense, something that's not consistent with b uh and here. So here's an example.

A

You know this finger. Let's say these are different fingers. This finger is sensing a feature: that's consistent with a and b this one, with b and c, and this one with c a and b. So I'm sorry.

F

That that's, assuming that every column has a model of b right. This assumes every column has a model of b yeah. um Every.

A

We assumed every column has learned every object, yeah and um yeah. So what would happen.

B

In in this case,.

B

Yeah, so each cell here would get three.

A

A vote of three, so you very you just basically end up.

A

um Yeah, so something else that could happen this again. Let's say the true object. Is d: we've got.

A

A

B, a so what would happen here.

A

You want to take a crack you're on the spot. Well, you have an equal votes for, b and c so.

A

Yeah, so what would happen here is the b and c ones would stay. So at this point the system still hasn't uniquely converged. Okay, and so now we have to sense something else to really uniquely converge. So when the column doesn't learn, there's a normal dot, it doesn't focus something wrong.

A

We're assuming every column knows, but then um you'd get like a burst of activity. I guess or you wouldn't, actually you wouldn't get the chips. Yeah yeah it. Wouldn't it wouldn't get enough temporal memory right so that ac will never have one before correct yeah.

A

So here um in the next step, you might you'll sense. Another three features, so here you might get b c a here. You might get dv. No, you won't! No okay,.

G

G

A

um Okay, I'm gonna, I'm gonna. Take you guys here.

A

It's not gonna fire.

A

So this this could happen.

A

This could happen so um now column, one is sensing, a feature which is consistent with b c and d uh column, two with a b c and d and column three, with b c d. So what happens in this case.

C

uh Definitely in columns one and three uh b, c and d should remain active and in column. Two. Probably it would just eliminate a yeah.

A

So that's not correct um thanks a lot.

A

It's probably because I forgot to say something earlier is that the remember these things are more stable, so if it was, it also has to be stable in the previous time. Step also has to be firing in the previous time step in order to win. Oh.

C

We're talking this is.

A

C

Is time yeah yeah, I'm sorry! This is time here. So this is sensation one. This is sensation, two all right. So what.

A

Would happen here is that actually this d cell will not, even though it has lateral support. It doesn't have um support from the previous time step and then these this one will also happen. So it'll still be b and c so stay locked into.

C

Vnc this is similar to the temporal memory mechanism. It's going to stay locked into the specific subset, even when it gets other confusing wait. How is that? How is that possible? Because at time step one, you had to be receiving sensory input that was associated with d in column, one yeah, okay and then in time, step. Two.

A

Remember after this, what stays active are only the vc cells because of this voting.

C

So, even though it got information consistent with d, only the b and c cells would stay active, but what's happening at time step two. As far as the raw sensory input that made d come online.

A

um You're sensing some, you move your finger to another location that happens to be consistent with these three objects. Okay, so it's getting sensory support for d yeah, it's getting lateral support for d yeah, but not from the previous tensor, so there's some persistence that we have the cells associated with d aren't depolarized right because they never reacted this kind of stuff yeah yeah, because I forget the exact rule. I have to look at the paper again, but we you have to be active in the previous step in order to stay active.

A

D

The way to think about.

B

A

Just enforced one one more time, step of stability in here, so the detailerization lasted a little bit longer.

D

We're trying to do is you're trying to narrow down your possible answers and there's two ways you could do it. A single column can do it by sensing over time. Right so uh and and then multiple columns can do it by voting at the same time, but they're all trying to do the same thing. In this example, the only you know d is not consistent across time and space.

D

It's it's it's five out of six of them, but not six out of six well b and c are consistent across five out of six six out of six, and so it's it's just you. You've got two ways of eliminating it by movement and by voting and and they're both doing the same thing. So imagine if I was just using column three when I and and I moved my finger well, I wouldn't introduce d it because bc is the only thing. That's consistent with time, one and time two.

D

So in that way, just like how many d's are there versus how many b's and c's are there and you're gonna see it's d is not a it's, not a contender, because it didn't exist through time.

D

Yeah. I think it's, I think, that's right. The way that you think of it is just think about one particle column over.

A

Time, first um and the things have to be active the previous time step in addition to the current uh activity from the current time step. So it's kind of what I'll.

C

Be said that the depolarization and the b and c cells last one step longer so really there's more than two time steps here like column, one had a b c d, then it voted and it went down yeah. Yes, then, in the next step it had uh b c and d e d came back alive. Briefly yeah you came back alive, but actually yeah. What's going on yeah, so there's these, so these are different sensations and for each sensation.

C

There are a couple of time steps so there's like a sensation, step and then voting steps and then a sensation, step yeah. So so, if the yeah, I don't understand,.

B

This, if the idea is that you.

C

Can't if d can't be resurrected.

A

Well, if these things, so the persistence is if, if these cells are active through voting, um they're going to stay, active they're going to be strongly active, so they're not even going to let these d cells become active they're just going to, because the winner take off mechanisms.

A

You know, I'm the.

C

I'm the leader you're, not gonna, they're, just strongly active, so the real sequence should be a b c d, sensation, step b c voting, step, yeah, b, c sensation, step d, just never got resurrected; it never got resurrected yeah. This would.

A

Be kind of the information that's consistent with d yeah, so I guess if I were to really draw out the neurons.

D

You know, but we're not sure what.

A

You said is correct. I think what.

D

What you're not showing is is here on your left panel you're, showing the uh the features, the sensory location layer and at that point, when a new sensory input comes in, even though that sensor input uh would be uh might be d you're not going to get uh it. It's already going to be narrowed down there as well you're, not really that column isn't.

D

That column is already said, a sort of uh it's it's location layer. uh Let me say this even in the column you're trying to narrow down to a very sparse representation. So you may not even represent d anymore, because um because d is inconsistent with the location and and uh uh maybe I'm not making sense. But my point is it's: there's it's there's more going on here too, and I think which I present is correct, but you know.

A

I went probably a little too fast. I should do it the way you you just said. It, then, is that I should say: okay, here's the information from the lower layers, that's consistent with these objects. Here's the actual cells that initially become active- and here are the ones that win right and then the next level. Here's the information coming in is consistent with b c and d, but because the bc cells are still active, these would never in the output layer. These cells would never become active.

D

Right right, if you think of it, like a temporal memory like a learning melody.

A

D

You you hear two notes in the melody: you've now eliminated a whole bunch of of uh possibilities. A third note comes in well. That third note could be in any other melody, but we're not going to even represent it and we're going to represent if it's possibly represented in the two choices we currently know. It's like. We there's temporal, there's temporal memory here. There's the system is not it's narrowing down over time, so you can't go back and represent that d.

D

uh It's just not it's the input's going to be d, but pretty consistent with the, but the input is not going to.

B

Be represented, it's only going to be representing the context of b and c yeah. So sorry robust against, like one.

A

Yeah, so that's something we.

E

That's a separate thing that someone could work through, but I think that needs some additional.

A

Work to make it really with us, or something like that, um yeah you have to remember. This is like we didn't even know how any of this would be possible at all with neurons.

A

We just worked on the simplest thing and just even the whole idea of having a location and the point of the columns paper is actually just you have with the location signal. You can now do all of these things, and that was a new concept at the time, but there are all these variations and extensions and corner cases and stuff that we didn't really have time to get in the paper we sort of moved on to other things, but those are all still valid for.

B

Exploration and we think about monty in a in a real practical system, you want to handle some of these many of these situations, so these are kind of research questions. I.

A

Guess um but you can see throughout it in the output layer, we enforced more stability in the neurons in a couple of different ways, and that does match the neuroscience.

C

So there's there's no arrow. I see going back from these layer two three or these output uh layers back to those input layers, yeah.

A

So there is in the paper I just didn't draw them in there. We can talk about that in a second okay yeah. I just want to make sure we cover that topic. Okay, that's actually a somewhat confusing topic: okay, yeah computationally! Is this just like an intersection, yeah yeah, it's exactly set intersection, but it's doing it over time in space yeah. So the question was: how could we do this with neurons in a way that maps the biology? This is the neuroscience paper, so voting is just set intersection. It's just said intersection.

A

That's it in in this case,.

A

Yeah, which is just sex you can think of as just sets in the clean case, um but once you have noise and when you have this many to one mapping and things like that, then sets kind of break down a little bit.

A

It's something more than just simple sense.

D

This this, from a neuroscience point of view, solved two huge mysteries in neuroscience. One was: how is it that your perception is stable when your inputs are changing and the second one was. Why do we find all these horizontal connections between columns because it didn't fit in anyone's paradigm for how the cortex work, and yet these these horizontal connections are very obvious um and they're everywhere?

D

So it was a real nice solution to both of those problems at the same time, and they were, they were very fundamental problems um confronting the neuroscience of the neurocortex. So you know the chance of this is being basically right is very high. I think extremely high details. You know- maybe not so much but.

A

Let me talk about the feedback, which is a little bit and then vivian. Maybe after that I can get to your. I should say the paper we did have feedback connections here.

A

um This is a somewhat confusing topic, so in the paper we have a specific rule that we implemented there. um When ua looked at evidence for these feedback connections, um it was somewhat sparse in the in the literature. It was actually hard to find evidence that there's actually feedback from their two three two. Therefore, um he found some papers that suggested there might be some, and what we were thinking is what this would do.

A

Is the output layer would bias the lower layers so that, if there's noise or if you skip, skip an input or something like this, that's another depolarization effect that happens here. There's these connections would be enabled dendrites, which which have a particular type of depolarization, in fact, but then what marcus realized after we had published this and that when he was doing the columns plus, is that we couldn't actually think of any scenarios when this blue arrow helped.

A

And we ran a whole bunch of scenarios with noise with and without these things, and these arrows didn't actually help. um So I we actually left somewhat confused about this. Maybe there are still scenarios where this helps, but it's kind of interesting that in the literature it's actually hard to find this connection, then we couldn't find that between these two layers specifically and there's feedback, you know other types of feedback, but this particular feedback connection.

A

We never really found a good, so the reasons we thought it would be. There didn't actually work that connection wasn't actually needed, so that was kind of interesting.

A

Right now, a little.

D

So we left kind of confused whenever I really.

A

That would just be apical support right, yeah. We did implement it so in the column of code it, um but then, when we tested it it would be just apical support and then there's different tiebreaking rules and stuff. That's there so with and without it we couldn't think of any.

D

Okay, so now some more real confusing stuff in the columns paper, we assumed that the representation location um was shared among objects that two objects could have the same representational location like oh, this is this. You know some corner in space, but in the columns plus paper in the frameless paper, we moved away from that to realizing that the actual representation of location could be unique to the object and therefore the information that changes, the need or even the perceived need for having this feedback.

D

The feedback was to help the lower layers differentiate. What the objects were. That's the idea was at least, but if the, if the lower layers already know or have a unique representation for the object, it's not necessary, um and so that's one big twist on this is when you go to a representational location that is sparse and unique to the object, then you don't need that feedback, and the other thing is that these layer, 23 cells, do project uh to other layers.

D

They project down to layers, fine and um and that's a very well known projection, and so they could be influencing the location layer directly, uh not not influencing the layer. Four sensory input layer but influencing the layer. um You know it could be telling it could be telling the location layer. Well, I know what object this is. Therefore, perhaps you should you should you know, start narrowing down your locations to be unique to this object. So it's much it's pretty complex um and I think there is.

D

There is feedback from this layer, but it's not as it was shown in the columns paper.

D

Hope I didn't lose too many people on that.

A

uh Vivian, did you have a question.

F

uh Yeah, so to the point that you mentioned jeff earlier, um so I understand it makes a lot of sense how the voting leads to the stability of perception during inference, but during training it seems like the stability is kind of externally enforced, at least. If I understand it right how you are doing it that you enforce it to have a stable representation.

F

Is that right? And if, yes, uh how would this line up with the biology.

D

Yeah, well, that is right um and you're. You know basically to learn what an object is at a very high level. You have to do what we call temple pooling. You have to say this pattern in this pattern in sequentially in time really represent the same thing, and the next pattern represents the same thing too in the next way. That's a fundamental definition. What it means to do object recognition. You have to have multiple patterns that are different inputs, but they represent the same thing.

D

So this has to occur one way or another, and uh we just assume that okay, we'll do temporal pulling meaning that we're going to assume that the pattern the moment ago is still active while the next input comes in and then that is still active and so on.

D

But it does, as you point out, ribbon forces to say: okay, we're in sort of a learning mode right now um we are trying to learn something new and we're going to assume that there's a constant object underneath and while we assume that we're going to move our sensors, I think that's a reasonable assumption that that, during learning of a new object, you would be in some sense concentrating on that and attending to it and enforcing those neurons to stay active which would be different than during a inference.

A

Yeah and that it's a much um it.

E

Makes many fewer.

A

Assumptions than like supervised learning and deep learning, where they're not only are we saying it's an object, we know we're saying specifically it's this set of cells that correspond with this cell that correspond to object 23.. So this is a weaker assumption, meaning it's making fewer assumptions about it.

A

It's just saying: oh, we have a new object, we're not going to tell you which cells have to be active, um but it does beg the question if you and we've talked about it recently- also like, if you learn part of an object and you go away and learn another object and come back to an object, how do you automatically determine that you're in some object and continue learning that and things like that? So those those are, I think, really interesting issues that we never kind of work through here, but there is.

A

There is information there, because if it would be, you know, temple memory cells would be bursting or there will be some surprise signal somewhere available. So somehow we could have just added.

G

F

I think it's a reasonable assumption that, while you're learning you have- and you kind of, can assume that you're staying on the same object for over some time, the one thing I feel like you you're missing a bit with with the approach of saying okay. This is the set of neurons that will be active, for this object is that you are not really learning bottom up from the sensory input, so it will be more difficult to share lower level features that are common across different objects or have more similarity in the objects representation.

F

D

I didn't I don't.

F

So you're saying from top down this will be the representation for this object, um so you can't uh learn bottom up, saying: okay, this object has similar sensory input to the one that I already know, so my representation will be similar to it. No.

E

F

An edge like that.

D

I think, let's be careful, because the system can recognize an object without this. Without this temporal pooling voting layer, it's not necessary if we narrowing down a unique representation of location and a unique representation of the feature. The system can narrow down and infer and learn objects.

D

What you don't have is a stable representation for er. It's like learning a melody. I can learn a melody and not know the name of the melody I say yeah. I know this melody. I can predict the next note. I can pick the next note, but if you ask me what the name is, I may not know the name, but I know the melody, um and so I don't have a stable representation for that melody.

D

I just know what the next note is, and the next note is in the next notes, so learning could occur and all this can occur from a bottoms up point of view. What's going on in this layer. Is it does two things? It allows adjacent columns to vote to reach a quicker consensus and it allows us to have now a stable representation that we can classify.

D

If you want to put a name on the object, but there's a lot of things, you know the shape or the things like a melody where you don't have a name for it and you haven't. You may not have even done this step.

D

uh You know what I'm saying: it's like: it's not required to recognize an object.

F

Yeah, I guess what I was thinking was, for instance, these dendritic segments. They are pattern detectors. So if two objects share the same feature, uh they should be able to also share the same dendritic, dendritic segment uh and and then.

D

But but these, but these dendritic segments in the in the voting layer are not features right. They're not representing.

F

D

At all, um they're representing the object, so why.

A

You know what one thing you might want is that the sdr and the output layer, if two two objects are somewhat similar, maybe there should be an overlap between those sdrs right that would be a nice um potentially a nice property to have so, if you have two different mods, they might have more similar sdrs than if you had a mug in a car or something right. So in that case, um what would happen is the dendritic segment or that represents mug, might have the same synapses than the dendritic segment. That represents a car.

A

I'm sorry, another one or you might have the same. Degraded segment might end up somehow, representing occasionally the same bug. Those kind of things could happen. uh We never really worked through a lot of that, but it wouldn't be that everything is always the same. It would still be some part of the representation would be similar. Some would be different well, this gets.

D

This gets this gets the problem that subatai always brings up, which is what multiple people brought up, which is a problem of um classification or categories right, and you know, there's mugs, there's, there's certain types of mugs. There's ceramic mugs, there's my mug, you know there's a whole bunch of things that we might say are similar or not, and in this scheme the way we're doing the sdrs here in the voting lab does not is not amenable to that.

D

um The the way we're doing the recognition in the location in the feature layers is amenable to that. um But it's in general it's a problem. We haven't really resolved.

D

I think when we started out when we first started thinking about sdrs, I was very excited because I I really got into the idea that there would be semantic overlap between the bits right, but when you, when you go to these really sparse representations, it's hard to have the semantic overlap.

D

um It's just there's not enough bits to do it and say if I only got 40 bits, active, 40 cells, active, there's, not enough. Those cells really can't represent something. It's just math doesn't work out that they could represent semantic meanings and I can do overlaps where you get the overlaps is when your sdrs are not so sparse, like the mini column str's there you have like 10 of the of the cells active or 10 of the mini columns active.

D

Now you really can have semantic overlap, but when you get to this very sparse representations, it's mathematically very difficult to imagine how it would work. So I think this is just an area that we haven't really finished uh thinking through. Yet um I'm not worried about it, but um it isn't. It is an open area.

A

Yeah, I didn't you know if we could get to the point where you have a new mug that you hadn't seen before you could still recognize it as a mug and then over time you might learn a very specific representation of that mark like if you've first time you come to the mend, and you see a momentum up, you still know, but after a while, you have very specific, you might have a very specific representation of the momentum.

D

One little detail: the neuroscience which I find intriguing um and I'm just trying to throw it out because it's for those who, like the neuroscience. But you know there.

F

Are layers there.

D

Are multiple layers in layers two and three, and some people have said, there's four different layers and layers, two or three and then they've mapped them out and so on, but there's generally an agreement about information flows vertically from the bottom to the top up through layers from layer, four to lower layer, three to mid layer, three of layer, two and so on.

D

And another thing intriguing thing is that layer two seems to be the sparsest of all ignoring layer, one for the moment um and and so there's a possibility that somehow your you're sparsifying the input as you go through these. You know vertically up to layers two and three: it's an intriguing idea.

D

I don't have a theory about it, but you know that's what the neuroscience says that they're not uniform uh it's much sparser than layer, two than layer three, and perhaps what you're seeing in layer three is some sort of representation where you have more overlaps, but in layer two, you don't um so you could be voting on a category and on a specific object at the same time.

D

So there's going to be an answer here, just interesting things to think about.

A

And maybe the hierarchy plays a role in there too. We haven't really talked about that yeah. You know it's quite specific in some places less specific than others. Things like that.

D

You know it's funny because a couple months back, I gave a little. I had one day in the research meeting. I suggested a possibility for how to do classification, but I can't remember what it was now.

D

What did I talk about anyway? Well, it's.

A

Probably recorded if you talked about it, every.

D

Day yeah, I know I'm starting to go some triangles with some little recordings.

C

I do this is going to sound like a stupid question at first, but bear with me um what does the stable representation in layers? Two and three do for you like in terms of acting in the world or an evolutionary advantage like if there's, if we don't have a use for that feedback from layer, two three back down to layer four?

C

Is there a connection from layer, two three to somewhere else that provides some advantage, because there must be some output from that output layer going not just to other output layers to enable you to act in the world or make predictions or something yeah. I mean yes, yeah. The.

A

Layer23 does project to higher levels in the hierarchy, uh for example,.

D

Not just not just to layer three but to layer four in the next four of the next level right, so that's so there is a connection there.

C

um A pathway there, um okay, but so there's that.

A

And there's going to be player, five.

C

A

But there's also a notion of attaching some sort of a label to an object, not not a textual label, but a just a stable concept associated with the mock. It's not also the specific point of touching, but there my percept of what a mug is or the percept that I'm touching a singular object is constant over some time.

A

How do you implement that and what we're saying is that this voting you know coming into it. You know collapsing to a singular representation. That's consistent everywhere. While you are sensing an object, that's sort of one manifestation enough, I'm not going to say the c word, but.

C

Sure you know layer, four is sensory and you know layers two and three as like percept, so there's sensation and then there's perception. So I'd be thinking, players two and three as a person. So.

A

Some stable representation of what you're sensing.

D

Certainly you're not aware of what's going on layer, four, you, you are totally unaware of it right, there's no consciousness of it. um You are to some extent aware of the stable representations.

C

Yeah that totally counters what my I had previously thought.

B

I thought layer.

C

Four was like you were definitely aware of that, so this is a big one. No.

D

No, like you're, not aware that your eyes are moving all the time right three times a second, the complete input to your brain. Your cortex is changing you're, not aware of it. Yeah.

A

D

Stuff is changing constantly.

A

Even you know, as I'm looking at you, it's changing constantly.

D

A

This is like your nose on the left side of my you know. Right now. Now is the nose on the right side of my right now it doesn't. I didn't notice that.

D

Let's, let's get so first of all, and there is feedback, as we said before, layer, two and three feed forward as soon as I just said in the cortex, they also feed back to layers five and the chord in the same column. So there is feedback.

D

I guess, there's.

A

Feedback here this I mean, if I drew all the connections.

D

So, let's talk about the evolutionary advantages. First of all, it allows you to infer, what's going on in the world much much faster, it's like if I can only touch things with one finger. If I can only look at the world through a straw, my abilities to react to the world and understand would still be there, but it'd be extremely slow.

D

It also allows me to take things like you know, sound and touch and hearing all these things that are partially available and reach a consensus, even though either none of the senses might be able, on their own, tell you what's going on, so it's very quickly reaching a reality like this what's happening, there's a huge advantage to that. Second advantage would be in your in your episodic memory and your hippocampus.

D

This is what you remember that you did right. You don't remember where your eyes were pointing at any millisecond here or any hundred milliseconds here, but you do remember that there was ben in this part of the room and they were super tight in this part of the room, and I was getting hungry, it's whatever. So those are the things you want to store in episodic memory. You don't want to store the activities of individual columns. You want to store like no.

D

This whole thing was here at this location, so that forms the basis of your memories, uh your your sort of temporary memories about the world um and that's essential for survival to say: oh yeah, it didn't matter where my eye was when I was looking at you. It matters where you were relative to my body and that's those floating layers. So there's a lot of evolutionary advantage to this.

C

Yeah, thanks jeff. I guess my question was. um I guess I didn't answer your question.

C

First of all, you added something really important to my understanding that uh you want to store basically something like those layer, 2 3 sdrs. You want to store a model of what's happening, not a model of where your eyes were pointing. So that's a really good point.

C

I'm trying to ask a slightly- uh and maybe we don't have an answer to this right now, but uh a further question of okay. So I have this layer, two three uh stable representation of the world- and you said it's evolutionary advantageous because it speeds up uh inferring. What's actually going on and my question is: how do I use that to actually do anything like the evolutionary advantage might be? I could react faster, but how is this stable representation? Actually helping me react, be like okay, so we have this voting going on.

C

What do we actually do? Well, I mean suppose.

A

This current sensory input is not consistent with a tiger in the bush right ready to attack me. It's just confusing right now, but the previous censoring was and the previous fight was, I mean, wouldn't you want to still say, there's a tiger.

C

That's that's not what I'm arguing. I agree with that. The question is, uh you have to be using it somehow, so the question is: how are we using that layer? Two three representation. I think.

D

Civil time is just saying: if you have a fear of tigers, um you have to wait till you recognize a tiger, and if it takes you four seconds to recognize the tiger versus you know, 100 milliseconds. Well, that's it! So then the evolutionary.

C

Advantage would be moving or something so there must be some relationship from these output layers to something that's involved in controlling movement.

A

Of course, so yeah yeah, so this whole particle column is very involved in controlling movement, of course, but as as jeff mentioned from layer23 there's feedback to layer five. So there are five within controls, movement or helps control movement, so those go sub cortically, but also this projects to higher levels as well. So this information does get transmitted all over the place.

D

A

More connections from there that I did okay.

D

Yeah, you know that yeah. I know that.

E

B

C

Obnoxious question.

D

It's not at all, I mean we're trying to carve out a piece of the problem which is inference you through movement of sensors and um and so that's what we focused on the columns in the columns plus paper. None of them talked about what you would do once you recognize something, and neither do most. You know deep learning papers. You know they think. Okay recognize. That's a cat! Well, okay, fine! What are you gonna do about it um so that wasn't the intent of that paper?

D

Those papers, but the all the connections are there to do stuff. With this I mentioned the episodic memory um so but I mentioned that it becomes the input the next layer, so that would be sort of building hierarchical, structured knowledge um and, um and then you know, the direct feedback to motor areas in each column. So there's a lot of things there, but we just haven't. We didn't take advantage. We didn't do anything without it. We didn't that wasn't part of these papers.

A

Lucas you've been pretty silent, but I think you had some questions.

E

Yeah, I just had a question about how deterministic is this algorithm but yeah? I think.

F

E

Answered them through the presentation that I kind of knew this the whole algorithm from before.

D

So what was the answer? Is it deterministic.

E

Well, not really right. If you have the possibility of dice and then you have to solve dice, it's not going to be obvious. Deterministic.

D

Well, well, I guess the question is: what do you mean by deterministic to me means that deterministic means given the same set of inputs? You'd have the same set of states internally. Is that right is that? How would you define it.

E

Yeah, given you have the same input, you always have the same output right. That would be.

D

So so, if if I was confused, if I couldn't tell between b and c that could still be deterministic.

E

B

Me answer it a slightly different way.

A

Because there is randomness in here we used randomness all over the place, but if you set the random seed in the code, you will always get the exact same output, exact same set of cells, everything, so it's totally deterministic in that sense.

A

But we do select cells randomly we subsample randomly select the output sdrs randomly you know, winning cells are selected, and so there is randomness yeah.

E

Yeah so, in my view, that's stochastic, I mean the setting the seed you're making is the fastest process deterministic, but that's still like stochastic.

A

Yeah right, so we use redness. We actually rely on randomness here, it's important for things to be random, to get the full scr properties, but it's not probabilistic in the sense that we're not really using probabilities, but we are. We are using randomness.

D

So so is this deterministic or not? I guess I don't really.

E

No, it's not it's, not it's not like you could have uh with the same input could lead to two different outputs. So.

D

Because you're, assuming like because you're saying the seed idea, that the random seed, that that doesn't count um yeah.

A

To me, it's really deterministic, but to.

E

Me, that's still.

A

Deterministic, uh like timing, you know, if you run on different machines, the timing doesn't impact stuff and uh order of execution doesn't matter anything. um So it depends on what your definition of determinism is. That's. What I was the future itself is. The voting procedure is totally deterministic. Yeah.

D

I guess I was confused by what that's how I guess it's different definitions of determinism all right, so I I'm excused for being confused. You could save advances.

D

There's multiple threads, the timing of the threads could make a.

B

Difference but here it doesn't uh for order of execution, and so there are definitely cases where the algorithm is deterministic, but it doesn't happen it's hard to develop this. Yes, one question: we get the intersection of union, which is in this particular case.

B

I mean intersection of the sets and the winner take all this equivalent uh in this clean case yeah, but it's over time, and especially, but it's over it's pure intersection, yeah yeah. So so what about the case? Like? Let's say we have this example here, where we have.

B

B, wins intersection.

A

Right yeah, so we're assuming here that every column gets consistent inputs. If the true object is b, it's never going to get something inconsistent with that. um If uh you could imagine some sort of a majority rule where, uh if there's you know if column three is just getting complete noise, maybe we still want to be at c to be active because that's uh if.

A

Or if you're not getting any input, um you can do it. You know these rules could still come into play. Remember I said, there's some persistence here. So if, um if at time in the first sensation you have b and c but the next sensation you're just getting random input, the b and c could still stay active. Potentially.

A

The other thing we've talked about is, if there's no activity here and if we have strong activity elsewhere, we could enforce dnc to become active, so there's sort of corner cases not corner cases.

B

But situations like.

A

Yeah, but in a practical system you might want stuff like that.

D

But one thing one thing you definitely want in the practical system is, is a column that was not sensing an object and now about to sense an object.

D

uh It should have an expectation of what it's going to sense um and- and so you would be ideally- and maybe I'm not 100 concerned about this, but ideally a column that doesn't have any input should still have an activation of some sort in its voting lab and- and it says, okay well, everyone around me is saying it's object b, so I'm not getting any input right now, so I'm not thinking about it. But in a moment I get input and given my location and another location, I'm getting an input.

D

Well then, I should predict x, you know, um so I think columns shouldn't be totally ignorant, so there there has to be a wave, and I don't remember how we did this in the columns paper. We did it.

A

I don't think we well that's where the defeat that was the idea behind this feedback.

D

Oh, oh yeah, so we didn't, we did do the voting then, and we so so. The idea there is a column could have activation in layer, 3 2, but not having any input right so, but it would still then that would then that would lead to its prediction. Okay, so that's what that was about yeah.

A

That was the thinking so.

D

A

I think that still occurs. It's just.

D

It's not going to go to layer. Four! It's going to go to layer five! So you don't know what that means. Yeah.

A

Yeah, so I think we're definitely running way over for such a short meeting but um says who ben doesn't want to stop so he must have yeah, but if you want to wrap up, we can't, but how about one more well? Did we address all the questions in slack? First of all, you had the most questions. Yeah did we get all of yours and I have three more of the three I asked I can. I can ask them later, but I think we addressed.

E

Some of them right so there's like follow-up questions that I had. um I think, if you can address the knife, everyone's not sorry, it'd, be good, because then we have like this single video that explains whole process and address other questions, so we can refer to it later. I'm fine keeping.

A

I'm fine going um it's up to you guys yeah same one.

A

I'm going to soon have to do something biologically.

B

The sensation being voted out for me temporarily.

B

My first one was that um these models were.

A

All two layers right: I wanted to expand this to more more than two layers. Then I would probably have those feedback connections. You were talking about those two little arrows. You grew before you. Let me ask what do you mean by two layers? You mean this is only between four and two three. Yes, so you mod like layer six, then I would need those other feedback connections momentarily through there right.

A

Yes, in the columns plus paper, we added this layer, six grid cell connections and we had a feedback between there four and there are six which is documented, and that was actually important. That paper. Okay, that's for sure it's important right, but in this one, two three between uh feedback from two three to four is not empirically as observable: it didn't do it. No, but maybe the stuff. We were just talking about earlier, where this column doesn't get any input at all, but the green ones do, and now it wants to. You know, bias those.

C

Yeah, that's my question too yeah. It's like previously. I was thinking of, and I think you even said at one point when I first asked you to go over voting, you described layer two three, as acting like a pointer down to a detailed model and another. You know machine learning parlance for thinking about that is like encoders and decoders. I've got this stable representation. 2 3. I might be able to decode that into some detailed model. That says that could make predictions about what I'm going to sense at this new location at this object. Yeah.

C

A

C

Yeah, the feedback definitely allows that. So that was the primary use case that I had in mind for layer 23 is that it would enable predictions um yeah, yeah.

A

C

But but that was not, but it didn't happen useful in simulations well in practice. Let's say you didn't have that this layer would get confused initially.

A

But this layer would not get confused because of the temporal persistence, so it didn't make any difference to the convergence of the output layer.

A

It would make a difference to therefore, but it didn't have any impact on layer. Two, three models: that's a subtlety yeah, okay,.

A

But since yeah I should say it didn't make any difference to our convergence, graphs and all of the how fast you recognize. Yes, how many and all this stuff, but yeah you would you could definitely see a difference here. Let's see worst things.

A

I mean the basic answer in neuroscience is, though, it's always more complex.

A

um I mean there's feedback that I think there's feedback that does not go into the dendrites, sometimes like you could have feedback into the viral segments or something else. But.

E

Also, the apical.

A

Stuff is a little bit complicated there's the way it works, not exactly the same as the basal dendritic segments, so it might so. For example, I think it might be possible to actually expose activity directly, just through really strong apical or there's this bursting stuff. That happens.

A

So it's a little I mean at the first order: approximation, okay, okay, I had another question about the. There was an example in the paper.

A

I thought was very nice, and that was if I have this digit, that I'm looking at and it occupies a very small patch on the retina, then I don't need that many columns to recognize it, but if that digit gets zoomed in and occupies a larger patch, then the ability to predict what that digit is is entirely dependent on the range of my horizontal connections in two three, so I would need more columns than I had before.

A

So my my question was: does this same system go doesn't still hold if I have like significantly more number of columns and if so is noise ever an issue.

A

We didn't do this in the columns paper. We did simulate the case of topology, where afterwards there was an intern who did that where, if you have lots of cortical columns, but there was here, we assume that every column is connected to every other column. So there we relax that assumption instead of a column, is only connected to its neighboring columns.

A

um You know and then can it still recognize objects and does this whole algorithm still work. So, basically, without any code changes uh we found it still converges pretty fast. It's a little bit, it's a little bit slower because it sometimes might take a couple of steps for information to. You know travel through using the same set of rules, but it's still convergence. It still works.

A

So that answered me a question or something I.

B

Guess yeah because you can't assume, obviously you can't have n squared yeah.

B

Okay, that makes sense.

A

um And the question that I wanted to ask the most um is: how does voting take into consideration hierarchical connections between different modules, so can voting happen between even heterocortical follows yeah yeah yeah, I'm treating this as like one yeah yeah, so can voting happen between layer, two three of one hierarchy versus um with another module of another another hierarchy. Can that happen.

A

um Yeah, if there are jeff, might have a better answer to this um so.

F

A

As the connectivity is there, it should be able this remember. This neuron has no idea where its functions are coming from. So as long as the connectivity is there, it should work.

A

There is also significant feedback projections that project onto the apical dendrites of these decks, so to the extent that the apical dendrite can participate in voting in a similar way it should it should work as well where's that coming from um higher levels.

D

I I was under the an and additional thinking that, if I have evidence for this, but I thought it was again remember these layer, two three cells um and all all parameter cells. They send axons elsewhere in the near cortex, and my understanding is electric three cells.

D

They make a lot of profuse connections in the in the existing column and nearby columns, but then they send to axons everywhere and- and that includes the other layer, two three cells in hierarchically higher regions- and this would make sense if the two regions are actually recognizing the same thing um uh it or or things that are associated with each other. um So my assumption has always been all along that. Yes, that voting occurs between hierarchical levels.

D

E

Makes sense, mostly between.

D

The ones that are nearby, like you know, one level up one rundown, but I don't from a mechanism point of view. I don't see why it wouldn't work and, and um it I I think it would. I think, in the evidence suggests that it does uh again. You know, like I mentioned before, you don't have- that the different columns don't have to all be voting on the exact same thing.

D

They just have to vote on things that are consistent with each other, so I can, an auditory column can can recognize a sound, but that sound could be associated with lots of different objects and that all works. Just fine, um and so again you know a a a column in v1 could be recognizing something like a um that is consistent with something in column. V2 is recommended, it doesn't have to be exactly the same thing all in all cases. So I think the general answer is yes.

D

Voting occurs between layers and levels of hierarchy, but it's complex in ways that we don't understand yet.

G

Did we tell that apical uh connection hierarchical paper connection? Do we cover that in any of our models in our published papers?

G

uh We we did model.

A

This this connection, but not this hierarchical connection,.

G

Do we do we think that there's any uh is that something we want to address, or is it not just not needed for our current models.

A

I know well, I think jeff has explained some of that, but so some of it, for example, you know certainly voting uh from other levels of the hierarchy. We do want to model that um there's also another similar concept of higher levels, imposing some sort of expectation on lower levels, which I think of is just another form of voting. Actually, I think, but people have shown that this, this feedback pathway.

C

Can act that way.

C

So this is uh often from layer six at the higher.

A

Level, so that's why I want to be a little bit yeah. You know and wavy here, um but as jeff said it might also be you know, connections, probably through hierarchical connections, so.

D

I think there's a general question here: kevin about april dendrites. So as our html neural model cells, we sell proximal dendrites, we show basal and distal dendrites um and we saw apical dendrites. We and and anthropodendroids are different. They seem to. They seem to recognize patterns similar to how the basal dendrites do. But then they don't sum at the soma in the same way and they have a different way of interacting with it's more like a multiplicative effect it feels like.

D

But you know when, when the apical dendrites recognize a pattern, it has a perhaps a multiplicative effect on them on the soma, and so we don't really know- and we have not specifically modeled that it's not because we don't think it's important because we haven't had a need to. We haven't figured out what to do with it, um and so every paranormal cell has apical dendrites every single one and uh it's clearly important and it must be playing an important role.

D

But we haven't been able to. You know identify a specific, not that we certainly tried you know, but we haven't identified a specific role for them in any of our models um and maybe we'll have to, but.

G

At the moment we haven't, we haven't done that.

G

Okay, fair enough. Thank you.

D

You know just to give you a back historical background. The way we go about this typically is not to say here's a feature of a neuron. What does it do? Typically we go about. Is here's a function that has to occur in the cortex or in the neural tissue? How could it be supported by the anatomy and, and so if we had a function that required apricot, then if this neighborhood of dendrite provided the solution to that would be great, but at the moment we're not sitting around going here. This thing was stuck on.

D

It fits okay. Enough said.

A

Yeah, so hopefully um you know what I tried to do here was to demystify it uh voting a little bit and just talk through step by step and be very concrete and literal.

A

It was good, um you know, there are certainly lots of things in here that we didn't it'd be kind of nice if someone were to sort of go back and take make a list of all the things that I said that we did have not done yet. That might be interesting. That would be a really good roadmap of just to have available.

A

I don't think that list exists anywhere.