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From YouTube: Implications of Traveling Waves (NRM - Feb 12, 2020)

Description

Continuing conversation about traveling waves (see NRM from Feb 12).

- https://www.nature.com/articles/nature08010
- https://www.ncbi.nlm.nih.gov/pubmed/22072668

Discussion at https://discourse.numenta.org/t/implications-of-traveling-waves-nrm-feb-12-2020/7188

A

Okay, we're good here.

B

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A

We're all good well.

B

I'll be online yeah, yeah.

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B

Wednesday 82 days ago, I talked about again talking about the weld a paper and, and we presented and I was confused by it, and so I was trying to walk through my thinking about it and then I had this idea, which I presented on Wednesday that we call this figure here. We had all these voltage controlled oscillators in the pic grid and trying to make sense of it and I said well. Really you were just tossing. My little cortical region would just be one row at leas and then I said.

B

If we it was it's possible that each of these ring up the oscillators is actually linear slab and the cortex. You have these traveling way, that's going to close coach Jetsons post around the circle, and so that and that, and then each slab is so. It looks like a. It looks like that. The old sort of a direction and velocity controlled thing up like this thing from above great. This is I'm. Sorry this is, we can go about you're right, so I marry off the track, so so I said well.

B

I was really intriguing idea and I try to get my head around. What was the meaning and that would work and.

B

Bouncing around this little crazy world up here, so I'm, trying to make sense of this and so well I have some thoughts about how one of the. If this were true. If this idea were true, what would be the implications of it? What what would it do and what would the capacity be in? But how would I even think about things like? What does it mean? Is this for true? So what I want to walk through my thinking that just is a way of practicing. It see what I got wrong and it's interesting turning around.

B

So again, if my mind will just point out we're looking down at the cortex, this is just a sort of classic boobies little ice cube block from the top you've got these orientation columns that go across approximately millimeter and then then there's these orientation slabs, which go in the other direction. As saying.

C

B

Week that I never understood, never understood why you have these slabs speculated over the years, but now we have a new idea to think about. Is that each of these slabs? It's essentially representing this, these voltage controlled oscillators at different peaks that different faces like that, like the analogy, was the way of study, so every hundred milliseconds for 120 milliseconds this whole this whole flat.

C

Would be oscillating as a voltage.

B

Which all lacerated, but the pink, would be traveling at practically these waves across cultures.

B

So how make sense of those first thing: I had to get my hand around I kept getting confused because there's two types of cells we're talking about here- one is the type of Stockholm HW self. That's what.

B

These the ones that they made it from and and the reason struggle with this, because in these voltage, controlled oscillator model, all these slabs are active at the same time, they're all oscillating, while the animals moving or the thing is moving they're, all oscillating, they're, all active we're in the cupola bezel. If you look at the cells like they put a sign up so degrading, they say no of the gratings movement best direction here. Well, these cells would be most active, he's a little bit less less pungent last night.

B

No activity over here so doesn't make any sense, because if you have anything active here so instead of either get it in their head that we really talk about to populations of cells, one population of cells indicates the direction in velocity. That's what whom abusal measurements, the cells and every candy column somewhere in fifty percent or less have some property that attraction and and velocity. So these cells, basically when they when something something moving across the visual field and we're talk about these- would be everything over there something moving across.

B

Then these cells, fire, higher frequency and and themselves are less though, but we need to translate that into voltage control, oscillator cells. Would you really do the cells in this paper are referring to and that's a different population in that population, while the animals moving those cells are in this case. In this model, did we sell throughout this entire grid? Those cells are all active at something close to theta and the ones that are in the slabs that are associated with the movement going slightly faster than the ones that are not in the flash gun.

B

So we're really talking about a different set of cells. Here these cells are held that we're sensing movement and turning that into voltage controlled oscillator in cell mechanism. That is yet to be specified and so I'm going to be talking now, for the most part now about themselves to control oscillator cells, which would presumably someplace even the cortex at this theory was correct and.

B

B

I couldn't showed it here up here up pointing out that there's a wildly animals moving there's some fatal frequency, which all these faults are control. Oscillator cells are oscillating.

A

B

And what it would mean is in look at their different frequencies across the slab I. Well, this is theta plus eight, and this would be theta plus four, and this would be theta plus four. The idea that maybe people differentially slightly I just poured into this place on another, but that this would be slightly oscillating faster than this, but they all go up in frequency. If you recall one of the requirements here was that as the animal moves that they all the baseline sales go up, but some more than others.

B

That was that little figure in that picture would show that this is the mean baseline theta. Frequencies is going up with speed, but then the ones that are in the direction of moving or open up before the lines, not the direction, wouldn't have gone west. So this is the electric plus 4, and that would be the plus 8 and somewhere in here we just have plus 6.

B

So that's the first thing now, if you didn't think about these travelling waves going across here again, it's like it within 100, milliseconds or 120 milliseconds, something like that. Every 20 milliseconds you're gonna have this like it's all cells. All the cells on the slab will find the same rate but they're just taking turns picking, and so the question anything is like. What are you never travelling wave?

B

Because if you look across, if you look across this direction- and you get Maggie by now- and this whole talk here, I'm going to talk about 8x8, I'm assuming but we're resently, each of these things is associated with many columns until there's understanding through number state, which is not a reasonable thing. I've done. This has a buddy.

B

So we're looking across the slabs here and I. Look at these guys right here, I! Look at a standing on each of these different I'm going to call these swimlanes. You see the slabs these, these yellows rule they're all slightly different frequencies, and so they'll be going in and out of phase right. So even if I started with with all st. pica their phase and then the way you start going up, what you see is, as the later goes up its going to start deflecting like this, because this one's going faster.

B

This is going slower and at some point.

C

They get all their stuff.

B

And so you would, you don't know apparent very quickly. You look like a cluster. You see things that all different phases, so the idea that there's a traveling wave that is moving across the surface I can't seem to make sense it doesn't.

B

You can just take the assumptions that these are at different frequencies and then they will there'll be a basically a fatal frequency movement across here, but each swimlane eats slab because slightly in our face and plenty of different treatments in how you measure this, you might look like a favorite, probably because you're gonna see and any one time you look at you'll- see if I can't will here here here. I'll see this traveling wave, but if I sample across here I won't see your wavefront I'll, see a bunch of things different points and that frequency.

B

So this point over here study migration up might pick populations of cells, data salesmen, and these reasons we're not going to see one wave front traveling across the surface. It's more like we have one wave per wavelength but get a pool, and each one is got a way of going down to explain and the waves are all similar frequency, but there's a divider between them and they get out cheeks. Now that says a lot about what would be the mechanism to make not happen, because you can't question how we do. What would the mechanism is.

D

B

Like animal say the distraction, BC different orientations and distraction, we don't mechanism has to know this is true, but if there's further now that the whatever mechanism is making there's going to be some mechanism that basically says the way it was chopping in this direction. It's not exactly the same way this traveling the structure. So it really can't be any interaction between these two well. There can't be any can't be tied together because I have to be independent, but.

B

I nobody sells them later woman. It was very strict, linear to.

D

Look like I've been lying, but the inhibitory along the line. Yes,.

B

Yeah, so what about later one is the a stellar linear element, but that's not true.

B

A

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Something is this like this. A very tight constraint like that could be the death knell for it theory, but it could also be a way of partially.

B

So I want down.

C

Your travelling bed mechanism must be perverse.

B

When lying- and so that's an interesting so now we have this idea, they have these different way of going across here, all roughly the same frequency a little bit more, a little bit less and they're kind of going any point any two or a couple, a couple of differences, these leggings next to each other, any feelings in general. Coming in and out of phase anytime, you look at it for any sense of cells. They become a minute. So thanks! Okay, that's weird! What can we do this next thing, I I?

B

Ask myself is when we've done this in the past is we've talked about the representational capacity of this and I'm.

C

Even know what the medium I.

A

Was representing how.

B

Am I going to use this was obvious. What I would do this, but I could start talking about the representation capacity of it in some way. So imagine if I just assumed there was eight little points in the end. It's not a continuous thing, so eight many columns that make many columns and, and so once that's if each of these many columns would be at a different phase, the same frequency but they're slightly in phase and so I'm just going to buy our eyes and say: okay, I'm gonna have one a beat Palance along here.

B

That I can have a little bit of a curve, but you know a little skull over, but let's go for eight points, so I say well, there's approximately eight cells will peak activity any point time. So I assume there's one. So, let's peak here and another cell this peak here a baby each of these slabs have once other that's that's at its peak and so really the dish. If I thinking about the way, there would be eight peak many columns at any one time in just image.

B

They say well how many different ways can you represent that how.

A

Many things can that represent, you can say wow that.

B

Was pretty simple right if I just want to look at all the possible combinations? That would be eight to the eighth power, which is about seventeen million, so maybe seventeen million different ways that I could pick one column pick active out of these eight slabs, so I want that down here, so the representation 17 million, let's assume you're, looking at all these. At the same time, you get that unique combination, age, definitely partners, but there's a weird problem here, because you think about in a very short time frame.

B

Let's say you have a problem like this: you've got this one's peak and this one's peaking, and this one speak and this TV and this month, whatever some on that right, yeah sure time saying these guys are all moving right. Instead of they're, all gonna move up roughly the same time because they're all going mm-hmm and slowly they kind of sing, but over a short period of time.

B

You know a period of a one cycle, they're all going to be just lockstep together. So this pattern, in some sense, is really no different. If I, if I, remove the high frequency component of it, this pattern is no different than the one shifted down here.

B

New information in it other than its top and left or anything else like player, I think that's useful information, but it's something that you know that's kind of limiting in some sense, so.

C

B

Component and I just assumed that all each shift of that same pattern or equivalent for some point of view, then I have about two million different ways that I can represent because it's 70 million by Friday today.

B

Then there's too many different possible ways that I could pick a relative offsets of the peaks okay.

B

The sumption, you know, I, don't know what could complicate could be occurring and he's so hungry. 12:20 dolls like animals, you know, are different things going on is that is that really critical that at this point in time, it's here in the next point time? It's like that's something we're going to take advantage of it could be. You know me I'm thinking about the precession type of time trend to be like that, but if I think about most.

B

Okay, so you got a bunch of these bumps that are active if I sample any three of them, any three that are active at the same time, they're going to all be it over 2080 they're, all gonna be over twenty means, a part separation here, and so, if I have a cell that looked at all three of those, any three I can just pick any three of eight directed at any point in time. That cell would look like the grisel, meaning I think this is what we've been think.

B

That's got that right, but that's the basic theory here.

D

And one can easily do this a little bit just to show that as soon as you, if you exclude calling and inputs and the difference between the inputs, at least when it agrees, then we impose that at least twenty degrees apart, a sufficient to get something, looks good like it's just not near maximum firing rates and the firing fields are very hot. Even some Punk's I cannot read almost died out and some other is strong, but.

B

Which is what we see in the tank paper anyway,.

D

Oddly enough, that is, obscene.

B

So because we always like I always want mechanisms that are not precise, right, I want to be able to say some cell need to know something an example subsample from some population, and that would be good enough now. The call.

C

We're just on there the Vizio's here.

A

C

Way mind you that associated.

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Each of these needs there's.

C

B

There's a whole bunch of cells underneath that so sometimes one cell erection there's a whole bunch of cellular or somehow and train to this to be zero signal here and so we're not even restricting ourselves. Just like I am sampling from three cells.

B

There's a lot of cells that are available to sample from like this I'm gotten there yet I'm talking about the representational capacity of the system, assuming it was like one VT, o / mini column, and so okay.

A

So now we're now we're talking.

B

Here right so now we're now we need I was having trouble translating this paper to the anatomy, for this idea to princess and and I thought of there I'm thinking like okay on any point time when the animals moving.

B

With them stop so, while the animal, which is fine, I, think that's actually good, while the animals moving, we might start out with one set of activities here and then, as we move. These things are all shifting and drifting in and out, but at any point I'm, if you sample, if you're sampling from some subset of these three of these cells, that so would be a proper grid cell in the movement direction. Velocity.

B

It's gonna be updating correctly and it'll be doing what we think of grid cells is doing, oh I might miss, don't even poser is a grid cell. It just says that if I sample two three of these things, then I would get rid like behavior and and I think Marcus. You said something a couple years ago about, maybe that these things themselves are actually doing the path. Integration, MSS and I'm still trying to get.

C

My head around that, because it's a very.

B

It's an intriguing idea: well just what you said right there.

C

C

Movement is causing like the face. These green cells are essentially just to read out.

C

Maybe error, correct, so.

B

What I think it's night I've always thought it in the past and okay, you basically to get past integration. You need to have a bunch of repeating out regular, repeating elements that, when you combine them together to give you this unique them, but I never thought of the regular repeating elements as being super fast, like as I still.

D

The interesting thing is that the actual integration, the actual integration of sort of the.

D

Velocity based path, integration is in the slight shift in the face of.

D

So the actual integration, only in one dimension, is in the slight increase in the face that you get over a theta cycle off the cell. That is, you know, direction on the right, so it is exactly the small shift right in the face. That is the actual integration it.

B

Only is the integration only occurs when you look at I. Just look at that one. We see. Oh, it's going at a faster rate. Okay, one PCO is.

C

Equivalent to a 1d grid cell- and it has.

D

This can be so compact and you're making do you're, building in time itself sort of block with it. It puts you it's just like one cell as the necessary input per many color. That is very, very digital in terms of what you need compared to what you need and it can modify exactly I. So the reason.

C

Why that can be so compact is.

D

Exactly because of all this timing, specificity because you're doing all of this intubation in these waves, I'm.

B

Understanding it at some level, it's linear, but there's still something it's different than I thought of it before I mean I, haven't put my finger on, but I'm still really I'm still very intriguing by this idea that really have a bunch of 1/b things and it makes it look like you have a 2d thing, or maybe we look like a 3d thing.

B

Initially, the question I had if I was trying to represent space and freedom actions do I need do I need.

B

To be I need, you can try and you arise in 2d. I need three three different three different thing: I get to do, I get another pattern, I guess I just have to then I get the sort of run going pattern here, activity and- and you will similarly point out that if I do like this, like it is triangle out of.

B

Three dimensions.

D

Center toxic face centered cubic grid is the correct representation for three-dimensional spaces. The most humans are good. So so, yes, here we get cubes, but their face. Centers force of a specific code.

A

B

States and I can.

D

I can show you the paper behind. It says this is geometry, there's different ways of packing oranges in a box.

C

A

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Is one way that is this.

B

D

B

A

D

Repeating element is not a dream, because that would flip around all the time, so the smallest repeating an element is actually a face. Centered.

B

D

You cannot repeat.

C

D

C

The lattice upside down yeah pull em around.

B

D

D

B

I'm trying to do is all about one dimensional and it must like a two dimensional thing, because that's what happens.

B

And somehow I would like n-dimensional to work the same way, I guess the question is, you know with interesting light I'd be here by sample any three of these.

B

It doesn't matter where in here any three octave at any point time, I will get this kind of lattice performance. Now, yes, it could be a little bumpy and a little wonky bubble. You see that in the questionnaires, if I.

B

Chose grid cell.

C

Light features in 2d and 3d is kind of mysterious, like very strange, and so is.

D

That we almost be finding doesn't suggest it's maximally compact.

B

Can I propose how you would.

D

Get to it three dimensional grid in this neural layer, okay,.

B

A

Before my ideas that these.

B

Guys these orientation columns could look Trudy, but they can basically suggest I. Remember I talked about in and out of the plane for vision. So my thing is: if these guys represent different, they can be, they can represent more in dimensional projections of any n-dimensional space, and the whole thing should work. Is that that's my starting assumption right.

D

Okay, yeah I, guess, theoretically, you could build something like that practice. You have across the question is: where are those cells and how does that work? So here's an idea, slight credit to to Kevin actually for bringing that up, because it made me look up to papers because to that because I was puzzled a little bit, but not to me like the IceCube model is highly like very extremely.

D

Like you know, stereotypical like this they're, not really parallel lines, and you know it's like yeah. Maybe that's.

B

Something I've seen you really here. None of that matters, yeah.

D

No I understand, as you can spin this whole thing.

C

And it's still fine, because it's about.

D

The connectivity- and we just you know it just- helps us think about the elements that we have. It makes me so I can sit on these. Thank you because, as can we point out in really one write these these sort of parallel, you know tracks of cells that have same orientation, selectivity, which you know might be multiple neighboring any comes off the same selectivity they are.

D

They are interspersed right with the ocular dominance clamps, and it has been shown that the cells that are on the edges between these ocular dominance columns are actually a disparity sensitive. So you so there are cells that code for spatial depth. What they did is actually the shows like point patterns and until they left on the right iron, and they prove that you know if you give them different depths. If you have the stereotactic, what's missing the right times fall and subject stuff, but so.

C

A

Of them is shifted right at the right way. Then.

D

It pops out to the front to the back yeah and there are cells at the edges between those. You know sneaking ocular dominance, columns in v1 that can do exactly that yeah, and so you would have a natural mechanism of cells that and like could potentially provide that input, and you couldn't neatly integrate them because he could be just the same see today's mechanism I agree that I.

B

Was a little just miserable on camera, pointing out you don't need to lie to do this, and so that is like an additional.

A

B

But it's not what I don't want to rely on that because, but it doesn't matter I think there are. There are flow detectors, cells.

B

So, but okay, so that's the same basic idea that our cells in detecting motion in and out of the plane and if I represent those and columns like this. That's all it requires right. So when I still have this still, maybe it maybe doesn't bug you Marcus, but I was done with the idea. We're trying to kid these, but beautiful little stocking. You know patterns here, but maybe that's just a fallacy. Maybe reality you just have enough of these one-dimensional things.

B

So yeah the the literal answer to your question of how many abuses you need for integration.

C

Three through three that ours are sufficiently different from each other. Now it's not going to give everything unique representations, of course, but it's going to it's going to be like three grid cell modules.

B

So what happens whatever do I have if I sample from more than three, even in 3d dimensions until I have more of these lines crossing like this. You.

A

Saw that in the original budget paper the first went there. There show the bill that was like three four six eight oscillators and then the show that gets better and better. It.

B

Gets better and better, but you also.

B

D

You're, nice, of course, and that's really important and I- think that's something you didn't didn't mention and it's worth thinking about, although that relies, of course, on a property that we set mechanisms so.

B

I, don't have a problem of that, because I think what's gonna happen here is is a general idea what's going to happen? Maybe this how I thought that if I give a learn, something I'm going to only learn something when the cells are people together, that's by definition. That's the only thing I'm going to learn so I'm going form some synapses in some way it's going to be one of the cells that are all peaked together.

B

Now, if I did want to reinstate that positions from essentially put right and all they do say, I'm an actor all those selves and I'm just say I'm going to do it started now and they're all men together and and then we'll basically pick up where we left off in some sense, so you don't require a minute in the theta rhythm that goes away when you're not moving. So it's not like. We need to seem to keep going and keeping you know.

B

It's basically saying alright, starting now we're all at the same peak start progressing, and where are we now who's active at the same time and and.

C

Then I say: oh wow, that position gold or life.

B

Or the people in same time, and then we progressed further so in a different direction. I, don't know that it seems to me that would naturally occur that you resync every time. You start having a great time. Every time you have a century and published drive this thing to suppose we're here. Let's get going, you could, if I could pick the.

A

Random one to say, I wasn't really am.

B

Let's finish by I'm, just going to pick some collection of shells or let's get going and did that work to fix them up to a I'm, not I, do have something kind of confused about I. Just don't know yet again, I want to point out that for every for every pattern that I might run aconite up here, these two there's a there's, eight of them that are shifted. That would be the same.

B

In some sense, they represent the same thing because they're over some period of time, those eight patterns are not really going to be they're, going to be tied together over some longer period of time, and the question is so I if I randomly sampled at any point in time. You know a bunch of cells here. Well, there are another set of cells that will occur on each one, millisecond Twitter and they're very different set of cells, and yet they represented some level of the same thing.

B

So I'm confused by that I wrote that down here I said they're eight sets of their excess.

B

What I recall you know separated by rows.

A

C

A

Are various sets.

B

Of these escapes uh pretty, but your every partner for every one of these two million patents there's variations on that recurring they're, basically the same. They really represent the same location and space at the same suit, good cell, if you will but they're they're a sesamum separated, Mohammed, rolling mill, silence and how and so I think.

D

About that there's very very many ways to build grids from those inputs else think that's the sort of the conclusion from that. Well,.

B

There seems to be a redundancy here that I would.

D

Like to understand better, but maybe that actually lends to robustness to the system at.

B

Night or might.

D

Represent additional.

B

Representational capacity or it.

A

B

Be saying it might be encoding something you never been. This whole idea that the intuitive idea that they've shown there by campus, that you can playback sequences within one cycle. You know so Isis representing a series of events that occur in the past.

B

I bet you could go back and read the literature about the procession.

B

Those recall him against mine might be related to this might be hey. This is mostly what I want to talk about today. I said: okay, so this to work. This is kind of appealing to me. So it's now a better understanding how this mechanism, with it kind of stalls we see what the kind of cells were so exist, bestows and in trouble ways that you could have some really intricate, how you drive result like properties and inventions and and and what it required and requires.

B

This is a swim, Lane specific state of wave, which is an odd thing, but that's what it requires and therefore requires some mechanism for words that could be good or bad. We can find I.

C

B

Wondering you know, I was thinking about the measuring that traveling waves in hippocampus new cortex I was reading the traveling wave. This traveling.

A

Paper I need to read it yeah, because when I read.

B

This I can ask myself what their mechanisms have shown. This kind of traveling wave roll these peak swaps. They see what they've seen that I would have noticed that when it were, they just were they just detecting that there was a way of going in this direction if I just but look at the LFP I'm, not sure.

C

What I can see that not sure I see my look at the.

B

Llp in this direction, I would see this way, but look at in this direction. I was seeing scrambled right and.

D

Then, and the problem is of course, that if we look at actual architecture like say, if you want cat cortex right, it's small really provide tube there. It's not one strict orientation.

A

That's what I was thinking for a while, like does that mean.

C

That that is the direction.

D

To the feet away and yes, there is a direction to the theta wave effect during sleep, like let's focus on speed right.

C

But the problem is.

D

That this direction doesn't align with like some orientation of an ideal ice cube thing because reality, there's like the celebrity nose and ah which I like in the in the colonists.

B

It's in a Maiden's, and this could be the biggest killer of this idea, or it could be the biggest support fence about it. Do you like if this is true, but damn this is gotta be what's going on, but if this isn't possible to have them put through fault their other.

D

One, it means them. Here's one.

A

Other thing that.

D

I was worried about and so.

C

You now have this like this nice. You know if.

D

A model right I mean the numbers are in a play. Is it dry but not completely, because, of course we know, as you pointed out, that there's like a 20 degree span, because what.

B

I just put like putting music size in any column.

D

What has me a little bit worried is.

A

D

Of the fundamental assumptions now is that the teacher kind of like repeats at the length of that you know ideal jus and the the problem with that is that the math on this speed of the theta doesn't really to.

B

The Ohio one, because.

D

I at least I did like muff, judging on the speeds of these theta waves that were reported in this one that you were reading and and I.

B

Figured so on this one hippocampal oscillations, yeah.

D

I think it's that.

B

Was right because remember I pointed out in his figure to that turned out to be about a millimeter to get a full shift, a full yeah.

D

Some ah I got to a lot of distance that maybe we can do them up together.

B

D

I myself by one to two orders of my knowledge so guys like I,.

B

Was Eve's guys are back? These are four different rows.

B

And those probes are half a.

B

Millimeter I guess 360 degrees back to the same phase. I spyler, exact.

D

Said looks, pale and the other way around I took the reported, traveling speed and applied that over estimates of hyper-calvinist size in neocortex. That would travel something like.

B

B

A

The next thing I.

D

B

With this is to start thinking about this in terms of many columns. Well, one thing is really by gosh. I have an answer, for is what to do about. These eight different sets are all equivalent. A little disturbing do that, like kind of that's, why I'm left with a question mark, because I don't understand that it really off coming over here, but the idea is that these are many columns and, and so presumably these deseos.

C

Are some settled sample.

B

B

But presumably cells that some subset small subset of the cells and each mini column and and and now other becomes, are going to be able to and then the whole mini column has to sort behaviors associated with that thing. In some sense, and now the other cells are going to be sampling from them, and so now we just like how do I take all the kind of theories we've had, whether it's like a sequence, memory theory where you have another picking this I get individual cells that have the same meaning.

A

Within many column, creases.

B

A representational capacity radically and but all the other things displacement sounds and, and all these other things we've talked about over the years. How would I try to read turn it all of that. In this context, it's.

D

A little rethinking but.

B

It's this additional information. It's tough but I, think.

B

Button and it'll it'll be sort of clear in interesting. Another thing it's struck me, but it's being of course, this whole I get up orientations a problem but you're kind of interesting to sort of an implied orientation, because the movement you're moving to it guys a lot of the good to understand about, but that's really what I want to get ahead. One more point: I want to make about this further.

B

C

Realizing that there is one core difference, I've been comparing these two 1d grid cell modules and that we can kind of reuse. All of that, like each of these swing lights, can be visualized as rain. In some sense, if you want to visualize what is current phases but there's a there's, a difference like it really became clear to me when the us, how many of these are going to be needed for 3d and I, said three and, as you add more, what would happen.

C

Florian answered gonna get nicer, but in the way I'm used to thinking of this. What's going to happen, it's your! How? How big your location spaces are? It's going to get larger, yeah.

B

A

So yeah you see where I'm going like.

C

As you combine, multiple of these like well.

B

There's not an extreme wedding on come on all eight right, I not have all eight bumps, then that means this is only going to become active one out two movie times, and so that means that the bump will.

C

Repeat, very rarely so, there's some contradiction here: where's where's this coming house. How is it becoming better and better grits, rather than larger and larger I.

B

D

I'm with you on you on the better and better comes to the see Tony said making I thought. Oh because the point is these different oscillators right. They are obviously like you have with phase shift here right. So let's call it fine right, and so, if you introduce additional oscillator yeah, but you can say, we've already have a preceding one, and so you have with mosey on here. If this one is supposed to be optimal, that it needs to line and face with the other ones.

C

A

D

Grid that you already have.

B

D

I didn't have this oscillator yeah. Then then you would have you go sonic wave of some sort right. It only improves to the next. If the next is to the.

D

Having make the assumption that, when the.

A

Readout sell the.

D

Seller listens to the two originals laters when this spikes right. It also resets the theta phase to all the three oscillators that are part of Justices fight, yeah, so which, which.

C

Gives you exactly.

B

Like they must live or me alive, no.

D

Itself, it's a self aligning mechanism. So why don't I spike.

B

If they weren't already lon right.

D

And the point is these things despite they might shift, they might.

B

Drift, they might not be perfect, but because it is assuming that they were perfect, but they're drifting, right, I'm.

D

B

D

The way that they do it in the hybrid model is actually get the simulation run for a couple seconds to jiggle all the databases into a coherent grid. They have a mechanism that automatically moves the face up or down it's a heuristic mechanism depending on you know how well it would fit the firing of this.

B

Of that, these guys are not aligned and.

A

B

Gives me my capacity right and.

D

If I just assume that I only.

B

Want to line them in lost capacity, I.

D

A

Say like well, the cells here.

B

And here I'm gonna move with them. It's like! Well, that's all the difference.

D

Think about it this way right, so you have I, don't know like a grid cell. You know I mean it's kind of like in the sheet, but I'm gonna draw it outside of here right and say it gets input from my. You know like three different three different visions, yeah. So.

C

This is my my grid.

D

So like feed out night, so in animal model, just take three inputs and what you would need for this to work as a proper grid where these things are aligned and it produces a nice, perfect exact weight. We know. That's, not true. Many are messy, but if it was supposed to be best, then you would need to make sure that every time that this is cell fires, you correct for slight drifts in the face. Okay, okay,.

B

But then that's just fixing an error if.

D

Continuously, every time yeah.

A

But I don't want to do that if the original timeline format.

B

These connections, these guys had to be synced and in other words that would inform the connection so but since you're saying well once I've learned these thing on, but but I don't want this gotta fire again. If they're not saying that's low point, I.

A

D

This guy say well anyway, that only happens in response to the postsynaptic firing.

B

Fire they won't sink. Not then.

D

It won't fire, so that means a grid. A grid cell look at the grid cell. Then that's one half nicely aligned oscillators yeah right: it's not a good cell. It really doesn't find much yeah all right, and so it's just not a bit. So maybe it's you know messy with, like one of today dose of medical classic band cell right. Maybe it's actually completely silent because all those later scans, each other out perfectly right, destructive interference, but that's all possible. The.

B

Gray cell is an ideal cell.

C

D

Has the phases.

B

Of its different.

C

Also latest align in.

B

Such a way that.

B

My life, when my grid cell became active I, just chose to make all right, so it's a first location under object, and so I have eight cells out here. Let's just connect all these cells right now, that is representing a specific location. Those seems of all on sync at post. The me now in.

A

B

Future if I know where I am based on sensor, input and I have to make this grid cell then. Yes, this grid cell should hold itself at the same time, but if I'm moving around I'm someplace else, Laurel and I move around and.

B

A

Not I saw it I said well, that's.

B

Good enough I'm gonna do these guys so.

C

The only the only way to make you find my point is the only.

B

Way for this, this fixing you're talking about go not is if the grid cell is coming from some sort of more of a sensory or.

B

I'm, driven by something I won't be doing by this. If he's alright I don't understand, there's two ways: a good selfie be driven one by some Center. A public place by looking at these oscillators were not lined up, then discussion, fire right, so I'm not going to fire and then correct them. I shouldn't fire right. The only way, if you're not talking.

D

About fixing leadership that is so large that the grid cell would not fire I'm talking about aligning realigning the theta oscillators that are part of the grid solar pretty well, but it shifted just a little bit 125 milliseconds. So.

C

A

Talking about making with sapphire.

B

D

Is some noise rejection, makings, okay,.

B

You're essentially saying but I, don't think that's I, don't then you're saying like okay I learned about all eight of these things, but now five of them are good and that's going to be good enough for me and I'll. Tell me all the street. Okay, that's basically saying it's possible I! Think there's not the way. I was think about it. But I was saying to like a passing point of view.

B

I want to start off by assuming that I'm going to make connections and they're all going to be good and then I can figure out what about norway's but I'm thinking about capacity issues. So imagine if I give you student imagine I require all eight to be perfect in this great cell would occur one out of two million powers actually whatever to actually be one. A 17-month yeah possible.

D

B

You know one thing you mentioned earlier was in run those papers, the idea that perhaps there's a cell here- and it's got multiple dendritic branches and there's a natural mechanism to force these dendritic branches of a hundred twenty degrees. Apart that the cell itself wants to do that. Yeah.

D

Is heavy and running mechanism because it turns out that the total firing activity, all the good cell, the total fine, to be over all at all time, yeah! It's maximized when the inputs are.

B

Sixty degrees, yeah, I, guess, okay, so my point I mentioned.

C

B

Because when I think about a grid cells sampling from this population bombs, moving around I got these and this guy's sample from them. How many is it going to sample? Well, there might be an additional mechanism: COI I'm, not gonna. Let you scandal two that are close in phase, because I want to find the ones that are certain separated apart. So there's.

A

Eight of them out there I'm gonna fortunate.

B

Stick to three or four, because this mechanism is this going to just just get rid of song, so there might be a way out so that not letting this get become a very specific sound. Otherwise you conform. Eight synapses and Miss Ellen only become.

B

Which is a really really big. Space is essentially like I'm, going to repeat.

B

So there may be a way of forcing this. It's something sensitive, to only do a stop sampling of these guys that are roughly more.

B

Anyway, good thing about here, one point: it's a sort of related, but it's all topical issue once one but is more and one.

D

Of us, we need one tiny point: I wanted to make sure, and that is a question also learning piece about it and that.

C

D

Interaction between orientation direction, yeah, yes, so the problem being and all stages that are like a hundred eighty degrees apart like where are they so they.

B

Talked about this right and.

D

Everything that we are both of those in here well, we.

B

Know from these all other recordings that if you go down in the remaini column, there's an orientation preference, almost all the styles, my all, but almost all have a directional sensitivity and there's some go on one way. With someone yell with enemy column, you see both right, I know: I, don't I didn't work that into this part, I knew who I thought about on this. You mustn't think about right now, so it's because what you want is that that would that would basically you want this sort of rain that they definitely.

B

So that mean I need to be corporate, that you.

D

Have appropriate done yet? Yes, I do already works with an exact same architecture, so the point that the hybrid would sell mother has.

B

A twists the the I know what you want some questions: how does it work in this picture? Yes, in.

D

This patient, the hybrid cell model, represented the NIP I just won a 2014 paper right had six PCOS because they just shows three different orientations. So maybe they chose you know horizontal.

B

D

So 122 so they had, but they had and had six because six different directions yeah in this case it would only be three yeah but the personal problem, because the type of model also says that the oscillator in a direction and the opposite direction. When you have all six need to be in phase the cool thing about the swimline model is that that is guaranteed. So the only little augmentation to this model is that this is not really one connection. This is actually a pair of escalators, so.

B

There's three pair okay, so so basically you're saying I have to have so weird, because if I have a forward oscillator and back and off later, that means when I have two different way from it.

D

Well, it's maybe one way from, but one is proceeding and the other one is. You know recessing. That would be too much yeah yeah, but the shift will be absolutely minor, keep in mind or my brother should like I'm just running visualize this or maybe clear.

B

Your head at maximum I'll speak off. Like you know, forty centimeters per.

D

Second or something right, maximum rotors beat by the change in theta is something like point, five five point: five something on that order right so, and that means that compared to the whole theta cycle of 125 milliseconds, you are now a six of that. Earlier later, it's actually very small fraction compared.

C

To the eight soap soap, you have that's not even the half cell difference right.

D

So it's not like the Peaks I'm going to be in radically different places, just that one slightly.

B

Higher every time then they separate yes.

D

But the cool thing is as soon as they make you it's on fire, it's resets to the same place, anyways! It's this whole.

B

System getting a little information I need to be able to pass on the great differently one direction in versus the backwards direction, and if I, miss and I ate advice to come up.

C

All the time I've lost that.

B

C

My differentiate you.

B

Can forward and backwards it's almost as if I would have left too easy. I flavored here and one is increasing it's because each one decreasing.

C

B

Everything the VCOs.

D

Only need two paths integrate until they make them to itself fire for that. The path integration is in the pizza, so I.

B

Know I I don't buy that I. Think word. Maybe I'm wrong about this idea that them that they're every time they.

B

Imagine what has to happen here to this system take off the grid cells for a moment, Catholic results. The Vizio's have to basically do a math integration system that that works from a point in some direction. I move I have to be able to represent how far, where I am in the new space right and now has to work in the people of good styles. Until.

B

Accessory, but even before that happens, I cannot be serving these guys. These guys are doing their parents. Integration I cannot reset them at all until I finished my movement and I. Don't.

D

Understand: I: don't I don't follow that argument? Why? Because.

B

Otherwise they stop integrating the some.

D

Of the integration is just in the grid cells.

B

Acquits Ellis is not required to do path. Integration. The grid cell, is a readout. It doesn't it if the readout exchanges, the dependent rather than I've, lost my path integration. So imagine this whole system should work before any grid cells fire. It's just.

D

Basically, yeah it's that insistence on that works completely without grid cells, essentially.

B

D

It explains why you think there's a need for this, keep.

B

Going on without CWC.

B

Noise, it's a big problem, but particular is.

A

B

Yes, the two radical ideas: you have to keep path, integrating as you move until and the point is any time in the future, there will always be some synchronous set of cells here. There's.

A

Always going to be some.

C

Secret stuff, so I don't need someone who don't read it out, but if I did this is going to be now. This takes me to set.

B

Of cells and that.

C

Means a module: if it's now we're going to make something happen again, it's going to be back there.

B

Again, so it can't it can't change a camp if I, if I lost mine, if I'm constantly changing these phases here, then that.

D

Is exactly what is required and also trying to finish mummified to work every time the the the you need to reset the face, because otherwise, these things to cool year? Yes,.

B

Yeah yeah, but they do go here in the sense that they know it's right. It's a more quiz issue. They just get lost.

B

D

In this case, I mean generally yes, but in this particular case of the different directions, which is a computer problem in this particular case. It's just always true that when you move in one direction, you're not moving in the opposite direction: okay,.

B

So fine with I'm with you here, I think all this works and these guys there's two SEOs near and they one remembers its forward and one represents backward and and and they they but then I will have two frequencies and those frequencies have to be maintained, going both ways. I'm good at that. But the idea that if there's two separate frequency and I constantly I think I constantly put them back in the face every single step of the time, then every.

D

Step at a time only when you integrate it.

B

Gives the quit cell should we the consult, remember to state where they're all in shades and the grid cell should only be reinstating states that when they're all in shapes it should not be reinstating states to say you know you're at the point X, but I'm gonna, but you're not reading it. I know a red point, so I'm just can force it on you. That only happens about June. My sense we did I think I may be well I'll read this paper again. Maybe you could point to that point where they're talking about this again.

D

Yes, like I I'm,.

B

Not reaching yet they're mean everybody, but I mean I still think this is an issue here. One thing you see question it just says.

B

What so, yeah these the cells that are measured by coupling basil um clearly sure okay same orientation, one cells becomes actually this way once you become that way very different, it's not that I need to be SEOs, for example,.

B

D

You don't see the the mathematical.

B

Meet no no I'm trying to no it's more functionally. What ladies.

C

C

That the only reason we need that we need both these two to have some that respond in one directions and someday to the other is to match people diesel we don't. We could have a path integrating.

D

System with this picture I here, without that you know, but it would not have seat up recession, it spectacles the direction from like the.

A

D

Purchased and like like it, this implementation with this officer pair this, otherwise, you can't explain what, because always processing yeah.

C

Maybe you can, you can talk.

B

About that maybe become possession is not how many goodies. Maybe what I need to do here?

B

It's all I ended was eight sets of leaves that are equivalent and also the idea of the procession and I have not worked that into this yet and I'd only been where procession I, don't know how to think about reception. This, yet I need to get there. So maybe I need to read that word newspaper down and think about procession. Think about how maybe that's the next time.

B

How would what what is procession II, you know I just know, I love it connecting that idea with this, like you know, and maybe I need to do- that. That would be good for next step for me and then I'm like resolve are on this wonder: standings your confusion about right these two things here. So let me take that one step along I want to talk about one more thing: I'm done. Okay,.

B

And this is just a partial: this is a picture of cortex now this is found this that these are the three finished up. My client, don't.

D

B

We struggled with is okay, we say, cortex is cortex and there's a common algorithm to the climate really solve the corresponding cortical region, and so the classic view is. You have sensory data, that's coming in from your senses. It goes the first or relay cells.

B

The thalamus goes the Coretech layer, 5 cells and cortex project out to some place up quarter key, which is a loan related thing, but the same style, axon splits, and that becomes the input to the next relay, which goes up to here and so there's always been a problem, because if you accept this view- and why would he be the sensory data here and these provisions motivated here and and and so so that was, this problem happens if I might really tell represents tens features in the primary list, but more commands and higher are in decline and it's inconsistent with the common algorithm.

B

So one solution we propose is I'm not abandoning yet, but it's. The solution we propose is that it's possible that the layer, 5 selves, are alternating on every phase of a cycle between a motor behavior and a feature or object.

D

Opposed type of nut roast a mountain.

A

C

B

Yes, that's right and there's some evidence that this would be a current and we thought about when we thought about the displacement cells. The way the original incarnation of displacement cells and I. Remember when Scott was here.

B

But they did that when, when, when you reform a reputation, location and then the next location that there is a transition between bike, a1 going from location, is base 1 to location, another location in space 1, it flips to being a location in space too, and so you have these two different representations. One is more of a object, representation, one's more of a motor representation. So that was our shoes. We proposed.

B

That sense that I'm not arguing that from the retina you're getting these things are not just features. They are direction and velocity vectors, and so we'll call that instead of motor, we'll call that a movement of some sort- and this is a movement- that's assessed from the sensory organs and so and then.

A

If you think about his movement.

B

Then you said okay. Well then, let's say this is not a motor command be coming out a layer of fog, but it's similar representation. It's a it represents direction, and so that is perception accordingly, but then that becomes the movement vector into the neck. So this.

C

Whole thing would be consistent if I love its.

B

Movements, everything is a little bit vector, but that means some other questions. So that's a new idea.

A

B

Been promoting our over several months, they haven't really spelled it out this way and that were actually the horn driver for the primary regions of the cortex in terms of knowing how you're rooting for the world how your senses are moving in the world is basically coming from the sensors not from the motor not from the motor commands, but actually from essentia data, which is later corresponding with subcortical motor area. So this is a learning thing. This is the sense thing, and then this is alarming.

B

This brings out so that's kind of nice. All the fun I might sing words on these. These lines here.

C

There must be something I'm sensing, it's not just.

B

Movement I need.

C

B

Some feature in the world.

B

So, where are they coming from? It's clearly gonna come from the sensory learning as well. So then the question is one possible answer is the sense feature in the movement are somehow commutes in it and I. Don't know that mean, but maybe the data coming from in, because multiple streams of data coming from sensory organs through the thousand separate of the thalamus and and I haven't looked at. What I did that day was one behind represent movement and one representing some sort of horse facial feature.

B

Another idea is well. We consistent with this is the on this idea here that this is a feature gonna. It's like to postpone this marker sourcing that that that we have this direct I just should say we have the sort of direct connection here between that could be the future pose. This could be the movement now I realize that. But then, when that NASA, then he said what's the equivalent here and it says, base.

B

A

B

B

B

This idea that think about this input.

C

Yes, yes, in the sense that you have no.

C

Explanation of why cortex is productive, protecting something that's like kind of overview kind of sensory. They know the different spin on it, but I don't know if you want to hear right now.

B

I think you just.

C

Like I can put it pretty quickly that that okay animals can do a lot without a cortex in a sense, there's a whole behaving animal already there yeah, then there's a cortex yeah. So what is cortex doing you could say the cortex gives us the ability to sense higher levels, things democracy or like just just do my basically. Democracy is an exaggerated hardcore version.

B

Of it, but there are things out there in the world that we can't sense with our sensors, because there there are multiple levels: revoked optimal levels of analysis. Remove cortex is giving us the ability to sense those things and, and the thing that's being output here, isn't a movement. It's just a it's just another feature that the cortex is letting the rest of your brain, bowels response and I thought. Let it look. It looks like it is our movement as protecting.

C

Two areas but then execute yeah.

B

I think sometimes like we hear meta-analysis it, but I also feel like without a cortex. Most animals would not perceive the structure. The basic objects very well that.

B

Now, without a cortex would not be able to see, this is fairly objects on this table. A separate object, making either the closest analogy I can come to. Is you know if I hear someone speaking Russian I, don't even hear the words it's so weird.

D

That stop install right.

B

It's just like it's this, like just there's no structure to it and are occasionally running the physical things in the world, like that. I've noticed in my lifetime, just right, rare that you see something that it just just it's a knife, usually some sort of optical illusion. But you just look at your I came in parses thinking.

A

Where the boundaries are.

B

So I think it's required for learning most basic structure in the world where you can eat something by saying aye I know the thing I want to eat is over there and I. Don't really know exactly a state or you know its position and I. Don't know.

A

B

Understand all the things around it doesn't really matter I'm just going over there and I. Don't really realize that maybe there's a rock in between I lose a lot or something like that. You guys these things go beyond that. I think.

A

If you're caught, you learn.

B

To get the most basic structure of the world to see things even the most basic things to feel those things the most be, but remember contradicts yeah well I. Just say like it's high-level things, so.

C

B

A

B

You know I think what the cortex is using a smartphone.

C

It was a mistake for me to start with democracy, but, like v1 also has these outputs.

B

Like that was basically yeah, I'm thinking like money, something something like a smartphone.

B

Every small movement related to the phone is control they're, not the final part, which is the cerebellar, but pretty close to the final part is going to be cortex and it's like you know yes, I, to manipulate the smartphone I have to move my fingers upper left-hand corner and touch this, and do that and pull this thing down, and so.

A

B

The most people- even it's almost you- know- objects a stapler or scissor. You know a smartphone requires the cortex to have a motor system to manipulate you know, I, don't know in terms of vision. It's not like that vision, you're, basically just controlling with your eyes anyway. Ok, let's leave it at that I.

B

Just there's a new thing for me to think about here that that we can understand the output of the rest as being movement vectors in the way we interpret people. Diesel's cells are really callosity instruction and there's lots of others again. I'm wondering there's so many other cells that they could not get the response specifically to the stimulus, the only they were trying and only time they got the first success. They had one had a moving edge, and that was an end goal on that. So basically everyone's.

A

B

This entire economy, about this he's moving edges and also roughly 50% of the cells of workers themselves to the other 50% cells are doing something else and they might be you know, attention would be find those voltage controlled oscillators. Would we find cells and cortex that that look like that behave like this? Is that from that picture right that paper, data oscillations.

B

Anyway, ok, that's it thanks. Man.

B

Ranging discussion yeah.

B

A

For watchin everybody.