Numenta Numenta Research Meetings, 12 Feb 2020

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

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Jeff Hawkins will talk about some papers he is reading on traveling theta waves, and how they might work in primary sensory cortex.

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

A

So we're going I have a super tiny thing. I just wanted to follow, just as the main topic today, but um I kind of overshot, a point that I was making when I was talking about how like yeah, we give up some accuracy and stuff when we spar stuck on ties and so on, but up but like I look forward to being over, then you know regain that I wish I hadn't drawn this dot higher than that I. Would what I want to be able to do?

A

Is this you the same thing with something cheaper like I'm, not going for anything but better, just just reclaim this.

B

So you're here you were in claiming we might do better you guys you want to get actuary, yes, but with less resource. That's that's the point. I want.

A

To make and I literally overshot it I shouldn't have gone.

C

Accuracy includes robustness.

A

D

Yes, I guess I would.

C

A

In the big sense of how well the networks do yeah.

C

I would include.

A

C

A

Pretty percent for sure I mean I, just called this cost. That means all sorts of things. No.

C

No, but in that bigger sense, I would put you not back for you plus, oh.

A

That's not amusing, okay,.

C

Well or if you differentiate some thirty Isis yeah.

A

But at the same, there's a trade-off between how good this isn't how expensive misses I feel like you can always block down from those two axes in some conceptual alright. So.

C

So figure there that's.

A

It that's all I had all.

B

Right flooring just walked in so we can going I'm gonna go all this stuff. I talked to you about yesterday, flooring mm-hmm, it shouldn't be very long, so I'm gonna do it. So yesterday, I started reading this paper. The cosine directional tuning of status over frequencies, which you I don't know if you review the whole paper just talked about one of the figures and I.

E

Mentioned: okay.

B

So I read this paper and another paper that I'm gonna talk about here and I.

E

Had an insight which.

B

I thought a couple of insights, which I thought were really interesting and I asked I was confused about something: I've talked to Marcus, first and then I discussed with Lori and Safari knows most of what I'm going to talk about. So the basic idea, I'm gonna, but that is, is quite simple and it relates to the cortical column model and I'm gonna end up talking about that again at the end. But there's a lot of background to it. So I'm, just gonna, run through a few things.

B

First of all, this papers, primary purpose, was to show that there are. It was well known that there are beta cells or state of bursting cells in the hippocampal complex in different places, and but the theory of the oscillatory interference requires that those cells have different frequencies, depending on which direction you're going. They have to be directionally tuned. So if you're moving in one direction that this the speed-up in them and the thinner frequencies it'd be faster.

B

If you're moving too slightly off, it's a little slower if you're moving off diagonal, it doesn't change so that so that and he needs people. This is a 2009 paper, I think of 2001. The a patient said that hadn't been shown before. So the main purpose of this paper was to illustrate in animals that there are cells that are directionally tuned and that, as the animals running the speed, the increase in the theta frequency is is tuned to the direction of the animal that they claimed.

B

That hadn't been shown before and that's what this paper was about, so I'm not going to review all that, so they basically said here we show were showing it, and this I thought this little figure here is useful to see this is a live recording from a single sound. What we're talking about here is cell goes through these little bursts and the bursts occur at the theta frequency. So that's what we're measuring when they're.

B

Like you know this is this like eight Hertz or someone down, and then they showed basically in different parts of the brain, oh brain. They showed that I'm, not these. What these figures were about, they're showing that they actually are directional each other we're gonna skip over of that. Yes, we found directional tuning sells some interesting stuff there, but I want to get to this figure, which fluorine brought up and was talking about and I was really confused when foreigners talking about nothing, do you fluorine I, just wasn't it was.

B

It was just a lot going on here that you can easily trick you up, and especially this lower part here of these little rings, and these rings up here, I didn't understand what the wings were and and I have a hypothesis that that's the point today, I'm gonna I'm gonna relate, what's going on in this picture to I think might be going on in the cortex.

B

Let me just walk you through this. This first part up here aids a little confusing they're, showing a rack moving across this one-dimensional track, and these are these are. This is all theoretical. Now, there's nothing. This is all mom, there's nothing biological here and they say what, if we had eight different fate ourselves that were directionally tuned as the rat is running at 25 centimeters per second, then some of these will be a little bit faster than other ones. So the theta eight is going to be the fastest frequency and theta.

B

One is the slowest frequency here. You can barely see that this position along here has nothing to do with the position along the track. It's just that the animal is running at twenty five, seven meters per second- so that's that was fooled. Me too I thought somehow this had to do with where the animal doesn't so.

D

At this rate, oops.

B

At this rate, you would see these these cells oscillating as frequency different slightly modificated frequencies, and then they point out. If you just look at any two of these cells, just two, you will see an envelope waveform like this, which is grid cell, like so because they come in your phase and out of phase inter phase and out of phase, and so as the animal will be running along the track. You see activity, no activity activity, no activity activity, no activity song. So that's what that was about then um I think.

C

That's something up the it's.

B

Just some Enya, so there's some. If you sum the two: you get this black oscillation and they're in phase and then there out of phase and they're in phase then they're out of phase because there's slightly different frequencies. So it's like it is wah wah wah. Do you have it background frequency? And so the idea is that during the top here, that's when you get those little bursts to spike to get the little Bursa spikes. Here you get the little burst of spikes here.

B

Actually, that's! That's! That's not the early versus spikes! Sorry! This is this is this is like a grid cell, a one dimensional grid cell. So if you just took two of these oscillations at different frequencies as the animals going along, you would see the new and you took a cell that looked at those two and sum them up.

B

That would be the that would be the what that cell would look like this thing then got me really confused and and I had to ask Marcus Marcus columbian what was going on same frequency, be like all the birthday to honor theta2 or something like that, and yet they're slightly out of phase so they're all oscillating at the same time, the same frequency but but they're doing it slightly out of phase.

B

I the the example I gave it so like it's like a wave and a stadium right, so everyone's standing up and sitting down to the scene, but the same frequency, but the actual peak of a wave is going around and around so this is gonna. Got you go around here within one theta cycle, so the eighth or tenth of a second all these cells are gonna, are they're all like going up and down up and down up and down right made up.

B

Okay, so that's called continuously. It never stops. Unlike a head direction, shall we oh it stops moving when the heads 20 animal stops, this never stopped, then they said well. If we had a whole bunch of these cells, these cells, so now and and then they came up with this chine- this really got me confused. It took me long to figure what that was going on this lower picture here, so, let's just walk through it.

B

These columns represent cells that are directional orientations and everything above one of these guys is a directional orientation, the same directional orientate, meaning they will speed up or slow down proportional to how much they're moving in that direction. Okay, so that was what he was talking about earlier. So if I just look at one row of these, that means I have a bunch of cells that are also that are going cycling through different peaks at the same frequency. But these would be out these.

B

The frequency at which they're going around would be different based on which direction you're heading right. So if you're, if you're heading in the preferred direction, that would be the fastest cycling around, because the theta frequency would be going faster in food in the antithetical in the anti preferred direction. That would be the slowest one going around, but you're still going around this direction. Here. Is this the sort of baseline speed the vertical axis? It's like?

B

How quickly does the speed increase based on how fast the animal movement and what I think it went and I confirm the floor yesterday. This is not a continuous function. These are basically like the step functions. You see in the n-terminal cortex, where you have a bunch of you, have a grid cell module, that's at one scale and then another great, so my join another scale and done great, so modular another scale.

B

So this is not a continuous function, so this might be one point four times faster than this, and it's like a different grid cell module, okay and I talked about in the past. I.

B

Don't think it's correct to look across these and I've made the argument that this is equivalent to like v1 in cortex and v2 in cortex and before in cortex, that is they're sort of separate they're working at different scales, and so it wouldn't count more complex is going to be mapping of rooms that work at best at different scales but they're, not necessarily interacting with each other. Okay, now I'm going to get to the the de new model, the whole thing I, don't know any questions about this. Yet yeah.

C

Is it possible that the modulation would be less than one because it looks like there's a slow at this last.

A

B

They talked about this in this paper, so it's a good question. I hope, they're gonna hurt it. The idea is you have a base frequency and, if you're moving in the preferred direction that it goes up. But if you assume that in the non preferred direction it would go down then the oak. Then, if you look across all these cells, the average rate would stay the same right because you got some are slowing down. So if you look at the local field, potential of the whole thing you wouldn't see everything speeding up.

B

You see something slowing down something speeding up and they point out that. That's not what observed in an animal which deserves an animal as the animal moves. Everything seems to get faster, so I'll show you one more picture as a sapling. I show you this one up here yeah this is the. This is a tricky little thing they're doing here.

B

What they're saying here is and there's evidence, but this is this- is for speculative of the theoretical and observed that if you look at any particular cell there's a there's a sort of a base- frickin theta frequency, if I go into guy and as the animal starts moving all the cells get faster, then the base frequency goes up and relative to that base frequencies, some get even more and some get less. So that's what's going on in this upper right. Drawing here.

E

B

So they're, like the circles are, here's is, is like the animals not moving. This is your base frequency. Now the animal starts moving the the base. Theta frequency goes up for everybody, that's the circles, but the ones that are up here see it says, preferred an anti that preferred one goes up even more and the anti ones go down a little bit, there's a little subtlety there.

E

And, as you see in the figure see somewhere, you get a point: two hearts increase if you are heading in the right direction and like a point how it's decreased when you're going in the wrong direction. So it's very small change yeah. But it is that's extra experimental data. Yes and.

B

We a we need a small change, because the way, if you want these, imagine the animals running along a track and we're talking, maybe 50 centimeters or a hundred centimeters between maybe some certain grid cells, the cell firing ones and firing twice. It takes a long time for that animal to get that fifty or hundred centimeters, and what we need to do is we need to go to these cells have to get in and out of phase and a slow.

B

They have to be so close in frequency that they it takes that long for them to get in and out of phase again.

D

B

Know what I'm saying so the differences between these frequencies have to be very small and that's what and that's what observed by the way. This figure here was problematic. For me, this B I wasn't gonna, mention it they're, showing variation in how these cells perform, and the variation is quite significant. I didn't understand this yeah they're, saying here, like you. Take this as one cell, this red dot here and they're saying this one cell sometimes could represent something as small as this.

B

Oh yeah, 30, centimeter spacing and another time in might represent a cut 75 millimeter spacing like it, didn't, really explain it. So I don't find just did that correct it out, but as a weird variation, all right, I'm. Looking back now and.

D

More questions.

B

That was a good question. Okay, just by the way, the reason they showed this picture before I would like to give my point: they're saying: look if you, if you just sample a couple of these like here, you see this. This is a grid cells here right they say if you seen this guy says if we just sample from you know a few of these rings that are 128 220 degrees apart. So this ring- and this ring- and this ring, you will end up with a cell you'll end up good cell.

B

If you have a cell that looks those that cell will have this sort of grid cell firing and up here we're assuming that they're moving faster, so they'd be closer together. That kind of thing they also make the point that if your sample across these think actually is going to happen, the brand new get bored or sells, and they make this argument. If you could, if you look at all these cells, you get place so I. Don't think that's right either. So I think really. The thing I think is right. Here.

B

Is these grid cells and and they're, pointing out that you can get grid cells by sampling from these these green? The time I know there's several levels of indirection going any that's why it's so hard to keep it in your head? These are like underway, so.

A

Yeah maybe I take this wrong, but I've questioned.

D

So it seems to me that the base rate of.

A

How quickly the waves going around the stadium doesn't really play a role and scale. It doesn't play a role in how close for.

B

You know it's: how quickly increases when you loop right.

A

It's so it's like the. What really matters is how the how the faces of these different things change well,.

B

There's way like mint on two stadiums: right, yeah,.

D

B

Time they're doing the same speed, yeah.

A

B

Now the animal starts moving well, the wave goes around faster, but in one team and go from faster than in the other Stadium they both get faster, but one gets faster, still. Yeah.

D

B

The difference and.

A

The thing that matters is how much faster the second Stadium is doesn't know the first, but.

B

It doesn't matter if the base rate of the issue doesn't.

A

Matter, it's just the fact.

B

I, don't think the two stains aren't even being compared you. This is another weird thing: I, don't understand this. Yet what they're saying here there's this is they are they're not getting into this issue here. I'm confused by this I need to do this further, but you remember the awesomes right inference model was about having a base theta and an increased theta, and that and that was to show the procession or the of the peaks they're.

E

Not even talking.

B

About that here, they're saying here there is no base theta they're, not even talking about the base. Theta they're, not comparing these.

E

Two actually, the difference between the very earliest 1d model.

D

That I showed, which was this idea.

E

That there's a base data than a higher one on the input, whereas the later models like, for example, the hybrid model that I showed doesn't have a base speaker so to speak, but instead uses pairs of oscillators in opposing direction. And if you can combine those, then you don't need. Then you don't need a base. Data, okay, I.

B

Need to understand that I don't yet understood the word you survive. I need to get returned, but in in here they're not really talking about that they're. Just.

E

B

You hypothetically propose that there are these cells that are all these cells that are all going at the same rate and they're all going in perfect synchrony like the labeling in them in the stadium, which was made up right.

B

They just made that up, then you could sample from them and if you samples from like three of them that are really like 120 degrees apart- and you said this cell here looks at it- looks at this blue cell here, which is the same as deep blue, all this blue cell. All these are the same cell. This is where they're the same cell, where it's responding in an area. If that's so looked at this cell and this cell in this cell, it would have this pattern of firing in the environment.

B

Okay, that's what they're saying there. It doesn't explain the procession at all. It just says: I would get a good cell if.

C

I did that, so what you're saying that there would be an opposition that I.

B

Know this is well here you're going to be, they is for Microsoft. Recently the optimal was 120 degrees. That's.

E

Why the best type of oscillatory interference model has 6 inputs, because.

D

C

Can't, oh there's.

E

A different ways to get to the all the different things you need like the great and the fetal position and the the.

D

Simplest possible model.

E

Is just assumed as somatic theta and a faster input, but it's.

D

Not the only way to get there and.

E

So it's ok, yeah! Ok! Thank you.

B

Alright, now we're gonna get to this point of today's talk. Discussion, I asked myself I said well, there's some compelling things about this and what some of the things.

E

They thought were compelling I.

B

Didn't find good knowing like how you could get a place out of it? I, don't think that's right at all, but I said this is an easy way of generating grid cells and it seems to there's some data behind it and so on I said, but where are these circular cells? Where is this ring attractor? You know: have we seen anything like that? Where would that exist? This requires a whole bunch of cells that are so.

E

Working together, they.

B

All work at the same frequency and yet somehow they're taking their turn like this, like then waver in the stadium, if that were true, it's kind of exists, someplace and I'm. Thinking like where would it exist in the neocortex, my first guest, which I think it's wrong was I, said I, said well, I'm, always looking for a role of a mini column, I said well. What, if.

D

I we're actually we're.

B

Just talking about one section of a minute like a one layer, but these are just all on one layer of the hippocampus they're, not.

E

Not everywhere.

B

So I said well what if it was like in in here I had these cells like this and they could be firing your aggression, my finances got your finders there I, don't think that's right! Then it occurred to me that there's another possibility and the other possibility and I'm not true. It was the order if I read this paper first, if I thought I can't remember now the other possibilities the following: let's go back to the classic Ice Cube model in the neocortex and the classic ice cream model.

B

The neocortex is you've got if they go across in one direction. Here you see these orientation changes and as I organized recently, I think we have missed, interpret these that these are not spatial features. These are almost all these cells are directionally, sensitive and I. Think these are in essence what these cells act, like you know, a dot product between. You know the movement in your preferred. They represent a preferred direction of movement of the eye or the finger. These.

B

This sort of organization exists everywhere into quite X, so these are essentially, you can use sensory input to drive what we're, how something is moving and I'm going to further you want, but I think this is.

B

These are like these are like the little things in the bottom of my figure down there, so the direction oriented and there and, as you put a sign of sort of grading in front of the animals eye or across your finger, or something like that, which your gaze, you get a very response rates of these things, depending on how this is mapping directly to the to the movement or, if it's angle and so I, think that is the right way to interpret many comes, and we can have to develop that into a further theory.

B

Whoever it was always going to miss me for those you've been in this room for a long time know that it always wondered if, when you look at this block that when you move in one direction, this is a first like a millimeter cube near cortex, top layer, bottom layer. Looking to the side here, down from the top you'll see that you as you move in this direction, you go across these orientations, but when you go in this direction, it's all iced up orientation, it's the same orientation sort of like struggle or mini-com here.

B

But if you go look at the many columns in destruction beyond this direction, all have the same orientation and I've always wondered. I said why? Why would you do what the pointy of having the replication you want to have all these things the same going in this direction? They always bothered and there's never been any explanation or a proposed explanation. I've ever heard of so you remember, we might call. It wondered um proposed various weird things that never worked out for that.

B

Then you occurred to me well, I wondered if if what you're seeing across here is, is there's this traveling wave across here, which is the the changing in the fade? It's like this. This is the stadium unwrapped right. This is this little circle dot, but it's unwrapped here. This paper called hippocampal.

B

Hippocampal theta oscillations are traveling waves. This was 2009 by loop, ANOVA and Cialis, and what they show here and I won't go through all the details of it, there's a lot of methodological stuff that they did to get this to work, but.

D

B

They basically show.

E

B

The hippocampus, not here but in the hippocampus, if I, were to look at a cube of the hippocampus.

B

Look at you big, hippocampus, that what do you see is the thing to us that the theta oscillations that are occurring are occurring in waves that travel in one direction its until the Selvig that the wave is going. This way, the way from the theater in that stadium is going traveling across the surface, and if you look carefully, this is a well-documented now I'm not going to go for all the details.

B

I I can't I've interpret this figure and I'm not going to try to interpret for you right now, but what it basically says in my wrong world is that you get a complete. You've got a complete 360 degrees in about one millimeter. Okay, this isn't hippocampus. This dimension here in the cortex is about one millimeter, and so.

E

It occurred to me that if.

B

The same mechanism that was happening in the hippocampus, where these theta waves are moving across that that could be happening in the cortex and, what's going on in this dimension, is you have a series of many columns that are occurring at different points in that circular stadium of the wave in the stadium?

B

So these guys in this, the cells in this slice we're all operating at the same frequency every all these many columns and these slides are all operating the same frequency that frequencies is tuned to the movement of the the of this sensor and whether it's part of the height of the figure or whatever, so they speeds up and slows down from the theta rhythm, but it's unraveling.

B

It's it's just a traveling wave the cross here and so now that that provides a potential explanation for why you have this slab like this, and it gives you all the information that they're proposing you need in which to build a grid cell module system.

B

I've never heard of anything like this being observed, of course, when the girl, diesel and all those people did this work, I don't think they were thinking about this. These these cycles at all they just they just didn't do that. So if this were true, this is a strong prediction. It's measurable, you can do it in they've shown they can do this with these multi tetrode arrays. That's what this paper does. They use out.

B

They use a two-dimensional multi tetrode array that they can plant on top of the cortex or the top of the hippocampus, and they can detect these traveled ways. You could do the same for the near cortex and and you I'm, giving this a fairly high likelihood, I, wouldn't say 99% but I'd, say greater than 80% chance that you would see that traveling wave there and now we're just excited to me now, as it gives me a for the first time.

B

I can start building out, perhaps a more complete picture about it's, this big big clue as to what the hell's going on in cortical cut. If we assume that this architecture, which apparently seen every right to go back and look at mount castles papers, I think mal council actually said this- that this slab idea exists in all modalities, that this might be how the quarter of columns are structured. One dimension is each is the change in the orientation of the movement.

B

It's it's the orientation of movement and the other is this this traveling wave and now you have the structure for building everything, so that was that was the thought for today.

C

Nice picture: what would be the direction across I'd.

B

Have to go back and review that the arc of the dominance issue- I, don't remember, Kevin I, obviously familiar with it. I can't remember, but I, don't remember the details there is also I.

B

Can I can I bring up a related topic up ahead, so there's been by ignorance, I, don't know the answer question, but there's something interesting to think about as well.

B

What I'm proposing is that that most of what we used to think like Oh, which cells are driven by motor behavior than they are they either the animal moves in the dark? The good cells get updated, but I also have shown that grid cells get updated. They must get updated by pure sensory input, but not in the example is a game.

B

If you're sitting watching some video on the screen and you're like a video game or something play a video game and as they move, that's the the person playing the game moves around your sense of where you are in the game. Changes to you know that I move forward, I moved over here and so there's. Obviously the grid cells representing where you think you that, where this player is in the world out there in this game, are being updated purely by sensory information, cuz I'm, not doing anything and so I.

B

That was one of my conclusions and I said to myself. I think that's the primary way that the system knows movement and I.

E

B

That now it's the same thing is happening if your finger, when you move you're, seeing over an object, there's sensors that detect the movement in direction and how fast you're moving and that's how and then the the mapping to motor is later Lord. Okay. So now, let's put it this way. So, if I think about a finger finger, really just I can only move. The surface of my finger can only detect movement in two dimensions, but that sound is slightly true. The eye I could learn in three dimensions and because all it requires is I.

B

If I have this field is expanding.

B

This way, I know I'm going into the field and playing still thing this one no like I would feel better I'm going left and right so occurs to me that in vision- unlike touch where we have this- that we could take advantage of the the not only the two eyes, but also the flow in and out, and so what, if that were true, then you would expect to see in visual cortex if I had cells and are not just sensitive to movement left and movement right, but into and out of the field of view and I.

B

Think there are cells like that.

C

They think they are in either like I'm, T or MST, or something okay.

B

So I'd be surprised if there weren't.

A

B

A

B

Like these cells respond, they can active one when you have something moving out of something right: moving across the field, what I would expect some cells that say no.

D

A

B

When things are moving like that or moving like this, can.

A

I start works when.

C

A

Light speed and.

E

A

B

This is because we really want to map three-dimensional structures right and in it's, it's tricky in touch, because it doesn't appear that I can sense in 3d in movement in 3d, so I have to have some additional mechanisms, and Marcus has talked about some things we might do, but but envision you might be that I really can sense movement in 3d directly in the sensory system and therefore I would not want to just have my my my orient my orientation columns, which are really my movement columns I wouldn't want to be as 2d.

B

You have one on blue strea every one of the representing movements in this direction in that direction. You know things moving around, so I move like this, and so on. So I would expect to see in cortex columns and maybe- and you said they there. So that's good I would expect to see columns that are directionally sensitive in 3d, the same idea but they're moving in and out of the plane and therefore we could we're gonna.

B

We need to learn and dimensional maps, and so we this will allow us to build an N dimensional that we could, instead of just having two dimensional orientations, we get a three dimensional orientation if you're talking about.

A

May columns that are selective in freedom.

B

No, each column is sensitive to movement in 1d right they have a 1d preference, so this would be like a one knee movement, preference and what we want to do is you have other columns that are percentage of movements in outside of the plane. Oh right.

A

B

We talked about like in the past, I've talked about how these columns could the spaceship ooh love it automatically. If it could, they would automatically find vectors. That would would that would cover the entire space and it could be sure dimensional. It could be three dimensions to be n dimensional right. We want a general purpose mechanism that says you just give me.

B

Some inputs and I will figure out how to map the n dimensions of that input, as best I can into a grid cell, like representation, and then I can start building n dimensional models of whatever it is that I'm looking at of sensing. So that's the goal, and these guys, even in the end of this in the end of the cosine, a directional trimming paper. The very last thing they talk about, which is interesting.

B

I think was newspaper was a newspaper Rosa Dylan. Oh here we go was a very violent.

B

You know everything.

B

Oh, they basically say this is a I'm gonna paraphrase because it's it's complicated. They say this could be a very general purpose system to map any kind of time, varying time varying state variable X, which essentially could be at any n-dimensional thing.

B

D

We go, the basic is there's the principle in the existence of such.

B

Oscillators in the nervous system would make it possible to since lights, almost any desired envelope function in the state space of X, thereby provided powerful, flexible mechanism for construction, but mental representations in biological neural networks. Basically, X represents its, so the unlimited number of properties and dimensions and they're saying this could be like reading between the lines. I'm saying that they're suggesting this is a very powerful mechanism that could be used for lots of different things.

B

That's what they are saying to be lots of different things, I'm, not sure the thinking the same things unthinking, but but they say this is a general-purpose system. So we really.

E

Would love to come up with a really.

B

General-Purpose methodology for how a common cortex could learn the structure or anything.

B

This idea that this theta thing this theta the way the staining way moves along. One dimensions of the cortex I found fascinating I did realize since yesterday, for and after I talk to you, there's a little bit of weirdness to it and I'll point out the thing that I think is weird that it makes it gives me pause in the in the theta wave paper.

B

They they show these. What this like? A this, a line of activities all time attention across like this is this tribal wave going across the surface of the hippocampus. But here, if we we're talking about these, these guys are going to have slightly different frequencies right there, because at any point, when something I'm going a little bit faster, something going a little bit slower and therefore there isn't a single wave going across here. The way that's going across here, there's going to be a one frequency and the one that's going across here.

B

It's gonna be that frequency some put some Delta and a small Delta, and so there's going to be sort of the there's. There's gonna be a slight there's gonna, be a gradient of frequency as you go from across this way, because there's a gradient of frequency energy going across this way, I rock that. So what does that means? I mean the wave sort of the the wave sort of like bends a bit. You know there's the way might go straight across in it. It starts looking like you know like this, that's a cross.

B

You know I loves interesting to think about.

B

But it's not it's not a killer. It's just like an interesting thing.

E

It's like I wouldn't be.

A

B

Perfectly straight lines going across, it would be kind of right, but anything. That's almost okay.

A

That almost supports the theory, because it makes it where these waves would be harder to find unless you were looking for them, but something.

D

Like that would make would explain.

E

A

Neuroscientists are.

B

It yeah that's right, but but.

A

You would have people would have accidentally not been after 50 years of neuroscience. Well,.

B

Okay, well, my point is the 2009 papers said no one took a look for traveling we're gonna go for traveling right, so.

A

One other thing else, just throw is useful to throw this.

B

Out of some point.

D

A

You know has really had been banging the drum of traveling waves in the past couple years: Terry Sejnowski, it has some recent stuff where like is a big review paper from 2018 ethic.

D

A

Is just reviewing traveling waves of cortex or traveling.

E

On cement, II just give a talk at the Simmons Institute. It's.

B

Actually, like, like.

E

Sharpness and the audience- and it's like an interesting conversation actually.

B

E

Talks about Thomas and I want to review like the lying paper of that, because it speaks in.

B

You show me that.

E

B

Of the nice things now.

D

Is I have a lot.

B

B

D

E

Was wonderful because just yes, I.

A

Came in I start.

B

Reading papers, instead of writing hands on that here, you were sitting in your.

A

Other chair, I.

B

E

Kanamycin just two things that I'm thinking about I.

B

Mean I'm not gonna. Take this absolutely.

B

E

The paper eyes on the video.

D

E

And so two things that I'm thinking about this one is that this model, because there's this this directional organization right in there, you know your cortical ice cube and the the question is right for one, and is it really true that the typical orientation of traveling theta waves in your cortex, which do exist and which none of these talks all about actually is sort of? You know oriented the right way to work with this?

E

B

First of all, didn't know that it was known to exist so now I guess it's.

D

All study already, but.

B

Yes, the prediction here would be: you see it in this exactly perpendicular.

E

To the orientation 19 of them in eCollege.

B

It doesn't say about what should happen to go in this direction.

B

That's all I should have been going in this direction. Is the frequency should change, but I wouldn't I, can't say anything else beyond that? Not only during a movement should be first yeah, don't move it. The frequency change but I'm not sure that that I'm not sure I, don't.

E

Think that I think that's misleading I think it's misleading to to stop the discussion about kata nuclear cells. With with the auto metric primitives of of the navigational system and cortex and hippocampus.

B

E

Think it's a mistake. Why.

B

Because if you're thinking of the constantinescu.

E

Paper, for example, yeah.

B

So you want to get away.

E

A little bit from like navigation right, what you really after is not necessarily you know, movements be the Sun Direction understand that is important, whether that's a moving finger or moving eyeball, or you know oil moving legs, but in order to be as generic as possible, what you want is simply a column that is detects, Y, preferential change in a you, know, incredible dimension, and if that happens, young legs and necks of.

B

Course that's cuz of a city, but the nice thing about thinking about it here is there's a lot of data on this Court's go is right, there's a huge amount of data. We can go looking. You know.

E

About what goes on.

D

Somatosensory cortex.

B

Exactly like this, and so I think, obviously we want a generic mechanism, and so, but I think also the reason I'm focusing on the century stuff is because I think this is a really big idea that no one I think everyone misinterpreted. What orientation nouns are I, think it's a complete misinterpretation. That is, we think of it. Like I was fooled by this too, that it would it's actually a special feature. It's not, it is a.

B

It is basically dividing up a little bit through a through a grid cell space or into some space, and that would true that would be true whether it was early vision or sometimes a few birds. It doesn't make a difference, but.

E

B

Think by by including primary sensory cortex in it, which no one is thinking about today, nobody's thinking as I know the thing that that stop may even occur in v1 and v2. That's why content doneski paper they looked at. You know.

D

Completely people.

B

Don't think that you want, does anything people think feelings aside.

E

Through that cheetah's I can come loose in that way.

B

Yeah, so so I think I think bringing that into the picture, because there's so much more data here, like this kind of architectures knowing.

E

D

Getting one those.

B

Of the prefrontal cortex looks like in terms of this kind of structure. You know, but yeah you're right the point we need them, genericized us to say well, what is the? What is the Guru principle is going on that if I stick this on top of an eyeball on get this butter stick on top of some other quarters, I'll put like it, yeah George.

A

D

To check in with your mental model like here, you're driving the ice cube version.

A

Out this, like the Hubel and Wiesel version out, but often the pictures in the cortex are more like pinwheels yeah. Do you basically just a doubt this and picture it like spiral around until.

B

They win it Sam up at the moment. Yes without any, there may be more to it right. Do the pinwheels really represent some other type of computational functions that I'm missing it I, don't know about you, I don't know, and they probably do but I don't know what it is yet so I'm just gonna go right now, so there are.

E

Parts of the cortex that really do look like.

B

This and there's other parts with really kind of spiraling into those vortex points. Writing the pinwheels. So I, don't know what the hell's going on there I.

A

Was thinking that, in fact, all of it is pen wheels and actual cortex? Actually one of primates, and- and this was just like they won't be so initial gasps.

B

No I think I think I could be wrong. I believe if you actually look at the cortex in the dimensions, that is that you can easily pick out one square millimeter things will look just like this and that the pinwheels are so that we should.

A

Really lots of bands and crazy.

B

It's just a question: dimensionality.

A

You get selected and get back well.

B

The question is, is this? Is one millimeter small amount that you can isolate sections.

D

B

Are basically your horse icon, like this versus incorporate.

E

B

Through I think it is 200 steps around, but it's weed easy to check. You just go find those pictures. Look.

C

Around have that the reason why I brought the pitch of the ocular dominance is that if we really need this stuff instead of features as a set of oscillators and their differences well, the difference between the ocular dominance gives you 3 D, directly yeah.

B

The reason I reason I tend to dismiss ocular dominance is I. Ask myself what can I do with one eye and there are very few things you can't do with one eye so.

E

I could watch the video game with one eye.

B

And have a sense that I'm moving in and out of way and all that stuff, so that doesn't require two eyes. Obviously two eyes adds advantage. It could give better depth perception, no doubt about it, but in particular.

C

One of the effects of use to create the illusion.

D

C

Depth is to vibrate things just a little bit where things in the foreground by Great, War and the things yes and.

B

C

Of structure can pick up that kind of phase difference as a spatial organization not required. You know wholesale movement, but just the fact that I getting you know this amount of amplitude of oscillation here versus this reality to DA solution here, but.

B

That's the kind of artificial thing, I think right. Well, I'm not sure I even need that, but.

C

It is one of the things to create the illusion, you know shoot so many of the three-member.

B

There's two things going on is: where are you not just it's 3d, it's like: where are you what the thing you're looking at, where is its work is just location, that's not the same as to be need to have a three-dimensional representation of space but I'm trying to locate where something is and I'm moving and I'm trying to cap integration to say well, if I knew where I am now and all sudden I move like this, and now you know I'm in a different location. That's not just the same as saying I'm perceiving of depth.

B

That is somehow you have to. You have to you're inferring movement through space through the sensory input and gendering. The concept of 3d is not generating movement through space. It's just saying, oh that thinks throwing this thing's closer right. You could do. There was static.

C

Position yeah so we're.

B

Trying to get to the point where we're saying it's like it's like good cells, like the map not moving in the space, where we're trying to imagine we're trying to imagine us this we're trying to imagine us moving through space and doing this. For this. You know this I'm trying to update my grid cells based on sensory input and I. Don't know yet I, don't I, know I, don't need that the two eyes to do that.

C

Key points that you just put out and said we even think of these as VCO techniques and what we do is we find features and then try to compute their disparity. But if what we're seeing here is really, you know.

D

These oscillations, and just by the fact.

C

That you know microscope aids or whatever you get this little disparity kind of going on. You could actually pick that up and bypass the whole notion of collecting a bunch of features and doing their disparity and say. Are there face differences between these?

C

You know cool big leagues, as someone would be in the same place every thing so.

B

That's that's figure-ground separation thing.

E

Like that, yeah.

A

You know saying: should I get a judge distance for this right.

C

And I'm saying that the the assaulter.

D

Amount of the phase differences.

C

Gives the capacity for for eliciting that single locally and you have to totally put it together but you're getting that direction? I think I'm learning this.

B

Is I'm gonna I'm gonna end this I'm running out of steam you, but this is the only part what we need here right. This is just one small part of what we need. This is just basically trying to create a reference frame for where the viewer is in the world and changing that reference frame where the real reasonable. That's all that this is accomplishing at this point in time. There's all these other things. There still has to be sensory input which gets assigned to these locations.

B

That's still touring here and- and these other issues about you know how far away something is. This doesn't calculate that it's just totally we're out and where my eyeball is yeah, so there's a lot more going on I, just I just feel like that. Does that this is a big clue. That's all, and it's.

D

Not the answer to.

B

Everything it's just like a piece that could be really important, and so now that I'm gonna try to build up a much better model of what's going on, at least in terms of this grid cell stuff, and that will become a substrate in which to figure out further things. um It's just a step, but it's an exciting step for me, because it's the first time I've ever had an idea of what might be what might be going on this dimension.

C

Across yeah costal rappin, right yeah and that's interesting.

B

Training yeah, that's what I think most people think that's what it is yeah so.

E

I think that was a perfect organization. If you want alright.

D

Well, no I think.

B

That yeah all right, I wanna someone else- wants to go in this river. My brother I just wanted this there's supposed to be really short topic, but I knew was a lot of background to get to it. That was it.

B

Thanks for watching.