Computational diversity and the mesoscale organization of the neocortex
Date Posted:
April 22, 2014
Date Recorded:
April 22, 2014
Speaker(s):
Gary Marcus
All Captioned Videos CBMM Special Seminars Description:
Abstract:
The human neocortex participates in a wide range of tasks, yet superficially appears to adhere to a relatively uniform six-layered architecture throughout its extent. For that reason, much research has been devoted to characterizing a single “canonical” cortical computation”, repeated massively throughout the cortex, with differences between areas presumed to arise from their inputs and outputs rather than from “intrinsic” properties. There is as yet no consensus, however, about what such a canonical computation might be, little evidence that uniform systems can capture abstract and symbolic computation (e.g., language) and little contact between proposals for a single canonical circuit and complexities such as differential gene expression across the cortex, or the diversity of neurons and synapse types. Here, we evaluate and synthesize diverse evidence for a different way of thinking about neocortical architecture, which we believe to be more compatible with evolutionary and developmental biology, as well as with the inherent diversity of cortical functions. In this conception, the cortex is composed of an array of reconfigurable computational blocks, each capable of performing a variety of distinct operations, and possibly evolved through duplication and divergence. The computation performed by each block depends on its internal configuration. Area-specific specialization arises as a function of differing configurations of the local logic blocks, area-specific long-range axonal projection patterns and area-specific properties of the input. This view provides a possible framework for integrating detailed knowledge of cortical microcircuitry with computational characterizations.
Biography:
Gary Marcus , Professor of Psychology at NYU and Visiting Cognitive Scientist at the Allen Institute for Brain Science, is the author of four books including the NYTimes Bestseller, Guitar Zero . He frequently blogs for The New Yorker , and is co-editor of the forthcoming book, The Future of the Brain: Essays By The World’s Leading Neuroscientists . His research on language, evolution, computation and cognitive development has been published widely, in leading journals such as Science and Nature .
This talk is part of the Brains, Minds & Machines Seminar Series 2013-2014 .
GARY MARCUS: I've had a very crazy weekend, so I did not visualize at all the crowd that would be here. I couldn't visualize the building because it didn't exist when I graduated from here many years ago. But I just want to say how warm I'm feeling inside right now, seeing so many old friends.
Before I get started, I want to call out Adam Marblestone. I think he would vaguely agree that he would hold up his hand. He's my collaborator, one of my two collaborators on this work. All the fault is mine because he keeps arguing that my arguments could be even stronger. So don't hold him responsible for the errors, but he's been a wonderful collaborator, as has Tom Dean at Google, who was just mentioned.
And I promised I would turn on a microphone. And one last thing-- Susan Carey, who's sitting in the front row, will be moderating a debate tomorrow at 5 o'clock, at Harvard in the Science Center B, between me and Josh Tenenbaum. And there will be almost no overlap between what we talk about today and what we talk about tomorrow. So don't feel that you'll be wasting your time to come up the street.
So what I'm going to talk about today is a view that the brain might have a canonical cortical computation. There might be one computation that's repeated many, many times throughout the cortex. And that might be the right way of understanding what's going on. And you could date this to a lot of different times.
I have a quote from Otto Creutzfeldt, who says it's assumed, basically, that the brain is a kind of filter. The cortex is a kind of filter that's identical for all neocortical areas. And what matters is essentially how you're connected up, where you're connected up in the cortex, but it's basically the same kind of circuit over and over again. And I have a kind of illustration of a cortical column, which people often associate with this idea, and a few quotes because I think in a minute you're going to tell me that it's a straw man and that nobody really believes the idea.
But you can find lots of quotes in the literature that at least sound like people believe this. Like, all parts of the neocortex might operate based on a common principle, with the cortical column being that unit of computation. Sometimes, people spell this out in a more learning-rule kind of way. So they say, there are only a few computational principles, and the variability of input is what gives us functional specialization.
I should say that the background to this is-- language and vision, for example, are obviously different kinds of things. So what we want to understand is why different parts of the brain are doing different things. And so one theory is there is one circuit that's repeated everywhere. And maybe what really matters is just what input you get.
So if you're connected up to auditory inputs, then you become part of auditory cortex. And maybe that's all there is to say because there's this one kind of circuit. So this is a fairly common view. And it's not a crazy view, I think, although I'm going to argue against it. There are at least five reasons to take it seriously. And I'm going to collapse mostly between the two versions of this view, one of which says there's a canonical circuit, and the other that says that there's a canonical learning rule, per se. And we can talk about that in the discussion if you'd like.
So one of the reasons that I think a lot of people are drawn to this-- there's a bunch of seats up front, if anybody cares. One of the reasons a lot of people are drawn to this idea is that the cortex is surprisingly uniform between areas and across species. So if you just read DFMRI literature and noticed that different parts of the brain do different things, or you just thought in terms of adaptation and tasks demands and so forth, you might expect that, say, Broca's area would look entirely different from visual cortex.
And I think it's a surprising fact that to a first approximation, they don't look that different. It's a surprising fact that most of the cortex does look at least relatively similar. It's also the case that, at least sometimes, in principle, computationally, you can take a single computational model and get it to do fairly different things in different domains. So Tommy has one version of this.
My NYU colleague X. J. Wang has another version where you take some mathematics and you show that with some kinds of relatively minor parametric changes you can actually get different kinds of behavior. And that would be consistent with the idea that you might just have one canonical circuit. Then there's a kind of apparent interchangeability of cortex.
And I don't see Mriganka in the room, but Mriganka Sur's experiments are often trotted out in this kind of argument. So the crude version of it is that he rewired visual input into auditory cortex. He didn't actually literally do the rewiring, and I think the retelling of it is kind of sloppy compared to what he actually did. But it does show some kind of interchangeability at some level. If you can get auditory cortex to respond in interesting ways to visual cortex, that does tell you that there's something shared.
Then there's a very interesting recent paper, which not everybody will be familiar with and I urge everybody to read even though I'm going to argue against it in some ways later, by Sean Hill and Henry Markram in PNAS in 2012. And the basic idea is that just by knowing what kinds of cells you have in a particular area, you can do a pretty good job of predicting how they connect together. So if we all presume that the computations you do are a function of your connectivity, and I can guess your connectivity by knowing just a little bit, then that says maybe there aren't such interesting differences between them.
So what they did is they looked in somatosensory cortex, and they actually went from one rodent to another. So I think they used rats, but it could've been mice. And they found that if you looked at somatosensory connections, and you said, here's a pyramidal cell. Here's a basket cell. What do these things typically do? Then you could get about 75% of the variance by the synapse level connections between them. And that suggests some kind of stereotypy in how things are connected.
And the Blue Brain, now the Human Brain Project, is premised on this idea that you can use statistical descriptions of connectivity to model the whole brain. So if modeling the whole brain requires that you know each individual connection and you have to empirically discover them doing your favorite version of electron microscopy and having undergraduates put together all the connections, we're going to be here for a really long time. But if it turns out that there are broad generalizations about how cortexes wire together, and if they turn out to be true across the cortex, then we might be able to make interesting simplifications. And it might be a lot easier to get that project off the ground.
And then there's the apparent success of hierarchical feature detectors and unsupervised learning. So people have found common algorithms that are able to do a lot of different things, maybe even to some extent in different domains. So there's a paper by Andrew [? Ing ?] and Andrew [? Saks ?] where they try to argue at least within sensory areas they can use a single common algorithm and get, say, facts about audition and facts about vision.
So all of these things are consistent, and then there's a kind of meta argument which is simply parsimony. I mean, who wants to have a theory with a lot of epicycles if you can find one central metaphor and you can predict everything else? And so why stipulate a whole bunch of different kinds of circuits if maybe we can actually get one to do everything that we need in order to capture what the brain is doing?
And so there has been a quest to characterize a single, canonical microcircuit. It's a common quest, I think. Sometimes, as I said, people will claim that it's actually a straw man and no one's really trying to do this. But there have been lots of people who've made this argument at some level. Usually when people try to spell out the idea, what they have in mind is some version of Hubel and Wiesel.
And I have a quote here saying that Hubel and Wiesel is the greatest single influence on the ways neuroscientists think about the brain during the second half of the 20th century. I think that absolutely right. I think it carries over today. So the basic idea is you have simple cells that feed into complex cells that feed into still more complex cells.
And I think people have gotten a lot of mileage out of this idea, and I don't want to argue that there's no reason that people should be doing it. I think it's a real part of the brain that we have hierarchical feature detection. I think it's a fundamental computation of the brain, but I don't think it's the only one. That idea itself is consistent with a lot of different empirical data. Hubel and Wiesel of course had some of their own over 50 years ago.
And it has culminated in things like some of the data that Christof Koch and his collaborators have collected where you have individual cells at the top of these hierarchies that are sensitive to things like Oprah Winfrey or Jennifer Aniston and not just to pictures of them, but also to written versions of those and so forth. And you can see them as at least consistent with Hubel and Wiesel sort of going further and further up the chain. It's also the impetus behind a wide range of computational models, going back at least to neocognitron in 1980.
It's the inspiration behind Jeff Hawkins' model, who has a slightly different version. Nowadays, you can't read too much in the tech world without seeing reference to deep learning, and deep learning is basically a variation on this theme. It's a clever variation because it's much better at interpreting its own features. So it used to be you had to build your own features. And now with deep learning, sometimes the machine can do a better job than people at figuring out what the features might be.
I just thought I'd have a brief dig on MIT here. I know that you would all say Ray Kurzweil is a straw man. And I won't comment on that except to say that your president here thought his recent book in which he defended a version of this, he thought it was a wonderful book. And so did Marvin Minsky. So it's popular in some parts of MIT.
The Google cat detector is in some ways the apotheosis of the hierarchical feature detector system. It looks at stills from millions of YouTube videos, and it does things like detect cats. It was a front page story in the New York Times when it succeeded in doing it. So you can basically do the equivalent of single-cell recordings, looking at its individual neurons, and say, what stimulus maximally activates this particular node in the network?
And some of them respond to cats, actually a lot of them probably, because there are a lot of cat videos on YouTube. As it turns out, people love their cats. But even so, even with the full resources of Google, I don't think anybody would claim that the cat detector is actually on par with human performance. It has problems, for example, with invariance. It has problems assimilating context and so forth.
So I don't want to argue that hierarchy feature detectors are wrong, that any of the work that's spent on them is misplaced. But I don't think that they're sufficient, either for artificial intelligence or for neuroscience. So let me give you some reasons to doubt the canonical circuit view.
One is there's no satisfactory account of what that circuit might be. And people have been working. Either you can go back to Cajal, or at least you can go back to 40 years. And nobody has yet figured out what it is. And I give the last word here to Bono while I take a sip of water.
OK, so if it's there, no one's found it. That's not a knock-down argument, of course, but people have been trying hard. It also offers no account of why cortical diversity is so pervasive. So if you actually look at the biology of the brain at any level of description, you don't see some master uniformity, other than maybe the six-layer cortex itself.
But if you look for example at connectivity between brain areas, it used to be obligatory. You could not give a neuroscience talk without the Felleman and Van Essen diagram on the left. And now we know that's a wild underestimate, so people redid it with macaque and with mouse. And some of you may have seen the Allen Brain Institute paper two weeks ago in nature. Every time people get a finer degree of microscopy or a finer degree of imaging, they find that Felleman and Van Essen were yet another order of magnitude oversimplifying in the diagram that we already thought was incredibly complex.
There's also complexity in how those layers connect to other brain areas and to each other and so forth. I won't go into that one in too much detail. There's enormous diversity at the level of neuronal subtypes. We don't even know how many neurons there are in the brain. If we were trying to find the explanation for one pattern recognition circuit, it's not obvious to me that we would want it or that we would find something like 700 or 800 different kinds of neurons.
Then there's complexity at the level of individual synapse that may turn out to be computationally pretty important. So there are hundreds of different proteins going on there that may allow different kinds of computations. So another quote from Cajal is, "unfortunately nature seems unaware of our intellectual need for convenience and unity and very often takes delight in complication and diversity." I think that's absolutely right at every level that people have looked.
So that doesn't absolutely militate against a single canonical circuit. There could be one very complicated circuit. It does, I think, absolutely militate against some versions of that view where what we're looking for are a few simple principles. So those who are looking for a silver bullet to explain the brain, as, say, Kurzweil seems to be doing, I think are definitely barking up the wrong tree if you actually look at the complexity of the brain.
And it highlights the fact that there are a lot of possible dimensions on which you could have variations. So let's suppose there was some master circuit. We'll say it's maybe a central pattern generator that we borrowed from invertebrates. Well, over evolutionary time, that might have diverged in a lot of different ways. And the diversity that I just described would give a substrate for that, such that you could have many different variations on themes that are subtly different in terms of what proteins are in what places, what kinds of cells are available, and so forth.
And the next issue I have with the canonical circuit view is that it makes almost no contact with developmental biology, with molecular biology, with evolutionary biology. There's a lot of biology out there that is just kind of being ignored, I think, in the majority, and certainly not all, but the majority of computational neuroscience. And in particular, it's this idea of highly-diversified families of related structures that I think comes through incredibly powerfully when you look at molecular biology, developmental biology, evolutionary biology.
So one of the things I did after I left here-- so I got my degree here basically studying what might be innate about the past tense verb system or something like that. And eventually after doing a lot of psychological work on that, I realized that innateness cashes out as a claim about developmental biology. And I started reading the developmental biology literature a few years after I graduated from here.
And the thing that's overwhelmingly impressive about it is the variation on themes. Over and over, you see variations on themes. And I don't see that idea, which seems so powerfully illustrated, showing up in the canonical circuit view. Another concern I have with the canonical circuit view is that, at least as instantiated as a hierarchical pattern recognizer, it doesn't actually explain the parts of cognition that I personally care about most, which are things like language, where we can get a few examples and generalize massively.
So my degree was on language, and eventually I got interested in the sort of detailed operation of the neural network models, the multilayer perceptrons that were popular at that time. And something that I discovered is there's a kind of Achilles heel to these models. So they're very good not only at learning their training examples but learning a sort of cluster of things around them.
So they generalize in a way, but they're very limited in how they can generalize. I think I have a figure in a second to try to illustrate that point. I have here some basic things that are all variations on the notion of the identity function-- f of x equals x. And I wrote a book called The Algebraic Mind, and the notion is that some of what we do as cognitive creatures is essentially algebra. And I stole the idea, I guess, from William James, who said that thought is a kind of algebra.
So we can take a function like f of x equals x. We can see it for a few examples. And we reach the conclusion, we make the induction, that it applies to all the examples in some possible class. Sorry, I should say that I eventually did experiments with seven-month-old infants to show that they could do a version of this inference. And as often happens in developmental psychology, someone eventually came back and said, nah, nah, kids can do it even younger.
So it turns out that newborns can actually do this generalization, the identity function, to elements they've never seen before. And what I found when I looked at the multilayer perceptrons and the logic of how they worked and started doing experiments with them is something that I called output independence. And basically what this means is, for example, if you train an auto associator, which is probably the most frequent use of these kinds of networks-- so it's a very common kind of system.
If you train it on the identity function, where your inputs are binary numbers, it will learn the cases that you train it on. But if you train it, for example, on even numbers, it won't generalize to odd numbers. So if you have one bit that it happens never to have seen before, the system doesn't know how to do it. This generalizes to a lot of other functions. So it's not just identity function.
I use that as a kind of simple example, but there are many functions in the class that I call universally-quantified, one-to-one mappings. And if you want to discuss the details of that in discussion later, that's fine. But suffice to say, there are a lot of problems that seem to fall into this form. And a lot of them have the character that language does, where you have a grammar. You can apply something to many cases, but it's not just in language.
It turns out that hidden units, which were all the rage then and have come back and are all the rage in AI now, they don't help. And it doesn't even matter how many layers of hidden layers you have. So you can have 10 hidden layers, and it won't help. So the metaphor that I used was a training space.
So you can think that the green examples here are the things that you've seen before. This is the one time I'll use the pointer. Can you still hear me if I go over here? So the green examples are the things you've been trained on, and then there's this cloud around those examples. And the models will actually generalize to them, but they won't generalize to the points that are outside that space.
So what happened historically, I think, is there was a lot of excitement about these models because they generalized at all. And they gave an alternative to generalizing with symbols. So the time when these models came out, symbol manipulation was the only theory people had about how you could generalize. And this was a genuinely different theory about how you could generalize.
But people stopped, I think, prematurely, and they said, ah, they generalize. This is great. We've got something that looks like the brain. We're done. We don't need symbol manipulation anymore. And what they were ignoring were the cases outside the training space, where those models actually weren't effective.
And in my own view, my own possibly rewriting of history, what happened to those models is they basically disappeared over time because they couldn't do things like language. They reemerged in souped-up form, and they're very good at certain classification tasks. So they're very good at speech recognition, for example, but they're still nowhere when it comes to natural language understanding, for example.
I won't go into this now in detail, but what I have here-- maybe I'll walk over one more time-- is an illustration of a paper that just came out in PNAS last year by Randy O'Reilly, Jonathan Cohen, and some other folks I don't know, where they have a model that actually can generalize, a neural network model that can generalize. And the crucial thing is that the way that it works is by building in the things that I projected in the 2001 book, Algebraic Mind, are indispensable. So a lot of neural networks tried to get rid of symbol manipulation, and basically this is actually a transparent implementation of symbol manipulation.
We can go over the details later, but just briefly, they have built in variables, instances, ways of representing given instances of variables, and ways for having operations like store and add and copy and so forth. And so it's sort of spoken in the same breath as all the other neural networks, but it's really fundamentally different in kind from the other neural networks that people have talked about. And I don't want to say the brain isn't a neural network.
Of course it's a neural network, but we want to know what kind it is. And what they are doing in order to get the data right, and here are the data, they actually did a version of the problem that I had been working on, the a rose is a rose problem or something like that. In the right bar here, they build in the extra machinery that's fundamentally different in kind. On the other bars, they used the traditional network case architectures. And those don't solve the kinds of identity over time problems that I was look at.
So what this shows you is you can build neural networks to solve extrapolation problems, but you can't do it by using the uniform architectures that have historically been popular. So the summary so far is that I think computational neuroscience has, to a large degree-- certainly not exclusively-- mostly looked under one street light, which is the street light of feature hierarchies. How can we classify things based on sets of features that get more and more abstract? And I think that's fine, but there are lots of other streetlights we need to be looking at.
My own favorite one is operations over variables because I don't see how you can really capture language without it. And there are others that people are starting to look at as well. But I think that a way of encapsulating what we've learned from neural networks, both by their successes and their failures, is you need a wide range of computational elements, not just one.
The canonical view, because I'm still on the part about why the canonical might be unsatisfactory, another problem is it gives no account about why language might be unique to humans. If we all have the same circuits, if rats and people all have the same circuits, you can make some arguments about size. And I think devotees of that viewpoint will say, we just have bigger brains.
But I'm doubtful that that's actually going to explain the whole thing. So small babies and pygmy human beings still have language, even though their brains are relatively smaller. So I'm sure that the size is a precondition, but I don't think that's the whole story.
So let me give you a few hypotheses, looking just for the moment at prefrontal areas versus sensory areas. But you could change the example. But just to be concrete, here's some kinds of hypotheses you might have. One is maybe prefrontal areas work just like sensory areas, and they just have different inputs. And this really is an idea that I see expressed in the literature.
Another is they might work mostly like sensory areas, but there might be minor parametric differences. So my colleague Xiao-Jing Wang in a certain sense is trying to develop this view. And I think it's good work to try to develop this kind of view and see how far you can push it. And he's doing interesting things, looking at, for example, maybe there are parametric differences in how persistent the neurons are in one area versus another, how long they lock in to a particular input stimulus, with the prefrontal areas presumably being more persistent than some of the sensory areas. And I think there's mileage to be gained there.
Another possibility is that prefrontal areas have some resemblance to sensory areas but are variations on a theme that differ both quantitatively and qualitatively, akin to the differences between a wing and an arm. So a wing and an arm have quantitative differences. They also have qualitative differences, like feathers or no feathers.
And then another possibility is prefrontal areas are totally different from sensory areas because they solve different sorts of adaptive problems. And that was kind of what I imagined in graduate school. I thought, you know, there's going to be a custom-designed circuit for Broca's area. And it just doesn't seem to turn out to be the case. And so part of this talk is my own struggle to reconcile what I understand about the diversity of cognition with the fact that the cortex is this relatively uniform [? sheet. ?]
And so I wind up here, in option number three. There must be variations on theme that are qualitatively different as well as quantitatively different. So here's a conjecture, and it's inspired by a kind of digital circuit that some of you will be familiar with and others not. And I'll tell you that thing, I guess, in a moment.
So the conjecture is that the cortex is not a single, repeated element. It doesn't consist of a single, repeated element, but maybe a set of different, heterogeneous elements that do different kinds of things. And I'll give some hypotheses about that in a second. And this allows us to do qualitatively distinct computations.
And the way that we should understand some abstract task, like language, is as a configuration of a whole bunch of different fundamental circuit types, not as one, writ large, with a lot of input. So the inspiration for this is something called an FPGA, which is a kind of digital circuit that is sort of like a computer that runs in parallel without software but just by dividing up all the computations so that they work essentially simultaneously. And the crucial thing is that you have a set of elements that at some superficial level all look identical, called logic blocks or something like that, logic cells.
So that would be these guys over here. And those logic cells, the point is even though there is sort of a common grid into which they all enter, they can each be individually customized to particular things. So there's a family of systems like this, called programmable logic devices. The old-fashioned ones did this trick by basically burning out wires.
So you could burn out the wires in one logic cell to make it an and gate, another one to make it an or gate, another one to make it do addition, another one to do digital signal processing. Now people have more sophisticated ways to do this. Technical details I don't think matter. What matters is that you have these blocks that are ostensibly similar, but they can be tuned to different computations-- arithmetic computations, signal detection computations, what have you-- the logic of a computer laid out in parallel.
So that's the view that I'm pushing. I'll kind of put it in context. So at the top, we have the canonical cortical circuits tuned by experience. On that notion, the anatomy is basically uniform. Computations are pretty much the same everywhere, but they differ in terms of the inputs. And they are tuned by experience.
Then, this is maybe not entirely fair, but you could read the FMRI literature as saying the anatomy is probably pretty heterogeneous. I mean, really, most of the FMRI literature doesn't really speak to it. But the impression you get is, hey, all these different parts of the brain doing really different things. So the computations are presumed to be heterogeneous, and people don't really talk about the wiring that much, except maybe DTI or something like that.
The third possibility, the one that I'm pushing, says that the cortex is an array of configurable, computational elements. The anatomy is largely share, but there's some molecular fine tuning in the individual blocks that makes those blocks computationally different from one another. Computations are tinkered variations on themes. They're not all identical, and they can be qualitatively different.
And the other real difference in emphasis here is a lot of the computational literature, for whatever reason, seems to me to be very empiricist, to assume that everything is tuned by experience. And I want to put a strong emphasis on the molecular contributions to the wiring, not to the exclusion of experience. It's obvious that we calibrate the brain based on experience. We do that constantly. We do that at multiple time scales over the whole life, over the course of a lecture, and so forth. But I think that the molecular cues are being left out.
So what might a block be on this general framework? Well, I think there are two places that we could look. One is bottom up stuff that we already know about neuroscience, and the other is top-down from cognitive science. I think there are a lot of candidates for what blocks might be. For example, topographic maps are a kind of wiring motif. It's basically a one-to-one map that we see over and over in the brain, and don't just see them in the sensory areas.
There's some arguments about how sharp they are outside of the sensory areas, but they seem to be pretty ubiquitous. Same with lateral inhibition-- this is something that we certainly see in lots of parts of the brain. It doesn't mean you see it in every single circuit, but it pops up a lot. Hierarchies of feature detectors have to be on the list of candidate blocks that the brain might be assembled out of.
If you buy the general view that I'm pushing, it doesn't entail that hierarchies of feature detectors are wrong. It just entails that that's one of the tools in the collection. Divisive normalization, winner-take-all networks, there are lots of things out there that you could look at from a bottom-up perspective. Then-- and I guess some of you might have just heard Randy Gallistel sort of give a different version of this spiel.
You could look to top-down things, and you say there are things that we know must be there. We have no idea how the brain actually implements them, but they've got to be there somewhere. For example, working memory storage-- we don't really have an adequate account of working memory storage. And I think Randy probably made this point in the talk he gave at Harvard a week or two ago.
We don't really have an account of variable binding. I actually think that variable binding and topographic mapping might be related in interesting ways. I could tell you later, but we don't have an account that we agree on for variable binding. There's got to be way of sort of copying and pasting representations. We don't know how that works and so forth.
So we might come up with a candidate taxonomy of neural building blocks by looking both bottom-up and top-down. And the notion is that what we want is that taxonomy. Right now, we only candidates. They could be instantiated in multiple ways.
Mostly, I think about these things as being sets of neurons, but I think it's important to think that individual neurons can also do fairly complicated computations. Christof Koch has a great paper making that point, and Randy Gallistel has referred me to some very interesting new data that make that argument as well. I suspect, actually, we'll find blocks at multiple levels of implementation.
My model here is gene regulation. If a rational creature built the biology of the animals on this planet, it would start with a kind of nomenclature kind of thing, where he's say, we're going to put gene regulation in the following format. And we're going to stick to it because it's going to be too insane to debug if we have multiple ways of doing gene regulation.
But if you look at what's actually been discovered in the last 15 years, there are at least half a dozen different levels at which gene regulation happens. Biology just turns out to be incredibly opportunistic and doesn't really care whether or not we can debug it. And I suspect the same thing might happen when we're talking about computational building blocks.
They might also even overlap one another. So the metaphor here might be an FM and an AM radio. They actually share a lot of circuitry, or they can share a lot of circuitry, even though they do distinct things.
I presume that these things are configured through a mix of molecules and activity. I'm not different from anybody else in attributing activity to being part of what's configuring things, but I am trying to put a bit extra emphasis on the molecular side of things. One particular hypothesis that I think is consistent with the Sean Hill work is that maybe there's a basic geometric scaffold that's pretty common across the cortex. But the last mile of that might differ.
Maybe 75% of it is in the way that they're kind of arguing. Although I'll come back to their argument later. But that would still leave a lot of room for the final synapses to be different in different areas or different circuits and allow you to have computational building blocks that were distinct even though there was a relatively stereotyped backbone to all of them. And again, coming back to the FPGA for just one second, that's what it's about. It's a stereotyped backbone that can be configured computationally for different problems.
Two key reasons why I think this conjecture deserves serious consideration-- the first is it's at least possible to think about functional diversity in this framework in a way that I just don't think really follows out from the uniform architectures. So if you believe in a one size fits all computation, it just doesn't give you purchase, I think, on why language and vision are so different from one another. I mean, I can't say that I have a full answer to that either, but I think that this gives you a place where you could start to think about, well, maybe the blocks are configured in interesting and different ways.
So on our proposal, the basic architecture of individual blocks is shared across the cortex. The local logic performed by each block can be individually tuned. And I'll come back to duplication and diversions, which I think is a key process here.
The second main reason, I think, for taking this conjecture seriously and trying to develop it and to see how it can be tested and articulated is that it's compatible with developmental and evolutionary biology. So I mentioned that after I left MIT, one of the things that I did was spend a lot of time trying to understand developmental biology. And I wrote a book, called The Birth of the Mind, that was sort of a report from what I had learned, I suppose. And the major thing that I emphasized there was the power of duplication and divergence throughout biology and why I thought that must be key to understanding the brain.
We didn't really have any data there. Now we have some. But that was what I thought was the key element for how are we going to explain the riddle of how humans, who have genomes that aren't that different from chimpanzee genomes, manage to be so different. Well, it must be that you have reusable blocks that have been tinkered in different kinds of ways. Or that was the argument that I made.
So the important thing about duplication and divergence, which is the idea that you can have a gene that builds something, and then you have copies of that genes. And then one of those copies can diverge. So if you have an important gene and you have a lot of variation in that gene, other things being equal, it's going to be lethal. You're going to die.
But if you have two copies, then one of them could do something new. One of my favorite examples of this is actually in color vision. So color vision, what you need are two photoreceptors that respond to different parts of the spectrum. Before that, before in our ancestry there was such a thing, a photoreceptors was responsive to one pattern of light. Suddenly when you have two-- from one wavelength-- you have two that are responsive in different ways, then you have an entirely different qualitatively different system possible, just by having this duplication and divergence process.
And the uniform architectures just ignore this. They don't talk about duplication and divergence at all. They don't get any traction from it. They don't incorporate it into their models. On our theory, that's central. The idea is you've got different blocks that have diverged overtime, presumably partly through duplication and divergence.
OK, that said, there's some apparently conflicting evidence that's definitely worth mentioning. I don't know why there's animation here. But one is the Sean Hill, Henry Markram study that I mentioned, where there's apparent stereotyping. So if there's stereotyping across the cortex, then how do you reconcile having the diversity of circuit types? And my first answer to that is we don't actually know that from that study.
That study is written that way, and it defends, essentially, the Human Simulation project on that basis. But they actually only look at S1. It's interesting that they look at somatosensory area 1 in one rat and can predict it in another rat. That's a kind of generalization. But they don't look at the key generalization for this hypothesis, which would be can I do that in somatosensory and predict what's going to happen in prefrontal areas, for example?
They just don't do that. There are various other issues also. They only looked in primate. It's possible that the interesting-- and I'll give you some data for that I guess, or at least allude to some data for that. It's possible that there's a lot of interesting variation in humans that you just don't see in the rats. I'll just tell you now. There's been a lot of gene duplication, especially in prefrontal cortex in human beings.
And so it could be you could look at rats forever, and you would never see some critical thing that has happened in our inventory of blocks. Then they also give no account of long-range connections. It's sort of complicated, but we could talk about that. And as I already said, predicting 75% is impressive, but that still leaves a lot of room.
And then it turns out, here's another PNAS paper that came out afterwards. There's already some data, for example, that the cortical barrel columns in a rodent in somatosensory S1 that they looked at is actually whisper specific. So even in the area that they looked at, there's some individualized things that they kind of neglected.
Then there's Mriganka Sur's experiments, and I don't know if we have anyone who's worked on those in this room. But a critical question in my mind has always been, can you do this generally? So in the Sur lab, they took auditory inputs. They got rid of the original destination, and those rerouted themselves into the visual cortex. They weren't rewired. They rerouted themselves.
The way I think about it is they have found the next-best partner that they could partner with. And the question is, could you do that arbitrarily across the cortex? If you could, then there would be no need for the kind of explanation that I'm giving. If it turned out the cortex was sufficiently interchangeable, you can reroute any piece into any piece, no sweat, no problem, that would not be good for this theory.
But it's never actually been shown outside of those areas. I asked Mriganka in an email, had he ever done it elsewhere? And what he said is they didn't try that hard to do it elsewhere. And you can make your own inferences, but I infer from that that it's not that easy to do it. 20 years or so later, we've not seen anybody, for example, rewire auditory input into prefrontal cortex and have success, for example.
Then there's a question of computational models, one from Tommy that I alluded to before. One from Xiao-Jing Wang that I referred to. There are probably a bunch of others. We get qualitative differences for quantitative tuning. And I don't doubt that such things are at play. I don't have any criticism of such models, but I think it's important to realize that evolution does both kinds of change-- both quantitative change and qualitative change.
So the giraffe's neck is an example of quantitative change. You just stretch out the neck, and you get a creature that can live in a different kind of niche. But there's also plenty of qualitative change often coming from duplication and divergence. And the stuff that I speculated about in 2004, there's a nice review by Geschwind and Rakic in 2013.
Gene duplication and divergence is clearly important in human prefrontal cortex. We don't know exactly what it's doing, but there's plenty of evidence it's there. And the most important point on this slide is there's just no a priori reason to believe that between-area differences or between-circuit differences are only quantitative. I think a lot of people have the default assumption. And maybe there's an argument for having it as a default, but not a strong default, that whatever differences there are are quantitative.
I'm sure there are lots of quantitative differences, but there's no argument that, given the machinery of developmental biology and evolutionary biology, that nature would be restricted only to quantitative changes. So our position is that uniform canonical microcircuitry just hasn't been shown to do the job. There's been 40 years of work on it, and nobody has gotten anywhere in explaining how Broca's area works or how to build a language module that does anything more than speech recognition and so forth.
People have been trying to push the hierarchical pattern recognition very, very hard, many, many people. And it's given us a very good account of categorization, but there's more to cognition. The molecularly programmed FPGA metaphor offers a different way of thinking about functional diversity.
So it's an exaggeration to say that we make any strong predictions. This is a framework. It's not a specific theory. This is a direction. I'm sort of saying, the field is looking east. I would prefer it if we would look west. I'm not saying where in all of west the right answer is going to be. But to the extent we can make some predictions here, they would be something like this.
We think that there are going to be fundamental structural differences, probably only revealed at the level of synaptic connectivity. Only when we can really fully understand synaptic connectivity and in particular cell types and different cell types and what they're doing will we really be able to tell. But we're predicting that there will be fundamental differences between different brain areas, that even though things superficially look the same, there are some really important differences.
We think these differences are likely to be governed by molecular cues and activity-dependent plasticity, like everybody else believes. And we think that these differences are going to have a powerful impact on the computations performed by each cortical area or each cortical circuit. Now I'm going to give you a little bit of evidence that's broadly consistent with that view.
One is there's a very nice review that just came out of anatomical differences across the cortex. So the differences are small, but they are actually visible. So you can tell the difference, if you know what you're doing, between-- I guess this is primary visual cortex versus agranular frontal cortex. There are measurable differences that are reliable. You have to be an anatomist to recognize them.
I'm not personally going to be able to tell. They're very subtle, but they're there. And if you do the right staining, you can see them. There are also gene expression differences across the cortex. They're small. It's not that Broca's area is 80% different molecularly than V1 or something like that. That's just not the case.
But there are systematic differences. The figure on the right is from an Allen Brain Institute paper from two years ago. And what the inset is showing is that gene expression is more similar the closer you are together. So the further apart you are in cortex, the more different your gene expression is.
It's worth remembering that you can get the differences between, say, a hand and a foot by maybe a 1% difference. So a hand and a foot, they're variations on a theme, but they're importantly tweaked to different kinds of problems. And that might be what we're seeing here.
So 95% of the molecular underpinnings of cortex are the same wherever you go. So the Krebs cycle is the same wherever you go. They're all made up of axons and dendrites and so forth. But there are some salient differences that are reliable, that are robust, and are correlated with where you are in cortex.
There's also the tools to, in principle, build the kind of individual blocks that we would like. The way I think about this is by analogy to synthetic biology and the kind of project that Craig Venter is undertaking and probably lots of people at MIT. There are the tools that if you wanted to build a biological system with different computational blocks in different places, you could do it.
One of the tools you would want is a common [INAUDIBLE] code, where you could say, I want this circuit to connect to other circuits in a different way from other circuits. So I'd like to be able to specify, using a set of molecules, destinations for particular cells. And another Allen Brain-- I think I said I consult with them. So there needs to be some disclosure here.
But another Allen Brain Institute paper in cerebral cortex that just came out last year shows at least one such common [INAUDIBLE] code, looking in, I think, it was layer 5 of mouse S1, same as the Sean Hill paper. You might also want ways of making very subtle differences in synaptic connectivity. And there's some recent work on neurexins, a particular kind of molecule that's involved in alternative splicing, that could get you a long way.
So it turns out that the hair cells in the cochlea, if I understand correctly, the main difference between them is not the proteins that you find, but the ways that those proteins are spliced. So you get sensitivity to different parts of the frequency spectrum, depending on subtle variations in splicing. Well, it turns out that there's a particular set of alternative splicing molecules that hang out in synapses. They actually allow you both molecular control, through cascades of genes, and activity-dependent control because they tie into some of those cascades. That could give you conceivably the kind of purchase that you would need in order to fine tune some of the circuitry, both molecular and through activity.
There's also some differences in evoked local fields in a paper that just came out that's pretty consistent with our overall agenda, although to be honest, I don't fully understand the argument. This paper just came out. So there are a number of at least possible places where we might turn to try to find the differences that we're speculating on. Just a few more slides. I'm winding down.
Everyone agrees that new techniques are critical to figuring out the brain, and I'm not trying to argue against that. We all agree that we need finer-grained ways of measuring neural activity. We need to understand what's going on at the level of individual cells. We need better genetic markers for individual cell types, and so forth.
But given finite resources, there are lots of different things that you could prioritize. And as people think about how to spend the money in the Brain Initiative, for example, this is obviously a pressing question. So you could, for example, map the neural activity of the whole brain, which was the predecessor proposal to the Brain Initiative. You could try to map the full connectome.
You could try to simulate the whole brain, as they are trying to do in Europe. You could exhaustively map one single area, as the Allen Brain Institute, at least initially, was planning to do. There was some change in their plan. But you could try to map visual cortex. Try to understand everything about visual cortex. You could catalog all the individual kinds of neurons in the brain, which is actually the first of a set of priorities first listed in a set of priorities from the NIH interim report for the brain mapping thing.
We are pointing to a particular goal as being, if not most important, at least one that should very much be prioritized, which is creating a taxonomy of mesoscale computational elements and characterizing how networks of those might be differentially configured between cortical areas. That says that the priority here should be on comparing between cortical areas. Is V1 like S1, like, say, some prefrontal area?
And it also says that what we should be prioritizing is coregistering things like activity, transcriptomics at individual cells, and so forth in individual pieces of brain tissue, trying to understand the details of, say, comparable cortical columns in different places. And there's some promising steps in this direction already. Clay Reid, who moved to Allen, has some techniques for doing this.
There's a science paper that just came out that Adam Marblestone in the back I think is an author on, allowing characterization of cell phenotype in situ, looking at gene regulation and cellular environment at the individual cell level. So there are some techniques that make this if not possible this year, maybe possible in five years. The key goal would be to articulate a table like this.
And I know you can't actually read it unless maybe you're in the front row. But the idea is very much in the spirit of [INAUDIBLE] to have a table that says, here are some possible computations. So running down the left column are things like rapid perceptual classification, working memory, decision making, variable binding, and so forth. Have algorithmic accounts of how those individual computations, configurable computations, might be implemented, then you want to understand something about the neural implementations, where they might be located in the brain.
On our view, that should be the central impetus right now at this stage in neuroscience, trying to build that taxonomy, trying to say, these are the basic computations. These are how they're realized. And we'll come back to things like language after we understand those elements. So instead of trying to understand language without understanding these individual pieces, let's try to get the pieces first.
The analogy here would be, you're not going to understand Microsoft Word if you don't know what a microprocessor is first and what the instruction set is of that microprocessor. We don't think is the only thing that one should do. We sort of have it highlighted as one block in a larger research strategy. It's a way of guiding hypotheses.
If there's one macro-level concern with the Brain Initiative Project and the European Project, it's that there are not a lot of hypotheses there. There's a lot of emphasis on data collection. We're trying, in some sense, to give an avenue for doing some hypothesis generation. So to summarize-- this is my last slide more or less-- comparatively little intention has been paid in computational neuroscience to models that incorporate rich sets of basic instructions.
Most of them have one. People work really hard to have the right basic instruction. For example, the Hawkins and George paper, which has been cited many, many times, is exactly of that sort. But architectures with rich sets of instructions are a natural thing to think about, given what we understand about the brain's development, about function, about evolutionary biology.
We're trying to give a conceptual framework for bridging between neural structure and computational function, and we think that starts by having a taxonomy of different circuit types. New tools mean that at least sometime, maybe in the next decade, this conjecture might be testable, though we'd be the first to admit that it's not testable today. And the last point, which relates to the previous, it's very early days for our approach. We would love some help.
So if anybody wants to email me, there's my email. We'll put the slides up on the CBBM website. And some of this is mentioned, and a lot of other folks' ideas are mentioned in the book that will come out later this year, the future of the brain. It's an edited book with a lot of leading figures in the field, some of whom agree with me and some of who don't. I think it's a good thing at this juncture for the field to get an overview of what's ahead. I thank you all very much.
[APPLAUSE]
AUDIENCE: Thanks, Gary. Questions? Yes?
AUDIENCE: How complex do you think these [INAUDIBLE]?
GARY MARCUS: I suspect that they actually exist in multiple levels. And the analogy, again, has to be to a computer. It might be an imperfect analogy. But it if you thought about what the circuit types are in a computer, you'd start by saying, well, there are and gates and or gates and NaNs and so forth. Then you'd say, but there's another level that we clearly need to characterize that makes lots of predictions about how the system works, which is you have things like, I don't know, two-bit adders, microprocessor instructions. You might even think about sub routine libraries.
And so probably, ultimately, you want to understand these things at different levels. We don't have a guaranteed answer. You should start here, or you should start there. I think we need to start gathering these things. At first, we might have a very heterogeneous set. And maybe we'll always have a heterogeneous set. Hopefully, eventually we'll have some understanding about how the blocks at different levels, if we're right on the right track, relate to one another.
And hopefully, eventually you'll be able to say, well, if you have three of these and two of those, you can interconnect them to make one of these. That's what we do when we describe how a computer works. So we say, if you've got a bunch of transistors that you put together in ands and or and nots, this is how you can build a two-bit adder. You can put those together, then you can make part of your microprocessor. This is how you do the addition in your microprocessor. And you sort of leapfrog one level to the next, and I think that's what we need to do here. In the back?
AUDIENCE: Can you comment a little more on what problems you think are difficult to solve without variable rebinding?
GARY MARCUS: Sure, so the number one problem I think is language. But I think anywhere where we have some abstract notion of something and we don't need to see a lot of examples in order to solve it, I think that's a candidate. So for example, if you reason about family trees, you can learn about the members of your own family tree. And you learn sibling relations and aunts and uncles and so forth, and that's cool.
But the nice thing about human beings is then you can apply it to some other family. So there was actually a connectionist model by Geoff Hinton, who's one of the great leaders in that field of family trees. And it basically learned this for a particular family, but the transfer was very, very difficult. Another way of putting is where there's transfer learning, variables are at least a good candidate hypothesis. I don't know if I want to say the null hypothesis.
But there's something that you should take seriously when you can transfer from one set of cases broadly to another set of cases. So the converse is where the categorization systems work is where there's very rich data, and you don't need to do that. So I was talking to Antonio Torralba about this earlier today.
He has these nice illustrations of what I call the long tail problem. So in his label me database, there are lots of labeled cats. You know, people like to label their cats. It's a little iPhone app. And you can go home, take a picture of your cat, and you label it. But you go out and, just like in Zipf's law in general, you go out to the right tail and there aren't any cases. When humans are doing pretty well out in that right tail, and the perceptron systems and their variants aren't doing well, that's where I would start looking for variables.
AUDIENCE: You mentioned the last mile of axon connections. What are some other candidates for configurability that you mentioned before [INAUDIBLE]?
GARY MARCUS: So you mean if configurability didn't live in the synaptic connections?
AUDIENCE: RIght.
GARY MARCUS: Well, I think some of it's probably also about long range connections, for example. I mean, you could think of, like, the basal ganglia as some wonderful subroutine. The cerebellum is another wonderful subroutine. We're not really sure what they are, but different circuits might call on those subroutines in different kinds of ways. And so that would be another sort of lever that you could manipulate.
Also not novel to us, but everybody has to agree that where your input comes from matters and how that input is mapped. So am I dealing with a one-dimensional input or a two-dimensional input? That's going to obviously enter into your configuration, too. I mean, I didn't stress that because there's nothing unique there. But that would be another lever. Yes?
AUDIENCE: So I have a question about your argument that functional diversity requires architectural diversity. So long as your architecture is Turing universal, I mean, it's going to be able to do whatever function [? of x ?] or whatever function it is that you want. So I mean, this might be an argument.
If you see a very wide array of functional capacities in the brain, that might be an argument that there are very general computational mechanisms. But in fact, we know that there is a perfectly general computational formalism, you know, anything that's Turing universal. So could you elaborate on why you think--
GARY MARCUS: I guess a couple things to say there. The first is, I have seen over the years many arguments about the Turing universality of neural networks, for example, in different forms. And the real problem there is that people confuse representation with learning. So you can represent any function in various classes of neural networks, but many of them are not very good at the extrapolation that I described.
And so it's really an issue of learning. That's one way I look at that question. The other way I look at it is, sure, you could say in fact that my laptop is basically a universal device that's doing many things. But when you really look at the laptop closely, the way that it does many things is that there are subroutines at many different levels, ranging from the instructions in the microprocessor that differ from one another to all the things that go into the APIs that allow me to draw windows and so forth.
And I wouldn't be able to come up with a useful characterization of any particular piece of software by just resorting to the fact that it's a Turing machine. I would want to know something about the instructions, the subroutines, and so forth. And so saying that it's a Turing machine doesn't get you away from the need to do that unless you only want the very abstract characterization. Those are my two answers. Maybe I'll think of a better one later.
AUDIENCE: Do you think the substructures you've been talking about could be encoded genomically?
GARY MARCUS: Yeah, I mean, that's part of the point is I think they're partly encoded genomically. So I don't think they're fully encoded genomically. I think that there is lots of room to tweak these things. And here's one of my favorite but overlooked biology papers of the last 20 years. Thomas Sudhof, who won the Nobel Prize for looking at synapses, did a study probably for entirely different reasons than I care about it.
But he created a knockout mouse. I think the gene was called munc-18. He knocked it out in a mouse. And he did this study where he looked to see what happened. And of course it kill the most because once the mouse is born, if you have no synaptic transmission you don't even breathe. You don't last very long.
But still, he went ahead and he looked anatomically with what was available 15 years ago. We might be able to do a better job now. But he look with what was available, and he saw no differences that he could measure in the brain organization of the mouse that had no synaptic transmission throughout embryo genesis, although there were gap junctions and so forth if you want to be picky about it.
But there's no synaptic transmission. And the mouse looked perfectly normal, except the brain didn't operates because there was no synaptic transmission. And then there's another great study by Zoltan Molnar that's kind of along the same lines. The take home message from studies like that is that genes can go a long way towards making a rough draft of the brain. It's only a rough draft. It's clear that there's an enormous amount of calibration, and calibration is really not even a fair term for learning.
That's just one instance of many kinds of learning mechanisms that do a lot of readjustment of that rough draft. But the rough draft can really be pretty sophisticated. And I think that the rough draft, on the view that I'm presenting, says, look. In Broca's area, we want a different basic set of circuits than we want somewhere else. And then, you know, we're going to have to learn the words and the language.
We're going to have to learn the syntax, but constrained, for example, by the fact maybe that we have hierarchical trees to begin with over here. And maybe in some other domain, we don't have hierarchical trees. So Josh, who I think is somewhere in the room in the back, has an interesting take on how you could learn among a set of priors. Could this be a tree? Could this be a ring? Could this be a ladder?
I think that's interesting work, but even on that work, those priors are given. And I think that part of what might be going on is that different parts of the brain actually, in his terms which we'll talk about tomorrow, have different priors. They're set up to do different kinds of computations, and then of course they're going respond to their inputs. Another question?
AUDIENCE: [INAUDIBLE] if you could functionally characterize one of these structures [INAUDIBLE] very, very well, half the genome could tell you about the rest.
GARY MARCUS: So I didn't have a lot of time to meet with people because I'm doing many talks while I'm here, and I'm not here very long. But one of the people that I met with while I was here yesterday was Hopi Hoekstra, who is up at Harvard. And she's doing these really interesting studies looking at different rodents that are ostensibly pretty similar but build their burrows in entirely different ways.
And I think that kind of work is one example of what you're talking about, where you might in principle try to understand what are the genetic levers that are being pushed that allow you to do this kind of behavior as opposed to that kind of behavior? And so I think that would be great. That's a potential avenue that could be really interesting.
AUDIENCE: [INAUDIBLE] for example, the association areas have [INAUDIBLE] and they also need an input from hippocampus to promote their memories. The input is needed simply to reinforce those longer connections because it's more difficult to maintain.
GARY MARCUS: I think that kind of stuff is part of the story. I don't want to cast aspersions on it. I just don't think it's the whole story. So I think that if you have different kinds of circuits, you're going to want to feed them with different kinds of information. You're going to want to have different properties about persistence. But you're also going to want properties like-- some computations, for example, might be many to one. And some might be one to many and one to one. And you're going to want to sometimes specify that in advance of experience and not have to rely just on the basic flow of information to derive those. You're going to be better off.
There's often in debates about innateness a kind of burden tennis, I think is Jerry Sameth's term, where you go back and forth. And you say, it's your responsibility to explain this thing. And people often have this default that if it could be learned, it must be learned. And I think this is really silly. I think there are lots of domains in which, over a long period of evolutionary time, if there's some way of pre-wiring something, some large but not complete degree, evolution is going to take that avenue.
So horses get up and walk, and we probably can do certain kinds of analyses from the minute that we're born. And it's not just a function, I think, of those kinds of differences that you mentioned, even though I think those are important, too.
AUDIENCE: One last question.
AUDIENCE: I have a [INAUDIBLE] question. [INAUDIBLE] some work with speech recognition under different noisy conditions for [INAUDIBLE] it does do really well, if not [INAUDIBLE].
GARY MARCUS: Yeah, there's another great paper. I don't think it's out yet. I just heard about it with the MNIST handwriting database that's kind of making the same point.
AUDIENCE: OK, so the question that I had was just looking from a computational point of view, there is no reason that [? journalists ?] have to have [INAUDIBLE]. In fact, some of your colleagues [INAUDIBLE]. So are you arguing for something along those lines? Or are you arguing something [INAUDIBLE]?
GARY MARCUS: I mean, I'm willing to-- I think we should be looking for an eclectic solution because I think that's how biology works. Like the example I gave of gene regulation-- biology takes every avenue it can to do gene regulation, to do error correction. I'm sure that biology is going to use a lot of different resources to get different kinds of computations done. And so I think probably most of the things that people have proposed, there's going to be some reflection of. And we actually should be looking for the union, not quite literally, but come closer to looking for the union of these different proposals than trying to find the one true thing that's going to rule them all. That's my general take. All right, thank you very much.
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