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Speaker 1

00:00

The following is a conversation with Tomasso Poggio. He's a professor at MIT and is a director of the Center for Brains, Minds and Machines. Cited over 100,000 times, his work has had a profound impact on our understanding of the nature of intelligence in both biological and artificial neural networks. He has been an advisor to many highly impactful researchers and entrepreneurs in AI, including Demis Hassabis of DeepMind, Amnon Shashua of Mobileye, and Christophe Koch of the Allen Institute for Brain Science.

Speaker 1

00:34

This conversation is part of the MIT course on artificial general intelligence and the Artificial Intelligence Podcast. If you enjoy it, subscribe on YouTube, iTunes, or simply connect with me on Twitter at Lex Friedman, spelled F-R-I-D. And now, here's my conversation with Tommaso Poggio. You've mentioned that in your childhood, you've developed a fascination with physics, especially the theory of relativity, and that Einstein was also a childhood hero to you.

Speaker 1

01:04

What aspect of Einstein's genius, the nature of his genius, do you think was essential for discovering the theory of relativity?

Speaker 2

01:12

You know, Einstein was a hero to me and I'm sure to many people because he was able to make of course a major major contribution to physics with simplifying a bit just a Gedanken experiment, a thought experiment. You know, imagining communication with lights between a stationary observer and somebody on a train. And I thought, you know, the fact that just with the force of his thought, of his thinking, of his mind, he could get to something so deep in terms of physical reality, how time depend on space and speed.

Speaker 2

02:01

It was something absolutely fascinating. It was the power of intelligence, the power of the mind.

Speaker 3

02:08

Do you think the ability to imagine, to visualize as he did, as a lot of great physicists do, Do you think that's in all of us, human beings? Or is there something special to

Speaker 1

02:20

that 1 particular human being?

Speaker 2

02:22

I think, you know, all of us can learn and have, in principle, similar breakthroughs. There are lessons to be learned from Einstein. He was 1 of 5 PhD students at ETA, the Eidgenossische Technische Hochschule in Zurich in physics.

Speaker 2

02:48

And he was the worst of the 5. The only 1 who did not get an academic position when he graduated, when he finished his PhD, and he went to work, as everybody knows, for the patent office. And so it's not so much that he worked for the patent office, but the fact that obviously he was smart, but he was not the top student. Obviously, he was the anti-conformist.

Speaker 2

03:13

He was not thinking in the traditional way that probably teachers and the other students were doing. So there is a lot to be said about trying to be, to do the opposite or something quite different from what other people are doing. That's certainly true for the stock market. Never buy if everybody's buying.

Speaker 1

03:36

And also true for science.

Speaker 2

03:38

Yes.

Speaker 3

03:39

So you've also mentioned, staying on the theme of physics, that you were excited at a young age by the mysteries of the universe that physics could uncover. Such, as I saw mentioned, the possibility of time travel. So the most out of the box question I think I'll get to ask today, do you think time travel is possible?

Speaker 2

04:03

Well it would be nice if it were possible right now. You know, in science you never say no.

Speaker 1

04:12

But your understanding of the nature of time.

Speaker 2

04:15

Yeah, it's very likely that it's not possible to travel in time. We may be able to travel forward in time if we can, for instance, freeze ourselves or go on some spacecraft traveling close to the speed of light. But in terms of actively traveling, for instance, back in time, I find probably very unlikely.

Speaker 3

04:45

So do you still hold the underlying dream of the engineering intelligence that will build systems that are able to do such huge leaps like discovering the kind of mechanism that would be required to travel through time. Do you still hold that dream, or echoes of it from your childhood?

Speaker 2

05:07

Yeah, I don't think whether, there are certain problems that probably cannot be solved, depending what you believe about the physical reality. Like, you know, maybe totally impossible to create energy from nothing or to travel back in time. But about making machines that can think as well as we do or better, or more likely especially in the short and mid term, help us think better, which is in a sense is happening already with the computers we have and it will happen more and more.

Speaker 2

05:48

Well that I certainly believe and I don't see in principle why computers at some point could not become more intelligent than we are. Although the word intelligence is a tricky 1 and 1 we should discuss what I mean with that.

Speaker 3

06:07

And intelligence, consciousness, words like love, is all these are very, need to be disentangled. So you've mentioned also that you believe the problem of intelligence is the greatest problem in science, greater than the origin of life and the origin of the universe. You've also, in a talk I've listened to, said that you're open to arguments against you.

Speaker 3

06:37

So what do you think is the most captivating aspect of this problem of understanding the nature of intelligence? Why does it captivate you as it does?

Speaker 2

06:47

Well, originally, I think 1 of the motivation that I had as, I guess, a teenager, when I was infatuated with theory of relativity was really that I found that there was the problem of time and space and general relativity, but there were so many other problems of the same level of difficulty and importance that I could, Even if I were Einstein, it was difficult to hope to solve all of them. So what about solving a problem whose solution allowed me to solve all the problems? And this was what if we could find the key to an intelligence 10 times better or faster than Einstein.

Speaker 3

07:37

So that's sort of seeing artificial intelligence as a tool to expand our capabilities. But is there just an inherent curiosity in you and just understanding what it is in here that makes it all work?

Speaker 2

07:54

Yes, absolutely, you're right. So I started saying this was the motivation when I was a teenager, but soon after, I think the problem of human intelligence became a real focus of my science and my research because I think for me, the most interesting problem is really asking who we are, right? Is asking not only a question about science, but even about the very tool we are using to do science, which is our brain.

Speaker 2

08:37

How does our brain work? From where does it come from? What are its limitation? Can we make it better?

Speaker 3

08:46

And that in many ways is the ultimate question that underlies this whole effort of science. So you've made significant contributions in both the science of intelligence and the engineering of intelligence. In a hypothetical way, let me ask, how far do you think we can get in creating intelligent systems without understanding the biological, the understanding how the human brain creates intelligence?

Speaker 3

09:15

Put another way, do you think we can build a strong AI system without really getting at the core, the functional, understanding the functional and the issue of the brain?

Speaker 2

09:25

Well, this is a real difficult question. You know, We did solve problems like flying without really using too much our knowledge about how birds fly. It was important, I guess, to know that you could have things heavier than air being able to fly like birds.

Speaker 2

09:56

But beyond that, probably we did not learn very much. You know, some, The Brothers Wright did learn a lot of observation about birds and designing their aircraft. But you know, you can argue we did not use much of biology in that particular case. Now in the case of intelligence I think that it's a bit of a bet right now.

Speaker 2

10:28

If you ask okay we all agree we'll get at some point, maybe soon, maybe later, to a machine that is indistinguishable from my secretary, say in terms of what I can ask the machine to do. I think we'll get there. And now the question is, you can ask people, do you think we'll get there without any knowledge about the human brain or that the best way to get there is to understand better the human brain? Okay, this is I think an educated bet that different people with different background will decide in different ways.

Speaker 2

11:11

The recent history of the progress in AI in the last, I would say 5 years or 10 years has been the main breakthroughs, the main recent breakthroughs, are really start from neuroscience. I can mention reinforcement learning as 1, is 1 of the algorithms at the core of AlphaGo, which is the system that beat the kind of an official world champion of Go, Lee Sedol, and 2, 3 years ago in Seoul. That's 1, and that started really with the work of Pavlov in

Speaker 1

11:59

1900,

Speaker 2

12:01

Marvin Minsky in the 60s, and many other neuroscientists later on. And deep learning started, which is at the core again of AlphaGo and systems like autonomous driving systems for cars, like the systems that Mobil Eye, which is a company started by 1 of my ex-post-docs, Amnon Shashua, that is at the core of those things. And deep learning, really the initial ideas in terms of the architecture of this layered hierarchical networks started with work of Thorsten Wiesel and David Hubel at Harvard, up the river in the 60s.

Speaker 2

12:47

So recent history suggests that neuroscience played a big role in these breakthroughs. My personal bet is that there is a good chance they continue to play a big role, Maybe not in all the future breakthroughs, but in some of them.

Speaker 3

13:03

At least in inspiration.

Speaker 2

13:05

At least in inspiration, absolutely, yes.

Speaker 3

13:07

So you studied both artificial and biological neural networks. You said these mechanisms that underlie deep learning and reinforcement learning. But there is nevertheless significant differences between biological and artificial neural networks as they stand now.

Speaker 3

13:27

So between the 2, What do you find is the most interesting, mysterious, maybe even beautiful difference as it currently stands in our understanding?

Speaker 2

13:37

I must confess that until recently, I found that the artificial networks, too simplistic relative to real neural networks. But recently I've been started to think that yes there are very big simplification of what you find in the brain. But on the other hand there are much closer in terms of the architecture to the brain than other models that we had, that computer science used as model of thinking, which were mathematical logics, you know, Lisp, Prolog, and those kind of things.

Speaker 2

14:19

So in comparison to those, they're much closer to the brain. You have networks of neurons, which is what the brain is about. And the artificial neurons in the models are, as I said, caricature of the biological neurons, but they're still neurons, single units communicating with other units, something that is absent in the traditional computer type models of mathematics, reasoning, and so on.

Speaker 3

14:50

So what aspect would you like to see in artificial neural networks added over time as we try to figure out ways to improve them?

Speaker 2

15:00

So 1 of the main differences and problems in terms of deep learning today, and it's not only deep learning, and the brain is the need for deep learning techniques to have a lot of labeled examples. You know, for instance, for ImageNet, you have like a training set which is 1000000 images, each 1 labeled by some human in terms of which object is there. And it's clear that in biology, a baby may be able to see a million of images in the first years of life, but will not have a million of labels given to him or her by parents or caretakers.

Speaker 2

15:56

So how do you solve that? You know, I think that there is this interesting challenge that today deep learning and related techniques are all about big data. Big data meaning a lot of examples labeled by humans. Whereas in nature you have, so this big data is n going to infinity, that's the best, n meaning labeled data.

Speaker 2

16:30

But I think the biological world is more N going to 1. A child can learn

Speaker 3

16:37

from a

Speaker 2

16:37

very small number of labeled examples. Like you tell a child, this is a car. You don't need to say, like in ImageNet, this is a car, this is a car, this is not a car, this is not a car, 1000000 times.

Speaker 3

16:53

So, and of course with AlphaGo or at least the AlphaZero variants, there's because the world of Go is so simplistic that you can actually learn by yourself, through self-play, you can play against each other. In the real world, I mean, the visual system that you've studied extensively is a lot more complicated than the game of Go. On the comment about children, which are fascinatingly good at learning new stuff, how much of it do you think is hardware and how much of it is software?

Speaker 2

17:26

Yeah, that's a good, deep question. It is in a sense is the old question of nurture and nature, how much is in the gene and how much is in the experience of an individual. Obviously, it's both that play a role and I believe that the way evolution gives, put prior information, so to speak, hardwired, it's not really hardwired, but That's essentially an hypothesis.

Speaker 2

18:02

I think what's going on is that evolution has, you know, almost necessarily, if you believe in Darwin, is very opportunistic. And think about our DNA and the DNA of Drosophila. Our DNA does not have many more genes than Drosophila.

Speaker 3

18:28

The fly.

Speaker 2

18:29

The fly, the fruit fly. Now we know that the fruit fly does not learn very much during its individual existence. It looks like 1 of this machinery that it's really mostly, not

Speaker 1

18:44

100%,

Speaker 2

18:45

but you know 95% hard-coded by the genes. But since we don't have many more genes than Drosophila, evolution could encode in us a kind of general learning machinery and then had to give very weak priors. Like for instance, let me give a specific example which is recent work by a member of our Center for Brains, Minds, and Machines.

Speaker 2

19:20

We know because of work of other people in our group and other groups that there are cells in a part of our brain, neurons, that are tuned to faces. They seem to be involved in face recognition. Now this face area exists, seems to be present in young children and adults. And 1 question is, is there from the beginning, is hardwired by evolution, or somehow is learned very quickly?

Speaker 3

19:54

So what's your, by the way, a lot of the questions I'm asking, the answer is we don't really know, but as a person who has contributed some profound ideas in these fields, you're a good person to guess at some of these. So of course there's a caveat before a lot of the stuff we talk about. But what is your hunch?

Speaker 3

20:14

Is the face, the part of the brain that seems to be concentrated on face recognition, are you born with that? Or you just, it's designed to learn that quickly, like the face of the mother and so

Speaker 2

20:26

on? My hunch, my bias was the second 1, learned very quickly. And it turns out that Marge Livingstone at Harvard has done some amazing experiments in which she raised baby monkeys, depriving them of faces during the first weeks of life. So they see technicians, but the technicians have a mask.

Speaker 2

20:53

Yes. And so when they looked at the area in the brain of these monkeys that where usually you find faces, they found no face preference. So my guess is that what evolution does in this case is there is a plastic, an area which is plastic, which is kind of predetermined to be imprinted very easily, but the command from the gene is not a detailed circuitry for a face template. Could be, but this will require probably a lot of bits.

Speaker 2

21:36

You have to specify a lot of connection of a lot of neurons. Instead, the command from the gene is something like imprint, memorize what you see most often in the first 2 weeks of life, especially in connection with food. And maybe nipples, I don't know. Right,

Speaker 3

21:54

well, source of food. And so, and then that area is very plastic at first and then solidifies. It'd be interesting if a variant of that experiment would show a different kind of pattern associated with food than a face pattern, whether that could stick.

Speaker 2

22:10

There are indications that during that experiment, what the monkeys saw quite often were the blue gloves of the technicians that were giving to the baby monkeys the milk. And some of the cells, instead of being face sensitive in that area, are hand sensitive.

Speaker 3

22:33

That's fascinating. Can you talk about what are the different parts of the brain and in your view sort of loosely and how do they contribute to intelligence? Do you see the brain as a bunch of different modules and they together come in the human brain to create intelligence or is it all 1 mush of the same kind of fundamental architecture?

Speaker 2

23:04

Yeah, that's an important question and there was a phase in neuroscience back in the 1950 or so in which it was believed for a while that the brain was equipotential, this was the term. You could cut out a piece and nothing special happened apart a little bit less performance. There was a surgeon, Lashley, who did a lot of experiments of this type with mice and rats and concluded that every part of the brain was essentially equivalent to any other 1.

Speaker 2

23:51

It turns out that that's really not true. It's, there are very specific modules in the brain, as you said, and people may lose the ability to speak if you have a stroke in a certain region or may lose control of their legs in another region. So they're very specific. The brain is also quite flexible and redundant so often it can correct things and kind of take over functions from 1 part of the brain to the other, but really there are specific modules.

Speaker 2

24:33

So the answer that we know from this old work, which was basically based on lesions, either on animals or very often there were a mine of, well, there was a mine of very interesting data coming from the war, from different types of injuries that soldiers had in the brain. And more recently, functional MRI, which allow you to check which part of the brain are active when you are doing different tasks, as you know, can replace some of this. You can see that certain parts of the brain are involved, are active

Speaker 3

25:29

in certain tasks.

Speaker 2

25:31

Yeah, that's right.

Speaker 3

25:32

But sort of taking a step back to that part of the brain that discovers that specializes in the face and how that might be learned, what's your intuition behind, you know, is it possible that sort of from a physicist's perspective when you get lower and lower, that it's all the same stuff, and it just, when you're born, it's plastic and quickly figures out, this part is gonna be about vision, this is gonna be about language, this is about common sense reasoning. Do you have an intuition that that kind of learning is going on really quickly, or is it really kind of solidified in hardware?

Speaker 2

26:09

That's a great question. So there are parts of the brain like the cerebellum or the hippocampus that are quite different from each other. They clearly have different anatomy, different connectivity.

Speaker 2

26:26

Then there is the cortex, which is the most developed part of the brain in humans. And in the cortex you have different regions of the cortex that are responsible for vision, for audition, for motor control, for language. Now 1 of the big puzzles of this is that in the cortex, is the cortex, is the cortex, looks like it is the same in terms of hardware, in terms of type of neurons and connectivity across these different modalities. So for the cortex, letting aside these other parts of the brain like spinal cord, hippocampus, cerebellum and so on, for the cortex I think your question about hardware and software and learning and so on, it's, I think it's rather open.

Speaker 2

27:28

And I find very interesting for us to think about an architecture, computer architecture, that is good for vision, and at the same time is good for language. Seems to be so different problem areas that you have to solve.

Speaker 3

27:49

But the underlying mechanism might be the same, and that's really instructive for artificial neural networks. So you've done a lot of great work in vision, in human vision, computer vision, and you mentioned the problem of human vision is really as difficult as the problem of general intelligence. And maybe that connects to the cortex discussion.

Speaker 3

28:11

Can you describe the human visual cortex and how the humans begin to understand the world through the raw sensory information. What's, for folks who are not familiar, especially on the computer vision side, We don't often actually take a step back except saying with a sentence or 2 that 1 is inspired by the other. What is it that we know about the human visual cortex? That's interesting.

Speaker 2

28:40

We know quite a bit, at the same time we don't know a lot. But the bit We know, in a sense we know a lot of the details and many we don't know and we know a lot of the top level, the answer to top level question but we don't know some basic ones, even in terms of general neuroscience, forgetting vision, you know, why do we sleep? It's such a basic question.

Speaker 2

29:11

And we really don't have an answer to that.

Speaker 3

29:14

Do you think, So taking a step back on that, so sleep for example is fascinating. Do you think that's a neuroscience question? Or if we talk about abstractions, what do you think is an interesting way to study intelligence or most effective on the levels of abstraction?

Speaker 3

29:30

Is it chemical, is it biological, is it electrophysical, mathematical, as you've done a lot of excellent work on that side, which psychology, sort of like, which level of abstraction do you think?

Speaker 2

29:43

Well, in terms of levels of abstraction, I think we need all of them. It's when, you know, it's like if you ask me, what does it mean to understand a computer, right? That's much simpler, but in a computer, I could say, well, I understand how to use PowerPoint.

Speaker 2

30:04

That's my level of understanding a computer. It's, it has reasonable, you know, it gives me some power to produce slides and beautiful slides. And now, You can ask somebody else, he says, well I know how the transistor work that are inside the computer. I can write the equation for, you know, transistor and diodes and circuits, logical circuits.

Speaker 2

30:29

And I can ask this guy, do you know how to operate PowerPoint? No idea.

Speaker 3

30:33

So do you think if we discovered computers walking amongst us full of these transistors that are also operating under Windows and have PowerPoint, do you think it's digging in a little bit more, how useful is it to understand the transistor in order to be able to understand PowerPoint and these higher level intelligent processes?

Speaker 2

31:00

So I think in the case of computers, because they were made by engineers by us, this different level of understanding are rather separate on purpose. They are separate modules so that the engineer that designed the circuit for the chips does not need to know what is inside PowerPoint. And somebody can write the software translating from 1 to the other.

Speaker 2

31:30

So, in that case, I don't think understanding the transistor help you understand PowerPoint, or very little. If you want to understand the computer, this question, I would say you have to understanding at different levels. If you really want to build 1, right? But for the brain, I think these levels of understanding, so the algorithms, which kind of computation, you know, the equivalent of PowerPoint, and the circuits, you know, the transistors, I think they are much more intertwined with each other.

Speaker 2

32:09

There is not, you know, a neatly level of the software separate from the hardware. And so that's why I think in the case of the brain, the problem is more difficult, more than for computers requires the interaction, the collaboration between different types of expertise.

Speaker 3

32:29

So it's a big, the brain is a big hierarchical mess. So you can't just disentangle levels. I think

Speaker 2

32:35

you can, but it's much more difficult and it's not completely obvious. And as I said, I think he's 1 of the, personally I think he's the greatest problem in science. So I think it's fair that it's difficult.

Speaker 3

32:51

That's a difficult 1. That said, you do talk about compositionality and why it might be useful. And when you discuss why these neural networks in artificial or biological sense learn anything, you talk about compositionality, there's a sense that nature can be disentangled, well, all aspects of our cognition could be disentangled a little to some degree.

Speaker 3

33:22

So why do you think, first of all, how do you see compositionality and why do you think it exists at all in nature?

Speaker 2

33:31

I spoke about, I used the term compositionality when we looked at deep neural networks, multi-layers, and trying to understand when and why they are more powerful than more classical one-layer networks like linear classifier, kernel machines, so-called. And what we found is that in terms of approximating or learning or representing a function, a mapping from an input to an output, like from an image to the label in the image, If this function has a particular structure, then deep networks are much more powerful than shallow networks to approximate the underlying function. And the particular structure is a structure of compositionality.

Speaker 2

34:33

If the function is made up of functions of functions so that you need to look on, when you are interpreting an image, classifying an image, you don't need to look at all pixels at once but you can compute something from small groups of pixels and then you can compute something on the output of this local computation and so on. It is similar to what you do when you read a sentence. You don't need to read the first and the last letter, but you can read syllables, combine them in words, combine the words in sentences. So this is this kind of structure.

Speaker 3

35:20

So that's as part of a discussion of why deep neural networks may be more effective than the shallow methods. And is your sense for most things we can use neural networks for, those problems are going to be compositional in nature, like language, like vision. How far can we get in this kind of way?

Speaker 3

35:46

Right.

Speaker 2

35:47

So here is almost philosophy.

Speaker 3

35:51

Well, let's go there.

Speaker 2

35:53

Yeah, let's go there. So a friend of mine, Max Tegmark, who is a physicist at MIT.

Speaker 3

36:00

I've talked to him on this thing. Yeah, and he disagrees with you, right? A

Speaker 2

36:04

little bit. Yeah, we agree on most, but the conclusion is a bit different. His conclusion is that for images, for instance, the compositional structure of this function that we have to learn or to solve these problems comes from physics, comes from the fact that you have local interactions in physics between atoms and other atoms, between particle of matter and other particles, between planets and other planets, between stars and other, it's all local.

Speaker 2

36:48

And that's true, but you could push this argument a bit further, not this argument actually, you could argue that, you know, maybe that's part of the truth, but maybe what happens is kind of the opposite, is that our brain is wired up as a deep network. So it can learn, understand, solve problems that have this compositional structure. And it cannot do, it cannot solve problems that don't have this compositional structure. So the problems we are accustomed to, we think about, we test our algorithms on, are this compositional structure because our brain is made up.

Speaker 3

37:42

And that's in a sense an evolutionary perspective that we've, so the ones that didn't have, that weren't dealing with the compositional nature of reality died off?

Speaker 2

37:55

We're not able to discover. Yes, but also could be maybe the reason why we have this local connectivity in the brain, like simple cells in cortex looking only at the small part of the image, each 1 of them, and then other cells looking at the small number of these simple cells and so on. The reason for this may be purely that it was difficult to grow long range connectivity.

Speaker 2

38:24

So suppose it's, you know, for biology, it's possible to grow short range connectivity but not long range also because there is a limited number of long range. And so you have this limitation from the biology. And this means you build a deep convolutional network. This would be something like a deep convolutional network.

Speaker 2

38:53

And this is great for solving certain class of problems. These are the ones we find easy and important for our life. And yes, they were enough for us to survive.

Speaker 3

39:08

And you can start a successful business on solving those problems, right? Like with Mobileye, driving is a compositional problem. So on the learning task, we don't know much about how the brain learns in terms of optimization.

Speaker 3

39:25

But so the thing that's stochastic gradient descent is what artificial neural networks use for the most part to adjust the parameters in such a way that it's able to deal, based on the label data, it's able to solve the problem. So what's your intuition about why it works at all? How hard of a problem it is to optimize a neural network, artificial neural network, is there other alternatives? You know, just in general, your intuition is behind this very simplistic algorithm that seems to do pretty good, surprising.

Speaker 3

40:05

So.

Speaker 2

40:06

Yes, yes. So I find neuroscience, the architecture of cortex is really similar to the architecture of deep networks. So there is a nice correspondence there between the biology and this kind of local connectivity, hierarchical architecture.

Speaker 2

40:28

The stochastic gradient descent, as you said, is a very simple technique. It seems pretty unlikely that biology could do that from what we know right now about cortex and neurons and synapses. So it's a big question open whether there are other optimization learning algorithms that can replace stochastic gradient descent. And my guess is yes, but nobody has found yet a real answer.

Speaker 2

41:11

I mean, people are trying, still trying, and there are some interesting ideas. The fact that stochastic gradient descent is so successful, this has become clearly not so mysterious. And the reason is that It's an interesting fact, you know, it's a change in a sense in how people think about statistics and this is the following, is that typically when you had data and you had say a model with parameters, you are trying to fit the model to the data, you know, to fit the parameter. Typically, the kind of crowd wisdom type idea was you should have at least twice the number of data than the number of parameters.

Speaker 2

42:12

Maybe 10 times is better. Now, the way you train neural network these days is that they have 10 or 100 times more parameters than data. Exactly the opposite. And which, you know, it has been 1 of the puzzles about neural networks.

Speaker 2

42:34

How can you get something that really works when you have so much freedom in, you know.

Speaker 3

42:40

From that little data you can generalize somehow.

Speaker 2

42:43

Right, exactly.

Speaker 3

42:44

Do you think the stochastic nature of it is essential, the randomness?

Speaker 2

42:48

So I think we have some initial understanding why this happens, but 1 nice side effect of having this over-parameterization, more parameters than data, is that when you look for the minima of a loss function like stochastic gradient descent is doing you find I made some calculations based on some old basic theorem of algebra called the Bezout theorem, that gives you an estimate of the number of solution of a system of polynomial equation. Anyway, the bottom line is that there are probably more minima for a typical deep networks than atoms in the universe. Just to say there are a lot.

Speaker 2

43:41

Because of the over-parameterization. A more global minima, 0 minima, good minima. So it's not

Speaker 3

43:50

too soon.

Speaker 2

43:51

Yeah, a lot of them. So you have a lot of solutions. So it's not so surprising that you can find them relatively easily.

Speaker 2

44:00

And

Speaker 3

44:01

this

Speaker 2

44:01

is because of the over-parameterization.

Speaker 3

44:04

The over-parameterization sprinkles that entire space with solutions that are pretty good. This is

Speaker 2

44:09

not so surprising, right? It's like, you know, if you have a system of linear equation and you have more unknowns than equations, then you have, we know, you have an infinite number of solutions. And the question is to pick 1, that's another story.

Speaker 2

44:25

But you have an infinite number of solutions, so there are a lot of value of your unknowns that satisfy the equations.

Speaker 3

44:32

But it's possible that there's a lot of those solutions that aren't very good. What's surprising is that

Speaker 2

44:38

they're pretty good. So that's a separate question. Why can you pick 1 that generalizes well?

Speaker 2

44:42

Yeah, exactly. But that's a separate question with separate answers.

Speaker 3

44:47

1 theorem that people like to talk about that kind of inspires imagination of the power of neural networks is the universal approximation theorem that you can approximate any computable function with just a finite number of neurons in a single hidden layer. Do you find this theorem 1 surprising? Do you find it useful, interesting, inspiring?

Speaker 2

45:12

No, this 1, I never found it very surprising. It was known since the 80s, since I entered the field, because it's basically the same as Weierstrass theorem, which says that I can approximate any continuous function with a polynomial of sufficiently, with a sufficient number of terms, monomials. It's basically the same, and the proofs are very similar.

Speaker 3

45:41

So your intuition was there was never any doubt that neural networks in theory could be very strong approximations.

Speaker 2

45:48

Right, the question, the interesting question is that if this theorem says you can approximate fine, but when you ask how many neurons, for instance, or in the case of polynomial, how many monomials I need to get a good approximation. Then it turns out that that depends on the dimensionality of your function, how many variables you have. But it depends on the dimensionality of your function, how many variables you have.

Speaker 2

46:20

But it depends on the dimensionality of your function in a bad way. For instance, suppose you want an error which is no worse than 10% in your approximation. You come up with a network that approximates your function within

Speaker 1

46:38

10%.

Speaker 2

46:40

Then, turns out that the number of units you need are in the order of 10 to the dimensionality, D, how many variables. So if you have 2 variables, D is 2, you have 100 units and okay. But if you have say 200 by 200 pixel images, now this is

Speaker 1

47:04

40,000

Speaker 2

47:05

whatever. And that- We

Speaker 3

47:07

again go to the size of the universe pretty quickly.

Speaker 2

47:09

Exactly, 10 to the 40,000 or something. Yeah. And so This is called the curse of dimensionality.

Speaker 2

47:18

Not quite appropriately.

Speaker 3

47:22

And the hope is with the extra layers, you can remove the curse.

Speaker 2

47:27

What we proved is that if you have deep layers, or hierarchical architecture with local connectivity of the type of convolutional deep learning. And if you're dealing with a function that has this kind of hierarchical architecture, then you avoid completely the curse.

Speaker 3

47:50

You've spoken a lot about supervised deep learning. What are your thoughts, hopes, views on the challenges of unsupervised learning with GANs, with generative adversarial networks? Do you see those as distinct, the power of GANs, do you see those as distinct from supervised methods in neural networks, or are they really all in the same representation ballpark?

Speaker 2

48:16

GANs is 1 way to get estimation of probability densities, which is a somewhat new way that people have not done before. I don't know whether this will really play an important role in intelligence or, it's interesting. I'm less enthusiastic about it than many people in the field.

Speaker 2

48:47

I have the feeling that many people in the field are really impressed by the ability of producing realistic looking images in this generative way.

Speaker 3

49:01

Which describes the popularity of the methods, but you're saying that while that's exciting and cool to look at, it may not be the tool that's useful for, so you describe it kind of beautifully. Current supervised methods go n to infinity in terms of number of labeled points, and we really have to figure out how to go to n to 1. And you're thinking GANs might help, but they might not be the right.

Speaker 2

49:24

I don't think for that problem, which I really think is important, I think they may help, they certainly have applications, for instance, in computer graphics. I did work long ago, which was a little bit similar in terms of saying, okay, I have a network and I present images and I can, so input is images and output is, for instance, the pose of the image. You know, a face, how much is smiling, is it rotated 45 degrees or not?

Speaker 2

50:02

What about having a network that I train with the same data set, but now I invert input and output. Now the input is the pose or the expression, a number, set of numbers, and the output is the image, and I train it. And we did pretty good, interesting results in terms of producing very realistic looking images. It was a less sophisticated mechanism, but the output was pretty less than GANs, but the output was pretty much of the same quality.

Speaker 2

50:38

So I think for a computer graphics type application, yeah, definitely GANs can be quite useful and not only for that, but for helping, for instance, on this problem of unsupervised example of reducing the number of labeled examples. I think people, it's like they think they can get out more than they put in.

Speaker 3

51:10

There's no free lunches, you said. So what do you think, what's your intuition? How can we slow the growth of end to infinity in supervised learning?

Speaker 3

51:24

So, for example, Mobileye has very successfully, I mean, essentially, annotated large amounts of data to be able to drive a car. Now, 1 thought is, so we're trying to teach machines, school of AI, and we're trying to, so how can we become better teachers, maybe? That's 1 way.

Speaker 2

51:47

No, you're, you know, I like that, because 1, again, 1 caricature of the history of computer science, you could say, is, begins with programmers, expensive. Yep. Continuous labelers, cheap.

Speaker 2

52:08

Yep. And the future will be schools like we have for kids.

Speaker 3

52:14

Yeah. Currently, the labeling methods, we're not selective about which examples we teach networks with. So I think the focus of making networks that learn much faster is often on the architecture side, but how can we pick better examples with which to learn? Do you have intuitions about that?

Speaker 2

52:39

Well, that's part of the problem, but the other 1 is, you know, If we look at biology, a reasonable assumption I think is in the same spirit that I said, evolution is opportunistic and has weak priors. You know, the way I think the intelligence of a child, a baby may develop is by bootstrapping weak priors from evolution. For instance, you can assume that you have in most organisms, including human babies, built in some basic machinery to detect motion and relative motion.

Speaker 2

53:38

And in fact, there is, you know, we know all insects from fruit flies to other animals, they have this. Even in the retinas, in the very peripheral part. It's very conserved across species, something that evolution discovered early. It may be the reason why babies tend to look, in the first few days, to moving objects and not to not moving objects.