Pod Insights Lex Fridman Podcast Vladimir Vapnik: Statistical Learning About this episode Vladimir Vapnik is the co-inventor of support vector machines, support vector clustering, VC theory, and many foundational ideas in statistical learning. His work has been cited over 170,000 times. He has some very interesting ideas about artificial intelligence and the nature of learning, especially on the limits of our current approaches and the open problems in the field. Video version is available on YouTube https://www.youtube.com/watch?v=STFcvzoxVw4. If you would like to get more information about this podcast go to https://lexfridman.com/ai or connect with @lexfridman on Twitter https://twitter.com/lexfridman, LinkedIn https://www.linkedin.com/in/lexfridman/, Facebook https://www.facebook.com/lexfridman, or YouTube https://www.youtube.com/lexfridman where you can watch the video versions of these conversations.
Transcript Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.
0:00 Lex Fridman? The following is a conversation with Vladimir Vapnik. He's the co-inventor of support vector machines, support vector clustering, VC theory, and many foundational ideas in statistical learning. He was born in the Soviet Union and worked at the Institute of Control Sciences in Moscow. Then, in the United States, he worked at AT&T, NEC Labs, Facebook Research, and now is a professor at Columbia University. His work has been cited over 170,000 times. He has some very interesting ideas about artificial intelligence and the nature of learning, especially on the limits of our current approaches and the open problems in the field. This conversation is part of MIT course on artificial general intelligence and the
0:44 Lex Fridman? Artificial Intelligence Podcast. If you enjoy it, please subscribe on YouTube, or rate it on iTunes or your podcast provider of choice, or simply connect with me on Twitter or other social networks at Lex Fridman, spelled F-R-I-D. And now, here's my conversation with Vladimir Vapnik.
1:19 Lex Fridman? Einstein famously said that God doesn't play dice.
1:23 Lex Fridman? Yeah.
1:25 Lex Fridman? You have studied the world through the eyes of statistics, so let me ask you, in terms of the nature of reality, fundamental nature of reality, does God play dice?
1:36 Vladimir Vapnik? We don't know some factors.
1:40 Vladimir Vapnik? Because we don't know some factors which could be important, it looks like God play dice.
1:50 Vladimir Vapnik? But we should describe. In philosophy, they distinguish between two positions, positions of instrumentalism, where you're creating theory for prediction, and position of realism, where you're trying to understand what God did.
2:09 Lex Fridman? Can you describe instrumentalism and realism a little bit?
2:13 Vladimir Vapnik? For example, if you have some mechanical laws. What is that? Is it law which true always and everywhere? Or it is law which allow you to predict position of moving element?
2:35 Vladimir Vapnik? What you believe? You believe that it is God's law? That God created the world which obey to this physical law? Or it is just law for predictions?
2:51 Lex Fridman? And which one is instrumentalism?
2:53 Vladimir Vapnik? For predictions. If you believe that this is law of God and it's always true everywhere, that means that you're realist. You're trying to really understand the God's thought.
3:10 Lex Fridman? So the way you see the world is as an instrumentalist?
3:15 Vladimir Vapnik? You know, I'm working for some models. Models of machine learning. So in this model, we can see setting. And we try to solve, resolve the setting, to solve the problem. And you can do in two different ways. From the point of view of instrumentalist. And that's what everybody does now. Because they say that goal of machine learning is to find the rule for classification. That is true. But it is instrument for prediction.
3:55 Vladimir Vapnik? But I can say the goal of machine learning is to learn about conditional probability. So how God played use? And is he play? What is probability for one? What is probability for another? Given situation. But for prediction, I don't need this. I need the rule. But for understanding? I need conditional probability.
4:23 Lex Fridman? So let me just step back a little bit first to talk about, you mentioned, which I read last night, the parts of the 1960 paper by Eugene Wigner, Unreasonable Effectiveness of Mathematics in Natural Sciences. Such a beautiful paper, by the way. It made me feel, to be honest, to confess my own work in the past few years on deep learning, heavily applied, made me feel that I was missing out on some of the beauty of nature in the way that math can uncover. So let me just step away from the poetry of that for a second. How do you see the role of math in your life?
5:08 Lex Fridman? Is it a tool, is it poetry? Where does it sit? And does math for you have limits of what it can describe?
5:16 Vladimir Vapnik? Some people saying that math is language which use God. So I believe.
5:25 Lex Fridman? Speak to God or use God?
5:27 Vladimir Vapnik? Use God.
5:27 Lex Fridman? Use God?
5:29 Vladimir Vapnik? Yeah. So I believe that this article about effectiveness, unreasonable effectiveness of math is that if you're looking at mathematical structures,
5:48 Vladimir Vapnik? they know something about reality.
5:52 Vladimir Vapnik? And the most scientists from natural science, they're looking on equation and trying to understand reality.
6:03 Vladimir Vapnik? So the same in machine learning.
6:06 Vladimir Vapnik? If you're trying very carefully look on all equations which define conditional probability, you can understand something about reality more than from your fantasy.
6:23 Lex Fridman? So math can reveal the simple, underlying principles of reality, perhaps?
6:28 Vladimir Vapnik? You know what means simple? It is very hard to discover them. But then, when you discover them and look at them, you see how beautiful they are. And it is surprising why people did not see that before. You're looking on equations and derive it from equations. For example, I talked yesterday about least-squared method. And people had a lot of fantasy how to improve least-squared method. But if you're going step by step by solving some equations, you suddenly will get some term, which, after thinking,
7:14 Vladimir Vapnik? you understand that it describes position of observation point. In least-squared method, we throw out a lot of information. We don't look in composition of points of observations. We're looking only on residuals. But when you understood that, that's very simple idea, but which not too simple to understand. And you can derive this just from equations.
7:40 Lex Fridman? So some simple algebra, a few steps will take you to something surprising that when you think about.
7:48 Vladimir Vapnik? Absolutely, yes. And that is proof that human intuition not too rich and very primitive. And it does not see very simple situations.
8:03 Lex Fridman? So let me take a step back. In general, yes, right? But what about human, as opposed to intuition, ingenuity?
8:16 Lex Fridman? Moments of brilliance? So are you so... Do you have to be so hard on human intuition? Are there moments of brilliance in human intuition? They can leap ahead of math? And then the math will catch up?
8:32 Vladimir Vapnik? I don't think so. I think that the best human intuition, it is putting in axioms. And then it is technical way.
8:43 Lex Fridman? See where the axioms take you.
8:45 Vladimir Vapnik? Yeah. But if they correctly take axioms. But it axioms polished during generations of scientists. And this is integral wisdom.
9:00 Lex Fridman? So that's beautifully put. But if you maybe look at, when you think of Einstein and special relativity, what is the role of imagination coming first there? In the moment of discovery of an idea? So there's obviously a mix of math and out of the box imagination there.
9:25 Vladimir Vapnik? That's I don't know. Whatever I did, I exclude any imagination. Because whatever I saw in machine learning that come from imagination, like features, like deep learning, they are not relevant to the problem. When you're looking very carefully from mathematical equations, you're deriving very simple theory, which goes far beyond theoretically than whatever people can imagine. Because it is not good fantasy.
9:59 Lex Fridman? Yeah.
9:59 Vladimir Vapnik? It is just interpretation. It is just fantasy, but it is not what you need. You don't need any imagination to derive, say, main principle of machine learning.
10:14 Lex Fridman? When you think about learning and intelligence, maybe thinking about the human brain and trying to describe mathematically the process of learning, that is something like what happens in the human brain. Do you think we have the tools currently?
10:32 Lex Fridman? Do you think we will ever have the tools to try to describe that process of learning?
10:36 Vladimir Vapnik? You, it is not description what's going on. It is interpretation, it is your interpretation. Your vision can be wrong. You know, when guy invent microscope, Leven Cook, for the first time. Only he got this instrument and nobody, he kept secret about microscope. But he wrote report in London Academy of Science. And his report, when he looking of the blood, he look everywhere, on the water, on the blood, on the sperm. But he described blood like fight between queen and king.
11:19 Vladimir Vapnik? So he saw blood, cells, red cells, and he imagined that it is army fighting each other. And it was his interpretation of situation.
11:32 Vladimir Vapnik? And he send this report in Academy of Science, they very carefully look because they believe that he's right, he saw something.
11:40 Lex Fridman? Yes.
11:40 Vladimir Vapnik? But he gave wrong interpretation. And I believe the same can happen with brain.
11:47 Lex Fridman? With brain, yeah.
11:48 Vladimir Vapnik? The most important part, you know, I believe in human language. In some proverb is so much wisdom. For example, people say that it is better than thousand days of diligent studies one day with great teacher. But if I will ask you what teacher does, nobody knows. And that is intelligence. And but we know from history and now from from mass and machine learning that.
12:25 Vladimir Vapnik? Teacher can do a lot.
12:27 Lex Fridman? So what, from a mathematical point of view, is a great teacher?
12:31 Vladimir Vapnik? I don't know.
12:32 Lex Fridman? That's an open question.
12:33 Vladimir Vapnik? No, but we can say what teacher can do. He can introduce some invariance, some predicate for creating invariance. How he doing it? I don't know, because teacher knows reality and can describe from this reality predicate invariance. But he knows that when you're using invariant, you can decrease number of observations hundred times.
13:02 Lex Fridman? So, but maybe try to pull that apart a little bit. I think you mentioned like a piano teacher saying to the student, play like a butterfly. Right? I played piano, I played guitar for a long time. And it, yeah, that's, there's, maybe it's romantic, poetic. But it feels like there's a lot of truth in that statement. Like, there is, there is a lot of instruction in that statement. And so can you pull that apart? What is, what is that? The language itself may not contain this information.
13:37 Vladimir Vapnik? It is not blah, blah, blah.
13:39 Lex Fridman? It is not blah, blah, yeah.
13:40 Vladimir Vapnik? It affect you.
13:41 Lex Fridman? It's what?
13:42 Vladimir Vapnik? It affect you. It affect your playing.
13:44 Lex Fridman? Yes, it does, but it's not the lang. It's, it feels like, what is the information being exchanged there? What is the nature of information? What is the representation of that information?
13:56 Vladimir Vapnik? I believe that it is sort of predicate, but I don't know. That is exactly what, what intelligence in machine learning should be.
14:04 Lex Fridman? Yes.
14:05 Vladimir Vapnik? Because the rest is just mathematical technique. I think that what was discovered recently is that there is two tie, two mechanism of learning. One called strong convergence mechanism and weak convergence mechanism. Before, people use only one. In weak convergence mechanism, you can use predicate. That's what play like butterfly. And it will immediately affect your playing. You know, there is English proverb, great. If it looks like a duck. Swims like a duck and quack like a duck, then it is probably duck.
14:50 Lex Fridman? Yes.
14:51 Vladimir Vapnik? But this is exact about predicate. Looks like a duck, what it means. So you saw many ducks that you're training data. So you you have description of how how looks integral looks ducks.
15:11 Lex Fridman? Yeah, the visual characteristics of a duck, yeah.
15:14 Vladimir Vapnik? Yeah, but you want and you have model for recognition ducks. So you would like so that theoretical description from model coincide with empirical description, which you saw on theory text there. So about looks like a duck, it is general. But what about swims like a duck? You should know the duck swims. You can't say it play chess like a duck. Okay, duck doesn't play chess. And it is completely legal predicate, but it is useless. So how teacher can recognize not useless predicate?
15:56 Vladimir Vapnik? So up to now, we don't use this predicate in existing machine learning.
16:01 Lex Fridman? And you think that.
16:02 Vladimir Vapnik? So why we need zillions of data? But in this English proverb, proverb, they use only three predicate. Looks like a duck, swims like a duck and quack like a duck.
16:14 Lex Fridman? So you can't deny the fact that swims like a duck and quacks like a duck has humor in it, has ambiguity.
16:23 Vladimir Vapnik? Let's talk about swim like a duck.
16:27 Vladimir Vapnik? And it does not say jumps, jump like like a duck. Why? Because.
16:33 Lex Fridman? It's not relevant.
16:35 Vladimir Vapnik? But that means that you know ducks, you know, different birds, you know, animals.
16:42 Lex Fridman? Yeah.
16:42 Vladimir Vapnik? And you derive from this that it is relevant to say swim like a duck.
16:47 Lex Fridman? So underneath, in order for us to understand swims like a duck, it feels like we need to know millions of other little pieces of information.
16:57 Vladimir Vapnik? I'm not sure.
16:58 Lex Fridman? We pick up along the way. You don't think so. There doesn't need to be this knowledge base. In in those statements carries some rich information that helps us understand the essence of duck.
17:10 Vladimir Vapnik? Yeah.
17:12 Lex Fridman? How far are we from integrating predicates?
17:16 Vladimir Vapnik? You know that when you consider complete theory of machine learning, so what it does, you have a lot of functions. And then you're talking, it looks like a duck. You see your training data from training data, you recognize like
17:41 Vladimir Vapnik? expected duck should look. Then you remove all functions, which does not look like you think it should look from training data. So you decrease amount of function from which you pick up one. Then you give a second predicate and then again decrease the set of function. And after that, you pick up the best function you can find. It is standard machine learning. So why you need not too many examples?
18:18 Lex Fridman? Because your predicates aren't very good?
18:20 Vladimir Vapnik? Yeah, that means the predicate very good. Because every predicate is invented to decrease admissible set of function.
18:32 Lex Fridman? So you talk about admissible set of functions and you talk about good functions. So what makes a good function?
18:39 Vladimir Vapnik? So admissible set of function is set of function which has small capacity or small diversity, small VC dimension example, which contain good function inside.
18:52 Lex Fridman? So by the way, for people who don't know VC, you're the V in the VC.
18:59 Lex Fridman? So how would you describe to a layperson what VC theory is? How would you describe VC?
19:06 Vladimir Vapnik? You have a machine, so a machine capable to pick up one function from the admissible set of function.
19:17 Vladimir Vapnik? But set of admissible function can be big. Say contain all continuous functions and it useless. You don't have so many examples to pick up function. But it can be small, small.
19:35 Vladimir Vapnik? We call it capacity, but maybe better called diversity. So not very different function in the set is infinite set of function, but not very diverse. So it is small VC dimension. When VC dimension is small, you need not, you need small amount of training data. So the goal is to create admissible set of functions, which is have small VC dimension and contain good function. Then you should, then you will be able to pick up the function using small amount of observations.
20:17 Lex Fridman? So that is the task of learning?
20:21 Vladimir Vapnik? Yeah.
20:21 Lex Fridman? Is creating a set of admissible functions that has a small VC dimension? And then you've figure out a clever way of picking up?
20:32 Vladimir Vapnik? No, that is goal of learning, which I formulated yesterday.
20:36 Lex Fridman? Yeah.
20:37 Vladimir Vapnik? Statistical learning theory does not involve in creating admissible set of function. In classical learning theory, everywhere, hundred percent in textbook, the set of function, admissible set of function is given. But this is science about nothing, because the most difficult problem to create admissible set of functions, given say, a lot of functions, continuum set of function, create admissible set of functions, that's means that it has finite VC dimension, small VC dimension, and contain good function. So this was out of consideration.
21:20 Lex Fridman? So how, what's the process of doing that? I mean, it's fascinating. What is the process of creating this admissible set of functions?
21:28 Vladimir Vapnik? That is invariance.
21:29 Lex Fridman? That's a variance. Can you describe the variance?
21:32 Vladimir Vapnik? Yeah, you're looking of properties of training data. And properties means that you have some function. And you just count what is value, average value of function on training data. You have model and what is expectation of this function on the model. And they should coincide. So the problem is about how to pick up functions. It can be any function. In fact, it is true for all functions.
22:15 Vladimir Vapnik? But because when I'm talking set, say, duck does not jumping. So you don't ask question, jump like a duck. Because it is trivial, it does not jumping and does not help you to recognize jump. But you know something, which question to ask. And you're asking it swims like a duck, like a duck. But looks like a duck, it is general situation. Looks like, say, guy who have this illness, this disease. It is legal.
22:53 Lex Fridman? Yeah.
22:53 Vladimir Vapnik? So there is a general type of predicate looks like. And special type of predicate which related to this specific problem. And that is intelligence part of all this business. And that where teachers involved.
23:11 Lex Fridman? Incorporating the specialized predicates. Okay. What do you think about deep learning as neural networks, these arbitrary architectures, as helping accomplish some of the tasks you're thinking about? Their effectiveness or lack thereof? What are the weaknesses and what are the possible strengths?
23:35 Vladimir Vapnik? You know, I think that this is fantasy. Everything which like deep learning, like features.
23:44 Vladimir Vapnik? Let me give you this example. One of the greatest books, this Churchill book about history of Second World War. And he's starting this book describing that in old time, when war is over,
24:03 Vladimir Vapnik? so the great kings,
24:08 Vladimir Vapnik? they gathered together, almost all of them were relatives. And they discussed what should be done, have to create peace. And they came to agreement. And when happened First World War, the general public came in power. And they were so greedy that robbed Germany. And it was clear for everybody that it is not peace. That peace will last only 20 years. Because they was not professionals. And the same I see in machine learning. There are mathematicians who looking for the problem
24:50 Vladimir Vapnik? from a very deep point of view, mathematical point of view. And there are computer scientists, who is mostly does not know mathematics. They just have interpretation of that. And they invented a lot of blah blah blah interpretations, like deep learning. Why you did deep learning? Mathematic does not know deep learning. Mathematic does not know neurons. It is just function. If you like to say piecewise linear function, say that. And do in class of piecewise linear function. But they invent something. And then they try to prove advantage of that
25:33 Vladimir Vapnik? through interpretations, which mostly wrong. And when it not enough, they appeal to brain, which they know nothing about that. Nobody know what going on in the brain. So I think that more reliable look on mass. This is mathematical problem. Do your best to solve this problem. Try to understand that there is not only one way of convergence, which is strong way of convergence, there is a weak way of convergence, which requires predicate. And if you will go through all this stuff, you will see that you don't need deep learning. Even more, I would say one of the theorem, which called representative theorem.
26:18 Vladimir Vapnik? It says that optimal solution of mathematical problem, which is, which described learning is on shadow network, not on deep learning.
26:36 Lex Fridman? And a shallow network, yeah. The problem is there. Absolutely. So in the end, what you're saying is exactly right. The question is, you have no value for throwing something on the table, playing with it, not math. It's like in neural network, or you said throwing something in the bucket, and or the biological example and looking at kings and queens with the cells or the microscope. You don't see value in imagining the cells are kings and queens and using that as inspiration and imagination for where the math will eventually lead you. You think that interpretation basically deceives you in a way that's not productive?
27:21 Vladimir Vapnik? I think that if you're trying to analyze this business of learning, and especially discussion about deep learning, it is discussion about interpretation, not about things, about what you can say about things.
27:41 Lex Fridman? That's right, but aren't you surprised by the beauty of it? So the, not mathematical beauty, but the fact that it works at all. Or are you criticizing that very beauty? Our human desire to interpret, to find our silly interpretations in these constructs? Like, let me ask you this. Are you?
28:08 Lex Fridman? Surprised, and does it inspire you? How do you feel about the success of a system like AlphaGo at beating the game of Go? Using neural networks to estimate the quality of a board? And the quality of the...
28:26 Vladimir Vapnik? That is your interpretation, quality of the board.
28:29 Lex Fridman? Yeah, yes.
28:30 Vladimir Vapnik? Yeah.
28:31 Lex Fridman? But it's not our interpretation. The fact is, a neural network system doesn't matter. A learning system that we don't, I think, mathematically understand that well, beats the best human player, does something that was thought impossible.
28:46 Vladimir Vapnik? That means that it's not a very difficult problem.
28:48 Lex Fridman? That's... So you empiric... We've empirically have discovered that this is not a very difficult problem.
28:55 Vladimir Vapnik? Yeah.
28:57 Lex Fridman? It's true. So, maybe, can't argue. So...
29:05 Vladimir Vapnik? Even more, I would say, that if they use deep learning, it is not the most effective way of learning theory. And usually, when people use deep learning, they're using zillions of training data. Yeah, but you don't need this. So I describe challenge. Can we do some problems which do well? Deep learning method with deep net using hundred times less training data. Even more, some problems deep learning cannot solve
29:49 Vladimir Vapnik? because it's not necessary they create admissible set of function. To create deep architecture means to create admissible set of functions. You cannot say that you're creating good admissible set of functions. You adjust it's your fantasy. It does not come from mass. But it is possible to create admissible set of functions because you have your training data. It actually for mathematicians, when you consider a variant, you need to use law of large numbers. When you're making training in existing algorithm,
30:32 Vladimir Vapnik? you need uniform law of large numbers, which is much more difficult. It requires VC dimension and all this stuff. But nevertheless, if you use both weak and strong way of convergence, you can decrease a lot of training data.
30:49 Lex Fridman? Yeah, you could do the three. The swims like a duck and quacks like a duck.
30:54 Vladimir Vapnik? Yeah, yeah.
30:54 Lex Fridman? But our... So let's step back and think about human intelligence in general. And clearly, that has evolved in a non-mathematical way. It wasn't... As far as we know, God or whoever didn't come up with a model and place it in our brain of admissible functions. It kind of evolved. I don't know. Maybe you have a view on this. But so Alan Turing in the 50s, in his paper, asked and rejected the question, can machines think? It's not a very useful question, but can you briefly entertain this useless question?
31:39 Lex Fridman? Can machines think? So talk about intelligence and your view of it.
31:43 Vladimir Vapnik? I don't know that. I know that Turing described imitation. If computer can imitate human being, let's call it intelligent. And he understands that it is not thinking computer.
32:00 Lex Fridman? Yes.
32:01 Vladimir Vapnik? He completely understand what he doing.
32:04 Lex Fridman? Yes.
32:04 Vladimir Vapnik? But he set up problem of imitation. So now we understand that the problem not in imitation. I'm not sure that intelligence just inside of us. It may be also outside of us. I have several observations. So when I prove some theorem, it's very difficult theorem.
32:31 Vladimir Vapnik? In couple of years, in several places, people prove the same theorem. So, Sawyer lemma, after us was done, then another guys prove the same theorem. In the history of science, it's happened all the time. For example, geometry. It's happened simultaneous. First did Lobachevsky, and then Gauss, and Bojai, and another guys. And it approximately in 10 times period, 10 years period of time. And I saw a lot of examples like that. And many mathematicians thinks that when they develop something, they developing something in general which affect everybody.
33:16 Vladimir Vapnik? So maybe our model that intelligence is only inside of us is incorrect.
33:22 Lex Fridman? It's our interpretation, yeah.
33:24 Vladimir Vapnik? It may be there exist some connection with world intelligence. I don't know.
33:31 Lex Fridman? You're almost like plugging in into.
33:34 Vladimir Vapnik? Yeah, exactly.
33:36 Lex Fridman? And contributing to this.
33:37 Vladimir Vapnik? Into big network.
33:38 Lex Fridman? Into a big, maybe in your own network.
33:41 Vladimir Vapnik? No, no, no, no.
33:43 Lex Fridman? On the flip side of that, maybe you can comment on big O complexity and how you see classifying algorithms by worst case running time in relation to their input. So that way of thinking about functions. Do you think P equals NP? Do you think that's an interesting question?
34:04 Vladimir Vapnik? Yeah, it is interesting question. But let me talk about
34:10 Vladimir Vapnik? complexity in about worst case scenario.
34:16 Vladimir Vapnik? There is a mathematical setting. When I came to United States in 1995, people did not know this is theory, they did not know statistical learning theory. So in Russia it was published two monographs, all monographs, but in America they did not know. Then they learned. And somebody told me that it's worst case theory and they will create real case theory. But till now it did not. Because it is mathematical tool. You can do only what you can do using mathematics. And which has a clear understanding and clear description.
35:00 Vladimir Vapnik? And for this reason, we introduce complexity. And we need this. Because using, actually it is diversity, I like this more. If you dimension, you can prove some theorems. But we also create theory for case when you know probability measure. And that is the best case which can happen in this entropy theory. So from mathematical point of view, you know the best possible case and the worst possible case. You can derive different model in medium. But it's not so interesting.
35:45 Lex Fridman? You think the edges are interesting?
35:48 Vladimir Vapnik? The edges is interesting. Because it is not so easy to get good bound, exact bound. It's not many cases where you have the bound is not exact. But interesting principles which discover the mass.
36:09 Lex Fridman? Do you think it's interesting because it's challenging and reveals interesting principles that allow you to get those bounds? Or do you think it's interesting because it's actually very useful for understanding the essence of a function, of an algorithm? So it's like me judging your life as a human being by the worst thing you did and the best thing you did versus all the stuff in the middle. It seems not productive.
36:40 Vladimir Vapnik? I don't think so, because you cannot describe situation in the middle, or it will be not general. So you can describe edge cases, and it is clear it has some model, but you cannot describe model for every new case. So you will be never accurate when you're using model.
37:08 Lex Fridman? But from a statistical point of view, the way you've studied functions and the nature of learning in the world, don't you think that the real world has a very long tail? That the edge cases are very far away from the mean?
37:29 Lex Fridman? The stuff in the middle, or no?
37:34 Vladimir Vapnik? I don't know that. I think that...
37:40 Vladimir Vapnik? But from my point of view,
37:45 Vladimir Vapnik? if you will use formal statistic, you need uniform law of large numbers.
37:55 Vladimir Vapnik? If you will use
37:58 Vladimir Vapnik? this invariance business, you will need just law of large numbers. And there's this huge difference between uniform law of large numbers and large numbers.
38:11 Lex Fridman? Is it useful to describe that a little more? Or should we just take it to...
38:16 Vladimir Vapnik? No, for example, when I'm talking about duck, I gave three predicates, it was enough.
38:24 Vladimir Vapnik? But if you will try to do formal distinguish, you will need a lot of observations.
38:31 Lex Fridman? I got you.
38:33 Vladimir Vapnik? And so that means that information about looks like a duck contain a lot of bit of information, formal bits of information. So we don't know that, how much bit of information contain things from artificial, from intelligence. And that is the subject of analysis. Till now...
39:00 Vladimir Vapnik? All business. I don't like how people consider artificial intelligence. They consider us some codes which imitate activity of human being. It is not science. It is applications. You would like to imitate, go ahead, it is very useful and good problem. But you need to learn something more. How people try to do, how people can to develop. Say predicate swims like a dog or play like butterfly or something like that.
39:43 Vladimir Vapnik? Then not the teacher says you, how it came in his mind. How he choose this image.
39:51 Lex Fridman? So that process.
39:52 Vladimir Vapnik? That is problem of intelligence.
39:54 Lex Fridman? That is the problem of intel. And you see that connected to the problem of learning?
39:59 Vladimir Vapnik? Absolutely.
40:00 Lex Fridman? Are they?
40:01 Vladimir Vapnik? Because you immediately give this predicate, like specific predicate swims like a dog or quack like a dog. It was chosen somehow.
40:12 Lex Fridman? So what is the line of work, would you say? If you were to formulate as a set of open problems.
40:21 Lex Fridman? That will take us there, will play like a butterfly, will get a system to be able to.
40:26 Vladimir Vapnik? Let's separate two stories. One mathematical story, that if you have predicate, you can do something. And another story, you have to get predicate. It is intelligence problem. And people even did not start to understand intelligence. Because to understand intelligence, first of all, try to understand what doing teachers.
40:54 Vladimir Vapnik? Half teacher teach. Why one teacher better than another one?
40:59 Lex Fridman? Yeah, so you think we really even haven't started on the journey of generating the predicates?
41:05 Vladimir Vapnik? No, you don't understand, you even don't understand that this problem exists.
41:11 Vladimir Vapnik? Because, did you?
41:12 Lex Fridman? You do.
41:13 Vladimir Vapnik? No, I just know name. I want to understand why one teacher better than another. And half affect teacher, student. It is not because he repeating the problem which is in textbook. He make some remarks. He make some philosophy of reasoning.
41:38 Lex Fridman? Yeah, that's a beautiful, so it is a formulation of a question that is the open problem. Why is one teacher better than another?
41:48 Vladimir Vapnik? Right. What he does better?
41:52 Lex Fridman? Yeah, what, what, what, why in every level? How do they get better? What does it mean to be better?
42:03 Lex Fridman? The whole?
42:04 Vladimir Vapnik? Yeah, yeah, from whatever model I have. One teacher can give a very good predicate. One teacher can say swims like a dog. And another can say jump like a duck. And jump like a duck carries zero information.
42:22 Lex Fridman? Yeah.
42:24 Lex Fridman? So what is the most exciting problem in statistical learning you've ever worked on or are working on now?
42:32 Vladimir Vapnik? I just finished this invariant story. And I'm happy that, I believe that it is ultimate learning story. At least I can show that there are no another mechanism, only two mechanisms.
42:52 Vladimir Vapnik? But they separate statistical part from intelligent part. And I know nothing about intelligent part. And if we will know this intelligent part, so it will help us a lot in teaching, in learning.
43:14 Lex Fridman? In learning.
43:14 Vladimir Vapnik? Yeah.
43:15 Lex Fridman? Do you know we'll know it when we see it?
43:17 Vladimir Vapnik? So for example, in my talk, the last slide was the challenge. So you have, say, NIST digit recognition problem.
43:27 Vladimir Vapnik? And deep learning claims that they did it very well, say 99.5% of correct answers. But they used 60,000 observations.
43:39 Lex Fridman? Yeah.
43:40 Vladimir Vapnik? Can you do the same using 100 times less?
43:44 Vladimir Vapnik? But incorporating invariance, what it means, you know, digit 1, 2, 3.
43:49 Lex Fridman? Yeah.
43:50 Vladimir Vapnik? Just looking at that, explain me which invariant I should keep to use 100 examples or say 100 times less examples to do the same job.
44:03 Lex Fridman? Yeah, that last slide in unfortunately, your talk ended quickly, but that last slide was a powerful open challenge and a formulation of
44:15 Vladimir Vapnik? Yeah.
44:16 Lex Fridman? the essence here.
44:16 Vladimir Vapnik? That is exact problem of intelligence. Because
44:23 Vladimir Vapnik? everybody, when machine learning started and it was developed by mathematicians, they immediately recognize that we use much more training data than humans need it. But now again, we came to the same story. Have to decrease. That is the problem of learning. It is not like in deep learning, they use zillions of training data. Because maybe zillions are not enough if you have a good invariance. Maybe you will never collect some number of observations. But now it is a question to intelligence.
45:09 Vladimir Vapnik? Have to do that. Because statistical part is ready. As soon as you supply us with predicate, we can do good job with small amount of observations. And the very first challenges will know digit recognition. And you know digits? And please, tell me in variants. I thinking about that, I can say, for digit three, I would introduce concept of horizontal symmetry. So the digit three has horizontal symmetry. So you mustn't say digit two or something like that.
45:49 Vladimir Vapnik? But as soon as I get idea of horizontal symmetry, I can mathematically invent a lot of measure horizontal symmetry. Or then vertical symmetry, diagonal symmetry, whatever. If I have idea of symmetry. But what else?
46:07 Vladimir Vapnik? Looking on digit, I see that it is meta predicate, which is not shape. It is something like symmetry, like how dark is whole picture, something like that.
46:28 Vladimir Vapnik? Which can serve as a predicate.
46:31 Lex Fridman? You think such a predicate could rise
46:35 Lex Fridman? out of something that's not general? Meaning, it feels like for me to be able to understand the difference between a two and a three, I would need to have had a childhood of ten to fifteen years, playing with kids, going to school, being yelled by parents. All of that, walking, jumping, looking at ducks. And now, then I would be able to generate the right predicate for telling the difference between 2 and a 3.
47:18 Lex Fridman? Or do you think there's a more efficient way?
47:21 Vladimir Vapnik? I don't know. I know for sure that you must know something more than digits.
47:27 Lex Fridman? Yes. And that's a powerful statement.
47:29 Vladimir Vapnik? Yeah. But maybe there are several languages of description these elements of digits. So I'm talking about symmetry, about some properties of geometry. I'm talking about something abstract. I don't know that. But this is a problem of intelligence. So in one of our articles, it is trivial to show that every example can carry not more than one bit of information in real. Because when you show example and you say this is 1,
48:12 Vladimir Vapnik? you can remove, say, a function which does not tell you 1. Say, it's the best strategy. If you can do it perfectly, it's remove half of the functions. But when you use one predicate, which looks like a duck, you can remove much more functions than half. And that means that it contains a lot of bit of informations from formal point of view. But when you have a general picture of what you want to recognize, a general picture of the world, can you invent this predicate?
48:55 Vladimir Vapnik? And that predicate carries a lot of information.
49:02 Lex Fridman? Beautifully put. Maybe just me, but in all the math you show, in your work, which is some of the most profound mathematical work in the field of learning AI and just math in general. I hear a lot of poetry and philosophy. You really kind of
49:22 Lex Fridman? talk about philosophy of science. There's a poetry and music to a lot of the work you're doing and the way you're thinking about it. So do you, where does that come from? Do you escape to poetry? Do you escape to music?
49:35 Vladimir Vapnik? I think that there exists ground truths.
49:39 Lex Fridman? There exists ground truth?
49:40 Vladimir Vapnik? Yeah, and that can be seen everywhere. The smart guy philosopher, sometime I surprise how they deep see. Sometime I see that some of them are completely out of subject.
50:00 Vladimir Vapnik? But
50:02 Vladimir Vapnik? the ground truth I see in music.
50:05 Lex Fridman? Music of the ground truth?
50:06 Vladimir Vapnik? Yeah. And in poetry, many poets, they believe that they take dictation.
50:16 Lex Fridman? So what what piece of music as a piece of empirical evidence gave you a sense that they are, they're touching something in the ground truth?
50:29 Vladimir Vapnik? It is structure.
50:31 Lex Fridman? The structure of the math of music.
50:33 Vladimir Vapnik? When you're listening to Bach, you see this structure, very clear, very classic, very simple. And the same in math, when you have axioms in geometry, you have the same feeling. And in poetry sometime you see the same.
50:50 Lex Fridman? Yeah.
50:53 Lex Fridman? And if you look back at your childhood, you grew up in Russia, you maybe were born as a researcher in Russia. You've developed as a researcher in Russia, you've came to the United States in a few places. If you look back, what were, what was some of your happiest moments as a researcher? Some of the most profound moments? Not in terms of their impact on society, but in terms of their impact on how damn good you feel that day and you remember that moment.
51:30 Vladimir Vapnik? You know, every time when you found something,
51:36 Vladimir Vapnik? it is great in the life. Every simple things. But my general feeling that I mostly, most of my time was wrong. You should go again and again and again. And try to be honest in front of yourself. Not to make interpretation, but try to understand that it related to grand rules. It is not my blah blah blah interpretation and something like that.
52:07 Lex Fridman? But you're allowed to get excited at the, at the possibility of discovery.
52:12 Vladimir Vapnik? Oh, yeah.
52:12 Lex Fridman? You'll double, you have to double check it, but.
52:16 Vladimir Vapnik? No, but how it related to another grand rules? Is it just temporary or it is forever? You know, you always have a feeling when you found something, how big is that? So 20 years ago, when we discovered statistical loading theory, nobody believed, except for one guy, Dudley from MIT.
52:46 Vladimir Vapnik? And then in 20 years, it became fashion. And the same with support vector machines. That's kernel machines.
52:56 Lex Fridman? So with, with support vector machines and learning theory, with, when you were working on it, you had a sense?
53:06 Lex Fridman? That you had a sense of the, the profundity of it, the how? That this, this seems to be right, this seems to be powerful.
53:15 Vladimir Vapnik? Right, absolutely, immediately. I recognize that it will last forever.
53:23 Vladimir Vapnik? And now, when I found this.
53:29 Vladimir Vapnik? Invariance story.
53:32 Lex Fridman? You feel the same?
53:32 Vladimir Vapnik? So I have a feeling that it is complete learning. Because I have proved that there are no different mechanisms. You can have some cosmetic improvement you can do, but in terms of invariance, you need both invariance and statistical learning, and they should work together. But also, I'm happy that we can formulate what is intelligence from that. And to separate from technical part. And that is completely different.
54:12 Lex Fridman? Absolutely. Well, Vladimir, thank you so much for talking today.
54:15 Vladimir Vapnik? Thank you.
54:15 Lex Fridman? It's an honor.
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