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From YouTube: Grid Cells for Conceptual Spaces (NRM Feb 19, 2020)

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Numenta Research Meeting - Feb 19, 2020
Discussion at: https://discourse.numenta.org/t/numenta-research-meeting-feb-25-2020/7238
Paper: https://www.cell.com/neuron/fulltext/S0896-6273(16)30707-3

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So basically, the paper essentially talks about the fMRI, with cell cortex grid cell studies done by nsq.

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And reviews that paper and just talks about you know where you can go.

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Was funny they said they should totally like. Sometimes the reviews are better than the original papers, because it gives the bigger context and yeah that actually explains just.

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Explain what that paper did and then they asked questions I.

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Was surprised about not confused about what I mentioned? It may be obvious to somebody else. I know Marcus might others when the question was, why does this 63 preference show up in there? For my sake, where's it being generated from and exactly what they proposed here was I. Think we, previous discussions is that oh there's always a conjunctive sells. We know about conduct ourselves and the conductor cells represent both greediness and direction of travel. All right I got the turn with.

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This nice little piggy we're starting Africa here's this grid that bunch of cells in there, which are itself, but they have a direction of travel and I.

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Think the term is.

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All perfectly lined up these 60 degree angles and therefore what you're going to really do it in the nineteen between. So it's not like you know so, and therefore I view if the activity of those conjunctive cells, if you measure them they've, been more active on 60 degree, points the directions and others which makes a lot of sense.

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But I never heard of this idea that the jump is over holding in Beyonce, Sudhir animals and maybe wonder I haven't depression, just switching topics a little bit: the head, Direction cells, I thought conduct ourselves where combination of grid and head Direction cells, I hate himself over the 60 granules.

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I thought they were more.

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So so this so to be I'm trying to tune through together they bring this up. They're saying: oh there's these conductor self observe direction and know about those, but I thought they'd be more appreciated the 60-degree angle. They never mentioned the fact that they were derived from head Direction cells, so so I just.

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And that's how they claimed.

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That was the original reason.

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Like that was the window, ler and Castleberry decided to go and run this.

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First fMRI study: they were using that.

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Conjunctiva cell explanation, the light.the later explanation of walking certain directions in the rhombus with letters secondary one they found the 60-degree thing was the first thing.

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Confused so there's nico that these cells were measured at 60 degrees. I look, they were. A combination has directions on grid cells, but those are not at 60 degrees. So.

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One answer is that so.

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Are still trying to figure this out? Why does this fMRI thing occur?.

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Paper was 2016. 3 is why there's no question okay, but in 2019 people are still saying. Is this happen? And and when you talk to the people who are setting this question, they tell you that that 60 degree thing about conjunctive cells. Most labs have tried to replicate it. In fact, oh the original I think star Bellini paper for 2007, where they found that that phenomenon of the 60 degree distribution.

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It may or may not be true, but other people haven't published contradictions of it, but people have tried to replicate it and didn't succeed and then just went work on her face.

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I quickly, point out that that really like also depends on what your favorite model of grid cells is because, if you're a fan of a can model, then you'd like to incorporate as much as you can in these conductive cells, whereas if you're, if you build you know, if you come, come from an oscillatory interference thing, then that has no relevance whatsoever.

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Also means that the the conjunctive cells don't have sort of you know that perfect organization, or or even directionality tuning of any choice, it's just an inhibitory surrounding yeah.

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The point of the matter is, is an assumption outside of the hybrid model or outside of the oscillatory plus scan mode, there's an assumption that there is some sort of directionality imposed on the whole network and so I think you could accept the hybrid models. Okay, hyper model requires that direction.

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Explain where that comes from. So, if you an argument, they don't they just say these cells exist and they show this lovely picture. So I'm gonna explain how it all works and you're saying that it's still controversial and.

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It's like a big important question, like the doler lab wedding. Merge was our love. That builder.

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Moved to Norway so.

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Another question on that is: if we're working in these abstract conceptual spaces, where does head direction come into play? No there's.

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No, the directional yeah.

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But that would be a completely different. That's not head direction so.

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That would be equivalent, so we would've made your argument that your finger touching something has equivalent to a head direction. It's your finger direction if you will call it back its orientation relative yeah.

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An orientation relative to the dimensionality of something, so we made that argument.

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I know above we know what we've done here but I'm staying in their argument. I don't understand.

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A conjunctive well.

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It seems that they actually, and so my thinking is well right- the lives of our dimensions. Well, that's my guess. This is from the data and so I.

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Concepts for the moment, don't really understand it and say: well, it's that's whatever. So.

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In the constantan SQ experience of something that they don't actually depict ever they just describe it and text is the the person who was like the subjects on the experiment. The way they were controlling their movement through bird space if they had the equivalent of they don't describe.

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It exactly but hey it's.

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Having like to essentially flippers and like a button, essentially yeah and I'm, just inferring, this is how it worked, but like they basically decide how to move these letters up and down, one is like the net velocity. One is like a leg velocity and by moving these up and down and then pressing the button that causes them even.

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Though they don't ever see this picture.

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That causes them to move in some direction, and that goes like space and now importantly, they never see this. They only ever see this, but the point is the equivalent of head direction in this picture is the setting of the two levers yeah.

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It's a sine cosine. You know.

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Had to look at the supplementary.

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Where they were trying to make sure that they have a percentage, this two-dimensional field of birds to the subjects so.

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They never gave the person that joystick yeah it's.

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This is not this.

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Is a how far to go in that direction? It's like you know it's like this.

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Then they go on to set of bullet points of light. These are things that.

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Weight of data analysis, but.

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Then they go on to the very last part of paper, which is next steps: understanding, constructional spaces.

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Unified computational principle in the brain for encoding, physical and conceptual spaces, as we doing that can be studied non-invasively in humans being with fMRI, raises the host of tantalizing research questions and so seems. Like some stuff, you were just asking students I like how our grid cells, dynamically, constructed or co-opted to encode, new concepts and I guess we're staying is like. Oh, we have this two dimensional grid cell thing and somehow they're managing the two. You know: dimensional spaces versus constructed and I need to learn.

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Properties like I think it's another quality of what determines we set the fields of conceptual grids, beta cells, and then they talk about board. It's like you know, borders and so.

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So there was this interesting paper uh looked at like sort of the evolutionary origin of mental models, and one thing they use this idea from special relativity of look the light cone and the idea is that, like the sort of space of mental models- and in this case you know this Facebook conceptual spaces, it's sort of limited by the sort of range of behaviors of the of the organism in the sense of like this is the sort of horizon that which we can like usefully plan, and so.

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In some of there's, an arbitrary element.

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To it right because at some point yes, you would like to say: okay, you know stop now, but you know, even if you're like projecting infinitely far into the past of the future. You're, basically doing this within some sort of constrained space, you're sort of repeating, let's say naive, you're repeating, is sort of the same set of instructions instead of just like branching out into like an infinite number of no.

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Naturally, occurring yeah.

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Basically, yeah based.

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On the type of movements we could do or yeah.

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There's a funny picture: I think you just.

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About whether there's a global layout of great choice, like is over the entire nail cortex with these all coordinated- and we would say absolutely not I mean, could we think that every little corner of a column is building is also models of the cortex?

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Ask that question and then how our higher dimensional space is representing and the cohesion spend a lot of time on that and I have a proposal on that. They didn't make it.

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And then the residence is one paper. This math is paper 2015.

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The geometrical thing right, that's where they're you get these face. Centered cubic lattices is an exact name to this.

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Anything else about this yeah.

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Even maybe just a couple of small things, so for one and what do we think of this idea that so, if there already is a good like organization and it's supported by you know some kin or oh I mechanism that generates this grid, there's a lot of value to reusing an existing grid rather than building one from scratch every time menu right. So one of the things they asked for, like longitudinal version of the concept you never want to see. You know that that that formation happen, which obviously doesn't you.

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Know I, don't tell you anything about.

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Exactly right and so I just wonder how do we think about this in the concept of like the cortical learning framework, like the idea of like using and reusing existing structures right to map? You know the your cognitive sort of space like into that, rather than you know, building it like. Oh.

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I have a strong opinion. All.

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Right I would love to hear it.

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It goes back to the idea that.

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Is that the ideal scenario would be that the cortex have to learn the dimensionality of these cortex just to learn the dimensionality of what is waiting at and but that learning is a longer term learning than the objects you're going to represent in that space right. So if this section of cortex learns about three-dimensional visual objects, whatever it builds around three national space is connect, trouble, learning anything else because it enough to start all over yet so it's like it first.

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Us to learn.

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Is basic dimensions based and within that everything into that dimensionality, so simple, three dimensional Cartesian coordinate space.

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Cyborgs well for sensory cortex. But what about high on.

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The same, if I built my conceptual ideas,.

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It's always very interesting when you compare a no silly example like political system system.

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Because Americans are so used to the sizing.

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Everything you know along stir politics like lines of you, know, Democratic and Republican. You know liberal and conservative, whereas in many other countries these things are a lot more multi-dimensional axis because they have five and eight party Parliament's with you know much more like where, where the political fault lines are along different dimensions,.

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Like a new and- and it seems like you know, you can't relearn and I think I heard herself structure.

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It's just like today.

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You can another way to phrases like every cortical column would have its own kind of learned, location spaces and then that's co-opted to learn anything new that that cortical column learns different. Cortical columns may have completely separated the.

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Pages, yeah and.

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Then, but in some things you have to be able to transform from one to another another like if I'm going to reach out and touch this pen I'm to be able to transform the coordinates space. In my.

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Cortex into egocentric, you.

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Hand center court.

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Be able to pick up my pen so there's all these coordinate transformations that also have to happen, but.

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There needs to be some consistency across columns right, otherwise you don't get a global fMRI signal that you can pick up like well. The grid angle like they're, the cardinal you know like.

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And then it would be inconceivable that near in cortical, columns and let say v1 would be someone.

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Might be some corporate, they won't become fully independent, I think. But even the question about you know the question about: are they operated in the same direction like you know,.

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Mean guess this goes to what they were asking for right. So when I say, if you just tell you, should use unsmooth and fMRI data and map the 6-volt multi-layer amplitude and face continuously in order.

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Grid cell regions and reveal whether the angle is consistent between a.

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It's all in the middle column here exactly.

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Then again, you know what is global right is global: five millimeters, apart or as global five centimeters apart right.

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Okay I mean that was pretty much it I just wanted to like ping. Our mutual understanding here.

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One last thing: to what extent do we think that I mean it's known for navigation, there's, probably six or seven modules, even though in rodent labs are typically record three or four just because of my ya grits and modules. Because of this spatial thing right, they presume that there's one or two more, that you could record from if they actually had arenas that, were you know, 100 meters, wide, there's.

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Some doing those experiments really really large tracks, I think I, remember, but.

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They need to rounding.

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That's cool like predicting for the people building these things yeah, it's a lot of data plus the thing afterwards, but I wonder for conceptual space. Do we even think it's necessary to have several different scales? I mean you like I know that Marcus like Miko and like that the defeat paper right argues for you know. Well, if you have an n-dimensional conceptual space, you can you know, map it down to 2d grades, but but they don't necessarily need to be a different scale right.

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You just need different orientations.

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May be some efficiency argument.

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So in the cortex you might, you might be multiple regions.

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So the answers.

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Not thinking it's necessary to have them on different scales, that is the thing that is necessary for navigation because of the unique nature of you know: large 2d environments and the evolutionary pressures to map that.

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It's not like personal.

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If anything that can't be to intermingle, because otherwise it should show up in the fMRI right if they were actually like, you know, on top of each other, because then they would you know different orientations and different scales would miss up the 6/4 modulation signals, I presume, but.

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Then again, I'm just asking questions.

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Ought to talk to use this. You know like 2d navigational terms for for this, but.

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The up to 10 into 10 categories: these are the different way the data changes in ten categories and envision that can be an orientation column and something else will be something different, but it doesn't know what it's doing. So, somehow all these questions don't really on the answers like what does the data suggest right? The movement in the data suggests that yes,.

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So, to some extent, my question even epitomizes the sort of the the ignorance that one acquires by looking at grid cells only through the lens of 2d navigation, which sounds odd. Given that you know that we'll discover there and that's how we all think about them or like.

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We have to kind of free yourself.

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From that thinking, if you're gonna apply it.

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Was like there was this thing that evolved with this one task or a couple tasks that we saw and, and it was probably very finely tuned for that set of tasks and then somehow the evolution discovered that you can generalize the algorithm.

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Once you've done that, you can find any task, let's just make as many copies of.

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It up to a lot of different things, but.

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There would be differences.

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Between you know the antibiotic coaches, you know that's.

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All like super fine-tuned.

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To do these things and then.

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This way change a few parameters, and now we have this generic version that.

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I wonder with all this conceptual space stuff in studying what grid cells do spaces. Sometimes it feels like the analogy of like studying the elephant, is a bunch of blind people and, like you're, grabbing the tail and we're just studying like one part of the system, and we can't see the whole thing and and and the level at which we're studying it might be right or might not be. The a lot of this seems like things.

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That have been studied before.

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More about mathematical environment, where people talk about manifold learning or embeddings like embedding things into Euclidean spaces, is a thing that existed before grid sellswords network work discovered, and it may be the case that by studying that and and realizing like wow grid cells, are just like the mechanism for how these spaces are implemented, but but studying those the original algorithms for like local linear landmarks and the penalties, and some of this stuff Bruno has been doing recently with them with link manifolds flattening.

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It may be the case that we need a higher language like math, to understand this and then, and then this is like the bricks of how vinolas.

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I would argue you don't need to understand. I would suggest. I would accept you with that. Maybe that's a fruitful way of going about understanding any na. So it's a good observation but I think that says: okay, we better research papers on that falls to learn about it, but I, don't think you're gonna find an answer. There I mean they're gonna, be things of those things papers, they're just completely mess, so we don't have to be happening, I mean so.

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The whole idea of you know from what our goals here at events are not just to you know. We want understand how systems work and behavior generate behaviors and have sensors.

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Question is: how do you like the serendipity argument right? How do you make sure that, once certain observations are made that not you know super nicely on to some theoretical argument that people have made fifty years ago without even knowing about the brain? Just thinking about you know information, and how do you make sure that when that happens, somebody's there to say oh.

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The lab do we know this, whether.

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This clicks with you know.

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Like something.

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Is well explored, there's a whole literature on it.

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I mean it's just the whole thing right that.

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Is you never want to be stuck in one subfield.

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Not only am I right, there's nothing 1001 together, Nick isn't working das. What boundaries right, if that doesn't babies, released 15? These are the points of the question of this way.