字幕表 動画を再生する 英語字幕をプリント I want to thank the organizers for inviting me to this. This is way outside my usual area. I'm a mathematician, and the closest I get would be CIDCOM, but this has been a lot of fun. And I have this incredibly pretentious title. And so I'm going to try to explain to you what I mean by this. Online I have a bunch of videos that go into this in a lot more detail. So sort of think of this as a quick preview of the videos. And I have a lot of people to thank, not enough time to give them all the credit they deserve. So what I'm interested in is these sort of major transitions in evolution. But they're also changes in architecture, and you see increases in complexity and elaboration of networks. Unfortunately, those are the four most confused subjects in all of science. And engineers know a lot about these things, but they keep that to themselves. So I'm going to focus on two parts of this. Of course, you're interested at this stuff at the top. But I'm going to kind of use bipedalism, that transition, as an example. If we hadn't done that, none of the rest would have happened, so that's a really crucial-- they're all crucial, but that one's particularly crucial. And how do I explain universals? Well, my main way of doing it is with math. But we'll not do that today. We'll focus on trying to look at some diverse domains, so not just networking, but like I said, bipedalism and our brains and how our brains work. Currently, unfortunately, we have kind of a fragmented theory behind this. And so one of the objectives of my research is to try to get this to be not a whole nine subjects, but really one. And that's the framework to try to do this, is to create a theory which can then be used to understand these transitions. And again, lots of details in the videos. So now, I'm very different from this community. Maybe only one letter different, but that makes a big difference. But I think there's a lot of things that we're also interested in common. We want to have all these features. I may be more theoretical. Maybe you're more practical. But I think we also, again, maybe have different priorities but the same interests. And also dynamic and deterministic. And by deterministic I just mean in the way I think about the problems today, I focus on not average behavior, but kind of what goes on worst case. And so in bipedalism, one of the most important things is a trade-off between robustness and efficiency. Now of course, we'd like to be both. We'd like to be in the lower left hand corner. That's the ideal case. And if you compare us with chimps, for example, at distance running we're about four times as efficient as they are, and that's really substantial. And if you've got a bicycle, you get another factor of two or so, roughly, again, roughly. But much more fragile. And the bike makes the crashes worse, and so that's the trade-off we see in adopting bipedalism. And so what I want to do is think about these kinds of trade-offs. We'd like to be cheap, we'd like to be robust. But it's hard to be both. Now the cardiovascular physiology part of it is very interesting as well. We have a very upgraded cardiovascular system compared to chimps. If you want to read about that, that's a recent paper. And I have some, again, videos online on this physiology. So we'll not talk about physiology. We're going to worry about the balance part of it, and not worry about efficiency, but really robustness. And ideally, again, we'd be cheap, fast, flexible, and accurate. We'd have all these things. Again, I'm going to ignore the cheap dimension. PowerPoint only lets you really draw things in two dimensions, so we're going to keep projecting things into two dimensions. So again, we'd like to be fast, flexible, and accurate, but it's hard to be all of those things. So what I want to talk about is the trade-off in layered architectures, and focus on a very simplified view of what our brains do, which is planning and reflexes. And as an example, this task. This is not me. I'm more of an uphill kind of guy. So if this is me, we'd be watching a crash. But what we can see here is this higher level planning using vision is slow but very accurate. And then you have a lower level at the same time, a reflex layer, which is fast dealing with the bumps. So you've got the trail you're following and the bumps. And so we can think about this planning layer. It's slow, but it gives us a lot of accuracy, flexibility, it's centralized. It's conscious, deliberate. And it deals with stable virtual dynamics. But just the opposite of the reflex layer, which deals with the bumps. It's fast, but it's inaccurate, rigid. It's very localized and distributed, and it's all unconscious and automatic. And it deals with the unstable real dynamics to create that. So these are really opposite, completely opposite functions that the same nervous system multiplexes very effectively. And so we put those two things together. We're not ideal in the corner, but we behave almost as if we are. And so of course we'd like to be better, faster, cheaper. You can usually choose two or one at best. And again, we're going to focus on this trade-off between fast, accurate, and flexible. And again, projecting very high dimensions into these. And we're going to focus on just these aspects right now. And again, how do we talk about that? Well, again, we have a math framework for that, but I'm going to talk about how this cuts across many domains. So I claim that this is a feature universal, laws and architectures. And again what I mean by law is a law says, this is what's possible. Now in this context, this is what we can build out of spiking neuron hardware. But what is an architecture? Architecture is being able to do whatever is lawful. So a good architecture lets you do what's possible. And that's what I mean by universal laws and architectures. What I claim is, in this sort of space of smart systems, we see convergence in both the laws and the architectures. And so, again, I want to try to talk about this kind of picture, but in some diverse domains. So what are some of the other architectures that look like this? Well, one that you're obviously familiar with is this one from computing, where we have apps sitting on hardware mediated by an operating system. We don't yet really understand what the operating system is in the case of the brain. We know it's got to be there, and we know it's got to be really important, but we're a little murky on it and exactly how it works. So one of the things that I'm interested in is kind of reverse engineering that system. So you're very familiar with the universal trade-offs you have here. So for example, if you need absolute the fastest functionality, then you need special purpose hardware. But you get the greatest flexibility by having diverse application software. But that would tend to be slower, and you've got that trade-off. And then Moore's Law, of course, shifts this whole curve down as you make progress. Unfortunately, there's currently no Moore's Law for spiking neurons. We're kind of stuck with the hardware we have. But the operating system is crucial in tying these two things together. So now we have a computer science theory that more or less formalizes some aspects of this in a sense that if you want to be really fast, you have to have a very constrained problem, say, in Class P. But if you want to be very general in the kind of problems you solve, then unfortunately your algorithms are necessarily going to run slower. It turns out, at the cell level we have the same sort of trade-offs. If you want to be fast, you better have the proteins up and running, but your greatest flexibility is in gene regulation and also gene swapping. So what we have here is these convergent architectures, the fundamental trade-off being that you'd like to have low latency, you'd like to be fast, you'd like to be extremely accurate. But the hardware that we have available to us doesn't let us do those simultaneously, and there's a trade-off. And then we exploit that trade-off to do the best we can with good architectures. So I want to talk a little bit more about this in a little more detail. And I want to kind of go through and use this example of balance as a way of seeing a little bit more detail about how these systems work. And I want to sort of connect the performance with the underlying physiology a little bit. So what we're going to do is we're going to do a little experiment using your brains. And so one thing things I want to do is use vision. And I want you to try to read these texts as they move. So it turns out, up to two Hertz you don't have too much trouble doing this. But between two and three Hertz, it gets pretty blurry. And that's because that's as fast as your eye can move to track these moving letters. Now I want you to do a second experiment, which is to shake your head no as fast as you can while you're looking at this. Now I don't mean big, I mean really fast, OK? And it turns out no matter how fast you shake your head, you can still read, certainly, the upper left. So it turns out your ability to deal with head motion is much faster than for object motion. So why is that? So first of all, evolutionarily why, and then mechanistically why. So there's a trade-off. Object motion is flexible and very accurate, but slow, whereas head motion is fast but relatively inflexible. We'll see why that is. So why is that? Well, when you do object motion tracking, you're using vision. Shouldn't be surprised by that. So vision is very high bandwidth, but it's slow, several hundred milliseconds of delay. That's why you get this two to three Hertz bandwidth. So slow but very flexible. So your visual system did not evolve to look at PowerPoint slides, yet you're sitting here doing that. And it's also very accurate, and we'll see in a minute why the accuracy is there. For head motion, you have a completely separate system that doesn't use vision directly. It has this sort of rate gyros in your ear.