WEBVTT 00:00.000 --> 00:03.040 The following is a conversation with Vladimir Vapnik. 00:03.040 --> 00:05.280 He's the coinventor of the Support Vector Machines, 00:05.280 --> 00:07.920 Support Vector Clustering, VC Theory, 00:07.920 --> 00:11.200 and many foundational ideas in statistical learning. 00:11.200 --> 00:13.640 He was born in the Soviet Union and worked 00:13.640 --> 00:16.320 at the Institute of Control Sciences in Moscow. 00:16.320 --> 00:20.640 Then in the United States, he worked at AT&T, NEC Labs, 00:20.640 --> 00:24.280 Facebook Research, and now as a professor at Columbia 00:24.280 --> 00:25.960 University. 00:25.960 --> 00:30.320 His work has been cited over 170,000 times. 00:30.320 --> 00:31.840 He has some very interesting ideas 00:31.840 --> 00:34.800 about artificial intelligence and the nature of learning, 00:34.800 --> 00:37.600 especially on the limits of our current approaches 00:37.600 --> 00:40.440 and the open problems in the field. 00:40.440 --> 00:42.520 This conversation is part of MIT course 00:42.520 --> 00:44.440 on artificial general intelligence 00:44.440 --> 00:46.840 and the Artificial Intelligence Podcast. 00:46.840 --> 00:49.600 If you enjoy it, please subscribe on YouTube 00:49.600 --> 00:53.040 or rate it on iTunes or your podcast provider of choice 00:53.040 --> 00:55.320 or simply connect with me on Twitter 00:55.320 --> 01:00.200 or other social networks at Lex Friedman, spelled F R I D. 01:00.200 --> 01:04.800 And now here's my conversation with Vladimir Vapnik. 01:04.800 --> 01:08.840 Einstein famously said that God doesn't play dice. 01:08.840 --> 01:10.000 Yeah. 01:10.000 --> 01:12.880 You have studied the world through the eyes of statistics. 01:12.880 --> 01:17.320 So let me ask you, in terms of the nature of reality, 01:17.320 --> 01:21.360 fundamental nature of reality, does God play dice? 01:21.360 --> 01:26.200 We don't know some factors, and because we 01:26.200 --> 01:30.520 don't know some factors, which could be important, 01:30.520 --> 01:38.000 it looks like God play dice, but we should describe it. 01:38.000 --> 01:42.080 In philosophy, they distinguish between two positions, 01:42.080 --> 01:45.480 positions of instrumentalism, where 01:45.480 --> 01:48.720 you're creating theory for prediction 01:48.720 --> 01:51.400 and position of realism, where you're 01:51.400 --> 01:54.640 trying to understand what God's big. 01:54.640 --> 01:56.800 Can you describe instrumentalism and realism 01:56.800 --> 01:58.400 a little bit? 01:58.400 --> 02:06.320 For example, if you have some mechanical laws, what is that? 02:06.320 --> 02:11.480 Is it law which is true always and everywhere? 02:11.480 --> 02:14.880 Or it is law which allows you to predict 02:14.880 --> 02:22.920 the position of moving element, what you believe. 02:22.920 --> 02:28.480 You believe that it is God's law, that God created the world, 02:28.480 --> 02:33.160 which obeyed to this physical law, 02:33.160 --> 02:36.240 or it is just law for predictions? 02:36.240 --> 02:38.400 And which one is instrumentalism? 02:38.400 --> 02:39.880 For predictions. 02:39.880 --> 02:45.400 If you believe that this is law of God, and it's always 02:45.400 --> 02:50.040 true everywhere, that means that you're a realist. 02:50.040 --> 02:55.480 So you're trying to really understand that God's thought. 02:55.480 --> 03:00.040 So the way you see the world as an instrumentalist? 03:00.040 --> 03:03.240 You know, I'm working for some models, 03:03.240 --> 03:06.960 model of machine learning. 03:06.960 --> 03:12.760 So in this model, we can see setting, 03:12.760 --> 03:16.440 and we try to solve, resolve the setting, 03:16.440 --> 03:18.240 to solve the problem. 03:18.240 --> 03:20.760 And you can do it in two different ways, 03:20.760 --> 03:23.840 from the point of view of instrumentalists. 03:23.840 --> 03:27.120 And that's what everybody does now, 03:27.120 --> 03:31.560 because they say that the goal of machine learning 03:31.560 --> 03:36.800 is to find the rule for classification. 03:36.800 --> 03:40.920 That is true, but it is an instrument for prediction. 03:40.920 --> 03:46.160 But I can say the goal of machine learning 03:46.160 --> 03:50.040 is to learn about conditional probability. 03:50.040 --> 03:54.440 So how God played use, and is He play? 03:54.440 --> 03:55.960 What is probability for one? 03:55.960 --> 03:59.960 What is probability for another given situation? 03:59.960 --> 04:02.600 But for prediction, I don't need this. 04:02.600 --> 04:04.240 I need the rule. 04:04.240 --> 04:08.480 But for understanding, I need conditional probability. 04:08.480 --> 04:11.800 So let me just step back a little bit first to talk about. 04:11.800 --> 04:13.960 You mentioned, which I read last night, 04:13.960 --> 04:21.280 the parts of the 1960 paper by Eugene Wigner, 04:21.280 --> 04:23.520 unreasonable effectiveness of mathematics 04:23.520 --> 04:24.880 and natural sciences. 04:24.880 --> 04:29.400 Such a beautiful paper, by the way. 04:29.400 --> 04:34.480 It made me feel, to be honest, to confess my own work 04:34.480 --> 04:38.400 in the past few years on deep learning, heavily applied. 04:38.400 --> 04:40.320 It made me feel that I was missing out 04:40.320 --> 04:43.960 on some of the beauty of nature in the way 04:43.960 --> 04:45.560 that math can uncover. 04:45.560 --> 04:50.360 So let me just step away from the poetry of that for a second. 04:50.360 --> 04:53.040 How do you see the role of math in your life? 04:53.040 --> 04:54.080 Is it a tool? 04:54.080 --> 04:55.840 Is it poetry? 04:55.840 --> 04:56.960 Where does it sit? 04:56.960 --> 05:01.400 And does math for you have limits of what it can describe? 05:01.400 --> 05:08.280 Some people saying that math is language which use God. 05:08.280 --> 05:10.280 So I believe in that. 05:10.280 --> 05:12.000 Speak to God or use God. 05:12.000 --> 05:12.760 Or use God. 05:12.760 --> 05:14.080 Use God. 05:14.080 --> 05:15.560 Yeah. 05:15.560 --> 05:25.680 So I believe that this article about unreasonable 05:25.680 --> 05:29.960 effectiveness of math is that if you're 05:29.960 --> 05:33.960 looking in mathematical structures, 05:33.960 --> 05:37.720 they know something about reality. 05:37.720 --> 05:42.480 And the most scientists from natural science, 05:42.480 --> 05:48.440 they're looking on equation and trying to understand reality. 05:48.440 --> 05:51.280 So the same in machine learning. 05:51.280 --> 05:57.560 If you're trying very carefully look on all equations 05:57.560 --> 06:00.640 which define conditional probability, 06:00.640 --> 06:05.680 you can understand something about reality more 06:05.680 --> 06:08.160 than from your fantasy. 06:08.160 --> 06:12.480 So math can reveal the simple underlying principles 06:12.480 --> 06:13.880 of reality, perhaps. 06:13.880 --> 06:16.880 You know, what means simple? 06:16.880 --> 06:20.320 It is very hard to discover them. 06:20.320 --> 06:23.800 But then when you discover them and look at them, 06:23.800 --> 06:27.440 you see how beautiful they are. 06:27.440 --> 06:33.560 And it is surprising why people did not see that before. 06:33.560 --> 06:37.480 You're looking on equation and derive it from equations. 06:37.480 --> 06:43.360 For example, I talked yesterday about least squirmated. 06:43.360 --> 06:48.120 And people had a lot of fantasy have to improve least squirmated. 06:48.120 --> 06:52.360 But if you're going step by step by solving some equations, 06:52.360 --> 06:57.680 you suddenly will get some term which, 06:57.680 --> 07:01.040 after thinking, you understand that it described 07:01.040 --> 07:04.360 position of observation point. 07:04.360 --> 07:08.240 In least squirmated, we throw out a lot of information. 07:08.240 --> 07:11.760 We don't look in composition of point of observations. 07:11.760 --> 07:14.600 We're looking only on residuals. 07:14.600 --> 07:19.400 But when you understood that, that's a very simple idea. 07:19.400 --> 07:22.320 But it's not too simple to understand. 07:22.320 --> 07:25.680 And you can derive this just from equations. 07:25.680 --> 07:28.120 So some simple algebra, a few steps 07:28.120 --> 07:31.040 will take you to something surprising 07:31.040 --> 07:34.360 that when you think about, you understand. 07:34.360 --> 07:41.120 And that is proof that human intuition not to reach 07:41.120 --> 07:42.640 and very primitive. 07:42.640 --> 07:48.520 And it does not see very simple situations. 07:48.520 --> 07:51.760 So let me take a step back in general. 07:51.760 --> 07:54.480 Yes, right? 07:54.480 --> 07:58.840 But what about human as opposed to intuition and ingenuity? 08:01.600 --> 08:02.960 Moments of brilliance. 08:02.960 --> 08:09.480 So do you have to be so hard on human intuition? 08:09.480 --> 08:11.840 Are there moments of brilliance in human intuition? 08:11.840 --> 08:17.520 They can leap ahead of math, and then the math will catch up? 08:17.520 --> 08:19.400 I don't think so. 08:19.400 --> 08:23.560 I think that the best human intuition, 08:23.560 --> 08:26.440 it is putting in axioms. 08:26.440 --> 08:28.600 And then it is technical. 08:28.600 --> 08:31.880 See where the axioms take you. 08:31.880 --> 08:34.920 But if they correctly take axioms, 08:34.920 --> 08:41.400 but it axiom polished during generations of scientists. 08:41.400 --> 08:45.040 And this is integral wisdom. 08:45.040 --> 08:47.480 So that's beautifully put. 08:47.480 --> 08:54.040 But if you maybe look at when you think of Einstein 08:54.040 --> 08:58.960 and special relativity, what is the role of imagination 08:58.960 --> 09:04.480 coming first there in the moment of discovery of an idea? 09:04.480 --> 09:06.440 So there is obviously a mix of math 09:06.440 --> 09:10.800 and out of the box imagination there. 09:10.800 --> 09:12.600 That I don't know. 09:12.600 --> 09:18.080 Whatever I did, I exclude any imagination. 09:18.080 --> 09:21.080 Because whatever I saw in machine learning that 09:21.080 --> 09:26.440 come from imagination, like features, like deep learning, 09:26.440 --> 09:29.320 they are not relevant to the problem. 09:29.320 --> 09:31.960 When you're looking very carefully 09:31.960 --> 09:34.280 for mathematical equations, you're 09:34.280 --> 09:38.000 deriving very simple theory, which goes far by 09:38.000 --> 09:42.040 no theory at school than whatever people can imagine. 09:42.040 --> 09:44.760 Because it is not good fantasy. 09:44.760 --> 09:46.720 It is just interpretation. 09:46.720 --> 09:48.000 It is just fantasy. 09:48.000 --> 09:51.320 But it is not what you need. 09:51.320 --> 09:56.960 You don't need any imagination to derive, say, 09:56.960 --> 10:00.040 main principle of machine learning. 10:00.040 --> 10:02.760 When you think about learning and intelligence, 10:02.760 --> 10:04.560 maybe thinking about the human brain 10:04.560 --> 10:09.200 and trying to describe mathematically the process of learning 10:09.200 --> 10:13.160 that is something like what happens in the human brain, 10:13.160 --> 10:17.200 do you think we have the tools currently? 10:17.200 --> 10:19.000 Do you think we will ever have the tools 10:19.000 --> 10:22.680 to try to describe that process of learning? 10:22.680 --> 10:25.800 It is not description of what's going on. 10:25.800 --> 10:27.360 It is interpretation. 10:27.360 --> 10:29.400 It is your interpretation. 10:29.400 --> 10:32.080 Your vision can be wrong. 10:32.080 --> 10:36.160 You know, when a guy invent microscope, 10:36.160 --> 10:40.560 Levin Cook for the first time, only he got this instrument 10:40.560 --> 10:45.440 and nobody, he kept secrets about microscope. 10:45.440 --> 10:49.080 But he wrote reports in London Academy of Science. 10:49.080 --> 10:52.040 In his report, when he looked into the blood, 10:52.040 --> 10:54.480 he looked everywhere, on the water, on the blood, 10:54.480 --> 10:56.320 on the spin. 10:56.320 --> 11:04.040 But he described blood like fight between queen and king. 11:04.040 --> 11:08.120 So he saw blood cells, red cells, 11:08.120 --> 11:12.400 and he imagines that it is army fighting each other. 11:12.400 --> 11:16.960 And it was his interpretation of situation. 11:16.960 --> 11:19.760 And he sent this report in Academy of Science. 11:19.760 --> 11:22.640 They very carefully looked because they believed 11:22.640 --> 11:25.160 that he is right, he saw something. 11:25.160 --> 11:28.240 But he gave wrong interpretation. 11:28.240 --> 11:32.280 And I believe the same can happen with brain. 11:32.280 --> 11:35.280 Because the most important part, you know, 11:35.280 --> 11:38.840 I believe in human language. 11:38.840 --> 11:43.000 In some proverb, it's so much wisdom. 11:43.000 --> 11:50.240 For example, people say that it is better than 1,000 days 11:50.240 --> 11:53.960 of diligent studies one day with great teacher. 11:53.960 --> 11:59.480 But if I will ask you what teacher does, nobody knows. 11:59.480 --> 12:01.400 And that is intelligence. 12:01.400 --> 12:07.320 And what we know from history, and now from mass 12:07.320 --> 12:12.080 and machine learning, that teacher can do a lot. 12:12.080 --> 12:14.400 So what, from a mathematical point of view, 12:14.400 --> 12:16.080 is the great teacher? 12:16.080 --> 12:17.240 I don't know. 12:17.240 --> 12:18.880 That's an awful question. 12:18.880 --> 12:25.120 Now, what we can say what teacher can do, 12:25.120 --> 12:29.440 he can introduce some invariance, some predicate 12:29.440 --> 12:32.280 for creating invariance. 12:32.280 --> 12:33.520 How he doing it? 12:33.520 --> 12:34.080 I don't know. 12:34.080 --> 12:37.560 Because teacher knows reality and can describe 12:37.560 --> 12:41.200 from this reality a predicate invariance. 12:41.200 --> 12:43.480 But he knows that when you're using invariant, 12:43.480 --> 12:47.960 he can decrease number of observations 100 times. 12:47.960 --> 12:52.960 But maybe try to pull that apart a little bit. 12:52.960 --> 12:58.120 I think you mentioned a piano teacher saying to the student, 12:58.120 --> 12:59.880 play like a butterfly. 12:59.880 --> 13:03.720 I played piano, I played guitar for a long time. 13:03.720 --> 13:09.800 Yeah, maybe it's romantic, poetic. 13:09.800 --> 13:13.160 But it feels like there's a lot of truth in that statement. 13:13.160 --> 13:15.440 There is a lot of instruction in that statement. 13:15.440 --> 13:17.320 And so can you pull that apart? 13:17.320 --> 13:19.760 What is that? 13:19.760 --> 13:22.520 The language itself may not contain this information. 13:22.520 --> 13:24.160 It's not blah, blah, blah. 13:24.160 --> 13:25.640 It does not blah, blah, blah, yeah. 13:25.640 --> 13:26.960 It affects you. 13:26.960 --> 13:27.600 It's what? 13:27.600 --> 13:28.600 It affects you. 13:28.600 --> 13:29.800 It affects your playing. 13:29.800 --> 13:30.640 Yes, it does. 13:30.640 --> 13:33.640 But it's not the language. 13:33.640 --> 13:38.000 It feels like what is the information being exchanged there? 13:38.000 --> 13:39.760 What is the nature of information? 13:39.760 --> 13:41.880 What is the representation of that information? 13:41.880 --> 13:44.000 I believe that it is sort of predicate. 13:44.000 --> 13:45.400 But I don't know. 13:45.400 --> 13:48.880 That is exactly what intelligence in machine learning 13:48.880 --> 13:50.080 should be. 13:50.080 --> 13:53.200 Because the rest is just mathematical technique. 13:53.200 --> 13:57.920 I think that what was discovered recently 13:57.920 --> 14:03.280 is that there is two mechanisms of learning. 14:03.280 --> 14:06.040 One called strong convergence mechanism 14:06.040 --> 14:08.560 and weak convergence mechanism. 14:08.560 --> 14:11.200 Before, people use only one convergence. 14:11.200 --> 14:15.840 In weak convergence mechanism, you can use predicate. 14:15.840 --> 14:19.360 That's what play like butterfly. 14:19.360 --> 14:23.640 And it will immediately affect your playing. 14:23.640 --> 14:26.360 You know, there is English proverb. 14:26.360 --> 14:27.320 Great. 14:27.320 --> 14:31.680 If it looks like a duck, swims like a duck, 14:31.680 --> 14:35.200 and quack like a duck, then it is probably duck. 14:35.200 --> 14:36.240 Yes. 14:36.240 --> 14:40.400 But this is exact about predicate. 14:40.400 --> 14:42.920 Looks like a duck, what it means. 14:42.920 --> 14:46.720 So you saw many ducks that you're training data. 14:46.720 --> 14:56.480 So you have description of how looks integral looks ducks. 14:56.480 --> 14:59.360 Yeah, the visual characteristics of a duck. 14:59.360 --> 15:00.840 Yeah, but you won't. 15:00.840 --> 15:04.200 And you have model for the cognition ducks. 15:04.200 --> 15:07.880 So you would like that theoretical description 15:07.880 --> 15:12.720 from model coincide with empirical description, which 15:12.720 --> 15:14.520 you saw on Territax there. 15:14.520 --> 15:18.440 So about looks like a duck, it is general. 15:18.440 --> 15:21.480 But what about swims like a duck? 15:21.480 --> 15:23.560 You should know that duck swims. 15:23.560 --> 15:26.960 You can say it play chess like a duck, OK? 15:26.960 --> 15:28.880 Duck doesn't play chess. 15:28.880 --> 15:35.560 And it is completely legal predicate, but it is useless. 15:35.560 --> 15:41.040 So half teacher can recognize not useless predicate. 15:41.040 --> 15:44.640 So up to now, we don't use this predicate 15:44.640 --> 15:46.680 in existing machine learning. 15:46.680 --> 15:47.200 And you think that's not so useful? 15:47.200 --> 15:50.600 So why we need billions of data? 15:50.600 --> 15:55.560 But in this English proverb, they use only three predicate. 15:55.560 --> 15:59.080 Looks like a duck, swims like a duck, and quack like a duck. 15:59.080 --> 16:02.040 So you can't deny the fact that swims like a duck 16:02.040 --> 16:08.520 and quacks like a duck has humor in it, has ambiguity. 16:08.520 --> 16:12.600 Let's talk about swim like a duck. 16:12.600 --> 16:16.520 It does not say jumps like a duck. 16:16.520 --> 16:17.680 Why? 16:17.680 --> 16:20.760 Because it's not relevant. 16:20.760 --> 16:25.880 But that means that you know ducks, you know different birds, 16:25.880 --> 16:27.600 you know animals. 16:27.600 --> 16:32.440 And you derive from this that it is relevant to say swim like a duck. 16:32.440 --> 16:36.680 So underneath, in order for us to understand swims like a duck, 16:36.680 --> 16:41.200 it feels like we need to know millions of other little pieces 16:41.200 --> 16:43.000 of information. 16:43.000 --> 16:44.280 We pick up along the way. 16:44.280 --> 16:45.120 You don't think so. 16:45.120 --> 16:48.480 There doesn't need to be this knowledge base. 16:48.480 --> 16:52.600 In those statements, carries some rich information 16:52.600 --> 16:57.280 that helps us understand the essence of duck. 16:57.280 --> 17:01.920 How far are we from integrating predicates? 17:01.920 --> 17:06.000 You know that when you consider complete theory, 17:06.000 --> 17:09.320 machine learning, so what it does, 17:09.320 --> 17:12.400 you have a lot of functions. 17:12.400 --> 17:17.480 And then you're talking, it looks like a duck. 17:17.480 --> 17:20.720 You see your training data. 17:20.720 --> 17:31.040 From training data, you recognize like expected duck should look. 17:31.040 --> 17:37.640 Then you remove all functions, which does not look like you think 17:37.640 --> 17:40.080 it should look from training data. 17:40.080 --> 17:45.800 So you decrease amount of function from which you pick up one. 17:45.800 --> 17:48.320 Then you give a second predicate. 17:48.320 --> 17:51.840 And then, again, decrease the set of function. 17:51.840 --> 17:55.800 And after that, you pick up the best function you can find. 17:55.800 --> 17:58.120 It is standard machine learning. 17:58.120 --> 18:03.280 So why you need not too many examples? 18:03.280 --> 18:06.600 Because your predicates aren't very good, or you're not. 18:06.600 --> 18:09.200 That means that predicate very good. 18:09.200 --> 18:12.520 Because every predicate is invented 18:12.520 --> 18:17.720 to decrease a divisible set of functions. 18:17.720 --> 18:20.320 So you talk about admissible set of functions, 18:20.320 --> 18:22.440 and you talk about good functions. 18:22.440 --> 18:24.280 So what makes a good function? 18:24.280 --> 18:28.600 So admissible set of function is set of function 18:28.600 --> 18:32.760 which has small capacity, or small diversity, 18:32.760 --> 18:36.960 small VC dimension example, which contain good function. 18:36.960 --> 18:38.760 So by the way, for people who don't know, 18:38.760 --> 18:42.440 VC, you're the V in the VC. 18:42.440 --> 18:50.440 So how would you describe to a lay person what VC theory is? 18:50.440 --> 18:51.440 How would you describe VC? 18:51.440 --> 18:56.480 So when you have a machine, so a machine 18:56.480 --> 19:00.240 capable to pick up one function from the admissible set 19:00.240 --> 19:02.520 of function. 19:02.520 --> 19:07.640 But set of admissibles function can be big. 19:07.640 --> 19:11.600 They contain all continuous functions and it's useless. 19:11.600 --> 19:15.280 You don't have so many examples to pick up function. 19:15.280 --> 19:17.280 But it can be small. 19:17.280 --> 19:24.560 Small, we call it capacity, but maybe better called diversity. 19:24.560 --> 19:27.160 So not very different function in the set 19:27.160 --> 19:31.280 is infinite set of function, but not very diverse. 19:31.280 --> 19:34.280 So it is small VC dimension. 19:34.280 --> 19:39.360 When VC dimension is small, you need small amount 19:39.360 --> 19:41.760 of training data. 19:41.760 --> 19:47.360 So the goal is to create admissible set of functions 19:47.360 --> 19:53.200 which have small VC dimension and contain good function. 19:53.200 --> 19:58.160 Then you will be able to pick up the function 19:58.160 --> 20:02.400 using small amount of observations. 20:02.400 --> 20:06.760 So that is the task of learning. 20:06.760 --> 20:11.360 It is creating a set of admissible functions 20:11.360 --> 20:13.120 that has a small VC dimension. 20:13.120 --> 20:17.320 And then you've figured out a clever way of picking up. 20:17.320 --> 20:22.440 No, that is goal of learning, which I formulated yesterday. 20:22.440 --> 20:25.760 Statistical learning theory does not 20:25.760 --> 20:30.360 involve in creating admissible set of function. 20:30.360 --> 20:35.520 In classical learning theory, everywhere, 100% in textbook, 20:35.520 --> 20:39.200 the set of function admissible set of function is given. 20:39.200 --> 20:41.760 But this is science about nothing, 20:41.760 --> 20:44.040 because the most difficult problem 20:44.040 --> 20:50.120 to create admissible set of functions, given, say, 20:50.120 --> 20:53.080 a lot of functions, continuum set of functions, 20:53.080 --> 20:54.960 create admissible set of functions, 20:54.960 --> 20:58.760 that means that it has finite VC dimension, 20:58.760 --> 21:02.280 small VC dimension, and contain good function. 21:02.280 --> 21:05.280 So this was out of consideration. 21:05.280 --> 21:07.240 So what's the process of doing that? 21:07.240 --> 21:08.240 I mean, it's fascinating. 21:08.240 --> 21:13.200 What is the process of creating this admissible set of functions? 21:13.200 --> 21:14.920 That is invariant. 21:14.920 --> 21:15.760 That's invariance. 21:15.760 --> 21:17.280 Can you describe invariance? 21:17.280 --> 21:22.440 Yeah, you're looking of properties of training data. 21:22.440 --> 21:30.120 And properties means that you have some function, 21:30.120 --> 21:36.520 and you just count what is the average value of function 21:36.520 --> 21:38.960 on training data. 21:38.960 --> 21:43.040 You have a model, and what is the expectation 21:43.040 --> 21:44.960 of this function on the model. 21:44.960 --> 21:46.720 And they should coincide. 21:46.720 --> 21:51.800 So the problem is about how to pick up functions. 21:51.800 --> 21:53.200 It can be any function. 21:53.200 --> 21:59.280 In fact, it is true for all functions. 21:59.280 --> 22:05.000 But because when I talking set, say, 22:05.000 --> 22:09.920 duck does not jumping, so you don't ask question, jump like a duck. 22:09.920 --> 22:13.360 Because it is trivial, it does not jumping, 22:13.360 --> 22:15.560 it doesn't help you to recognize jump. 22:15.560 --> 22:19.000 But you know something, which question to ask, 22:19.000 --> 22:23.840 when you're asking, it swims like a jump, like a duck. 22:23.840 --> 22:26.840 But looks like a duck, it is general situation. 22:26.840 --> 22:34.440 Looks like, say, guy who have this illness, this disease, 22:34.440 --> 22:42.280 it is legal, so there is a general type of predicate 22:42.280 --> 22:46.440 looks like, and special type of predicate, 22:46.440 --> 22:50.040 which related to this specific problem. 22:50.040 --> 22:53.440 And that is intelligence part of all this business. 22:53.440 --> 22:55.440 And that we are teachers in world. 22:55.440 --> 22:58.440 Incorporating those specialized predicates. 22:58.440 --> 23:04.840 What do you think about deep learning as neural networks, 23:04.840 --> 23:11.440 these arbitrary architectures as helping accomplish some of the tasks 23:11.440 --> 23:14.440 you're thinking about, their effectiveness or lack thereof, 23:14.440 --> 23:19.440 what are the weaknesses and what are the possible strengths? 23:19.440 --> 23:22.440 You know, I think that this is fantasy. 23:22.440 --> 23:28.440 Everything which like deep learning, like features. 23:28.440 --> 23:32.440 Let me give you this example. 23:32.440 --> 23:38.440 One of the greatest book, this Churchill book about history of Second World War. 23:38.440 --> 23:47.440 And he's starting this book describing that in all time, when war is over, 23:47.440 --> 23:54.440 so the great kings, they gathered together, 23:54.440 --> 23:57.440 almost all of them were relatives, 23:57.440 --> 24:02.440 and they discussed what should be done, how to create peace. 24:02.440 --> 24:04.440 And they came to agreement. 24:04.440 --> 24:13.440 And when happens First World War, the general public came in power. 24:13.440 --> 24:17.440 And they were so greedy that robbed Germany. 24:17.440 --> 24:21.440 And it was clear for everybody that it is not peace. 24:21.440 --> 24:28.440 That peace will last only 20 years, because they were not professionals. 24:28.440 --> 24:31.440 It's the same I see in machine learning. 24:31.440 --> 24:37.440 There are mathematicians who are looking for the problem from a very deep point of view, 24:37.440 --> 24:39.440 a mathematical point of view. 24:39.440 --> 24:45.440 And there are computer scientists who mostly does not know mathematics. 24:45.440 --> 24:48.440 They just have interpretation of that. 24:48.440 --> 24:53.440 And they invented a lot of blah, blah, blah interpretations like deep learning. 24:53.440 --> 24:55.440 Why you need deep learning? 24:55.440 --> 24:57.440 Mathematics does not know deep learning. 24:57.440 --> 25:00.440 Mathematics does not know neurons. 25:00.440 --> 25:02.440 It is just function. 25:02.440 --> 25:06.440 If you like to say piecewise linear function, say that, 25:06.440 --> 25:10.440 and do it in class of piecewise linear function. 25:10.440 --> 25:12.440 But they invent something. 25:12.440 --> 25:20.440 And then they try to prove the advantage of that through interpretations, 25:20.440 --> 25:22.440 which mostly wrong. 25:22.440 --> 25:25.440 And when not enough they appeal to brain, 25:25.440 --> 25:27.440 which they know nothing about that. 25:27.440 --> 25:29.440 Nobody knows what's going on in the brain. 25:29.440 --> 25:34.440 So I think that more reliable look on maths. 25:34.440 --> 25:36.440 This is a mathematical problem. 25:36.440 --> 25:38.440 Do your best to solve this problem. 25:38.440 --> 25:43.440 Try to understand that there is not only one way of convergence, 25:43.440 --> 25:45.440 which is strong way of convergence. 25:45.440 --> 25:49.440 There is a weak way of convergence, which requires predicate. 25:49.440 --> 25:52.440 And if you will go through all this stuff, 25:52.440 --> 25:55.440 you will see that you don't need deep learning. 25:55.440 --> 26:00.440 Even more, I would say one of the theorem, 26:00.440 --> 26:02.440 which is called representor theorem. 26:02.440 --> 26:10.440 It says that optimal solution of mathematical problem, 26:10.440 --> 26:20.440 which described learning, is on shadow network, not on deep learning. 26:20.440 --> 26:22.440 And a shallow network, yeah. 26:22.440 --> 26:24.440 The ultimate problem is there. 26:24.440 --> 26:25.440 Absolutely. 26:25.440 --> 26:29.440 So in the end, what you're saying is exactly right. 26:29.440 --> 26:35.440 The question is, you have no value for throwing something on the table, 26:35.440 --> 26:38.440 playing with it, not math. 26:38.440 --> 26:41.440 It's like in your old network where you said throwing something in the bucket 26:41.440 --> 26:45.440 or the biological example and looking at kings and queens 26:45.440 --> 26:47.440 or the cells or the microscope. 26:47.440 --> 26:52.440 You don't see value in imagining the cells or kings and queens 26:52.440 --> 26:56.440 and using that as inspiration and imagination 26:56.440 --> 26:59.440 for where the math will eventually lead you. 26:59.440 --> 27:06.440 You think that interpretation basically deceives you in a way that's not productive. 27:06.440 --> 27:14.440 I think that if you're trying to analyze this business of learning 27:14.440 --> 27:18.440 and especially discussion about deep learning, 27:18.440 --> 27:21.440 it is discussion about interpretation. 27:21.440 --> 27:26.440 It's discussion about things, about what you can say about things. 27:26.440 --> 27:29.440 That's right, but aren't you surprised by the beauty of it? 27:29.440 --> 27:36.440 Not mathematical beauty, but the fact that it works at all. 27:36.440 --> 27:39.440 Or are you criticizing that very beauty, 27:39.440 --> 27:45.440 our human desire to interpret, 27:45.440 --> 27:49.440 to find our silly interpretations in these constructs? 27:49.440 --> 27:51.440 Let me ask you this. 27:51.440 --> 27:55.440 Are you surprised? 27:55.440 --> 27:57.440 Does it inspire you? 27:57.440 --> 28:00.440 How do you feel about the success of a system like AlphaGo 28:00.440 --> 28:03.440 at beating the game of Go? 28:03.440 --> 28:09.440 Using neural networks to estimate the quality of a board 28:09.440 --> 28:11.440 and the quality of the board? 28:11.440 --> 28:14.440 That is your interpretation quality of the board. 28:14.440 --> 28:17.440 Yes. 28:17.440 --> 28:20.440 It's not our interpretation. 28:20.440 --> 28:23.440 The fact is, a neural network system doesn't matter. 28:23.440 --> 28:27.440 A learning system that we don't mathematically understand 28:27.440 --> 28:29.440 that beats the best human player. 28:29.440 --> 28:31.440 It does something that was thought impossible. 28:31.440 --> 28:35.440 That means that it's not very difficult problem. 28:35.440 --> 28:41.440 We've empirically discovered that this is not a very difficult problem. 28:41.440 --> 28:43.440 That's true. 28:43.440 --> 28:49.440 Maybe I can't argue. 28:49.440 --> 28:52.440 Even more, I would say, 28:52.440 --> 28:54.440 that if they use deep learning, 28:54.440 --> 28:59.440 it is not the most effective way of learning theory. 28:59.440 --> 29:03.440 Usually, when people use deep learning, 29:03.440 --> 29:09.440 they're using zillions of training data. 29:09.440 --> 29:13.440 But you don't need this. 29:13.440 --> 29:15.440 I describe the challenge. 29:15.440 --> 29:22.440 Can we do some problems with deep learning method 29:22.440 --> 29:27.440 with deep net using 100 times less training data? 29:27.440 --> 29:33.440 Even more, some problems deep learning cannot solve 29:33.440 --> 29:37.440 because it's not necessary. 29:37.440 --> 29:40.440 They create admissible set of functions. 29:40.440 --> 29:45.440 Deep architecture means to create admissible set of functions. 29:45.440 --> 29:49.440 You cannot say that you're creating good admissible set of functions. 29:49.440 --> 29:52.440 It's your fantasy. 29:52.440 --> 29:54.440 It does not come from mass. 29:54.440 --> 29:58.440 But it is possible to create admissible set of functions 29:58.440 --> 30:01.440 because you have your training data. 30:01.440 --> 30:08.440 Actually, for mathematicians, when you consider a variant, 30:08.440 --> 30:11.440 you need to use law of large numbers. 30:11.440 --> 30:17.440 When you're making training in existing algorithm, 30:17.440 --> 30:20.440 you need uniform law of large numbers, 30:20.440 --> 30:22.440 which is much more difficult. 30:22.440 --> 30:24.440 You see dimension and all this stuff. 30:24.440 --> 30:32.440 Nevertheless, if you use both weak and strong way of convergence, 30:32.440 --> 30:34.440 you can decrease a lot of training data. 30:34.440 --> 30:39.440 You could do the three, the Swims like a duck and Quacks like a duck. 30:39.440 --> 30:47.440 Let's step back and think about human intelligence in general. 30:47.440 --> 30:52.440 Clearly, that has evolved in a nonmathematical way. 30:52.440 --> 31:00.440 As far as we know, God, or whoever, 31:00.440 --> 31:05.440 didn't come up with a model in place in our brain of admissible functions. 31:05.440 --> 31:06.440 It kind of evolved. 31:06.440 --> 31:07.440 I don't know. 31:07.440 --> 31:08.440 Maybe you have a view on this. 31:08.440 --> 31:15.440 Alan Turing in the 50s in his paper asked and rejected the question, 31:15.440 --> 31:16.440 can machines think? 31:16.440 --> 31:18.440 It's not a very useful question. 31:18.440 --> 31:23.440 But can you briefly entertain this useless question? 31:23.440 --> 31:25.440 Can machines think? 31:25.440 --> 31:28.440 So talk about intelligence and your view of it. 31:28.440 --> 31:29.440 I don't know that. 31:29.440 --> 31:34.440 I know that Turing described imitation. 31:34.440 --> 31:41.440 If computer can imitate human being, let's call it intelligent. 31:41.440 --> 31:45.440 And he understands that it is not thinking computer. 31:45.440 --> 31:46.440 Yes. 31:46.440 --> 31:49.440 He completely understands what he's doing. 31:49.440 --> 31:53.440 But he's set up a problem of imitation. 31:53.440 --> 31:57.440 So now we understand that the problem is not in imitation. 31:57.440 --> 32:04.440 I'm not sure that intelligence is just inside of us. 32:04.440 --> 32:06.440 It may be also outside of us. 32:06.440 --> 32:09.440 I have several observations. 32:09.440 --> 32:15.440 So when I prove some theorem, it's a very difficult theorem. 32:15.440 --> 32:22.440 But in a couple of years, in several places, people proved the same theorem. 32:22.440 --> 32:26.440 Say, soil lemma after us was done. 32:26.440 --> 32:29.440 Then another guy proved the same theorem. 32:29.440 --> 32:32.440 In the history of science, it's happened all the time. 32:32.440 --> 32:35.440 For example, geometry. 32:35.440 --> 32:37.440 It's happened simultaneously. 32:37.440 --> 32:43.440 First it did Lobachevsky and then Gauss and Boyai and other guys. 32:43.440 --> 32:48.440 It happened simultaneously in 10 years period of time. 32:48.440 --> 32:51.440 And I saw a lot of examples like that. 32:51.440 --> 32:56.440 And many mathematicians think that when they develop something, 32:56.440 --> 33:01.440 they develop something in general which affects everybody. 33:01.440 --> 33:07.440 So maybe our model that intelligence is only inside of us is incorrect. 33:07.440 --> 33:09.440 It's our interpretation. 33:09.440 --> 33:15.440 Maybe there exists some connection with world intelligence. 33:15.440 --> 33:16.440 I don't know. 33:16.440 --> 33:19.440 You're almost like plugging in into... 33:19.440 --> 33:20.440 Yeah, exactly. 33:20.440 --> 33:22.440 ...and contributing to this... 33:22.440 --> 33:23.440 Into a big network. 33:23.440 --> 33:26.440 ...into a big, maybe in your own network. 33:26.440 --> 33:27.440 No, no, no. 33:27.440 --> 33:34.440 On the flip side of that, maybe you can comment on big O complexity 33:34.440 --> 33:40.440 and how you see classifying algorithms by worst case running time 33:40.440 --> 33:42.440 in relation to their input. 33:42.440 --> 33:45.440 So that way of thinking about functions. 33:45.440 --> 33:47.440 Do you think P equals NP? 33:47.440 --> 33:49.440 Do you think that's an interesting question? 33:49.440 --> 33:51.440 Yeah, it is an interesting question. 33:51.440 --> 34:01.440 But let me talk about complexity and about worst case scenario. 34:01.440 --> 34:03.440 There is a mathematical setting. 34:03.440 --> 34:07.440 When I came to the United States in 1990, 34:07.440 --> 34:09.440 people did not know this theory. 34:09.440 --> 34:12.440 They did not know statistical learning theory. 34:12.440 --> 34:17.440 So in Russia it was published to monographs or monographs, 34:17.440 --> 34:19.440 but in America they didn't know. 34:19.440 --> 34:22.440 Then they learned. 34:22.440 --> 34:25.440 And somebody told me that if it's worst case theory, 34:25.440 --> 34:27.440 and they will create real case theory, 34:27.440 --> 34:30.440 but till now it did not. 34:30.440 --> 34:33.440 Because it is a mathematical tool. 34:33.440 --> 34:38.440 You can do only what you can do using mathematics, 34:38.440 --> 34:45.440 which has a clear understanding and clear description. 34:45.440 --> 34:52.440 And for this reason we introduced complexity. 34:52.440 --> 34:54.440 And we need this. 34:54.440 --> 35:01.440 Because actually it is diverse, I like this one more. 35:01.440 --> 35:04.440 This dimension you can prove some theorems. 35:04.440 --> 35:12.440 But we also create theory for case when you know probability measure. 35:12.440 --> 35:14.440 And that is the best case which can happen. 35:14.440 --> 35:17.440 It is entropy theory. 35:17.440 --> 35:20.440 So from a mathematical point of view, 35:20.440 --> 35:25.440 you know the best possible case and the worst possible case. 35:25.440 --> 35:28.440 You can derive different model in medium. 35:28.440 --> 35:30.440 But it's not so interesting. 35:30.440 --> 35:33.440 You think the edges are interesting? 35:33.440 --> 35:35.440 The edges are interesting. 35:35.440 --> 35:44.440 Because it is not so easy to get a good bound, exact bound. 35:44.440 --> 35:47.440 It's not many cases where you have. 35:47.440 --> 35:49.440 The bound is not exact. 35:49.440 --> 35:54.440 But interesting principles which discover the mass. 35:54.440 --> 35:57.440 Do you think it's interesting because it's challenging 35:57.440 --> 36:02.440 and reveals interesting principles that allow you to get those bounds? 36:02.440 --> 36:05.440 Or do you think it's interesting because it's actually very useful 36:05.440 --> 36:10.440 for understanding the essence of a function of an algorithm? 36:10.440 --> 36:15.440 So it's like me judging your life as a human being 36:15.440 --> 36:19.440 by the worst thing you did and the best thing you did 36:19.440 --> 36:21.440 versus all the stuff in the middle. 36:21.440 --> 36:25.440 It seems not productive. 36:25.440 --> 36:31.440 I don't think so because you cannot describe situation in the middle. 36:31.440 --> 36:34.440 Or it will be not general. 36:34.440 --> 36:38.440 So you can describe edges cases. 36:38.440 --> 36:41.440 And it is clear it has some model. 36:41.440 --> 36:47.440 But you cannot describe model for every new case. 36:47.440 --> 36:53.440 So you will be never accurate when you're using model. 36:53.440 --> 36:55.440 But from a statistical point of view, 36:55.440 --> 37:00.440 the way you've studied functions and the nature of learning 37:00.440 --> 37:07.440 and the world, don't you think that the real world has a very long tail 37:07.440 --> 37:13.440 that the edge cases are very far away from the mean, 37:13.440 --> 37:19.440 the stuff in the middle, or no? 37:19.440 --> 37:21.440 I don't know that. 37:21.440 --> 37:29.440 I think that from my point of view, 37:29.440 --> 37:39.440 if you will use formal statistic, uniform law of large numbers, 37:39.440 --> 37:47.440 if you will use this invariance business, 37:47.440 --> 37:51.440 you will need just law of large numbers. 37:51.440 --> 37:55.440 And there's a huge difference between uniform law of large numbers 37:55.440 --> 37:57.440 and large numbers. 37:57.440 --> 37:59.440 Can you describe that a little more? 37:59.440 --> 38:01.440 Or should we just take it to... 38:01.440 --> 38:05.440 No, for example, when I'm talking about duck, 38:05.440 --> 38:09.440 I gave three predicates and it was enough. 38:09.440 --> 38:14.440 But if you will try to do formal distinguish, 38:14.440 --> 38:17.440 you will need a lot of observations. 38:17.440 --> 38:19.440 I got you. 38:19.440 --> 38:24.440 And so that means that information about looks like a duck 38:24.440 --> 38:27.440 contain a lot of bits of information, 38:27.440 --> 38:29.440 formal bits of information. 38:29.440 --> 38:35.440 So we don't know that how much bit of information 38:35.440 --> 38:39.440 contain things from artificial intelligence. 38:39.440 --> 38:42.440 And that is the subject of analysis. 38:42.440 --> 38:47.440 Till now, old business, 38:47.440 --> 38:54.440 I don't like how people consider artificial intelligence. 38:54.440 --> 39:00.440 They consider us some codes which imitate activity of human being. 39:00.440 --> 39:02.440 It is not science. 39:02.440 --> 39:04.440 It is applications. 39:04.440 --> 39:06.440 You would like to imitate God. 39:06.440 --> 39:09.440 It is very useful and we have good problem. 39:09.440 --> 39:15.440 But you need to learn something more. 39:15.440 --> 39:23.440 How people can to develop predicates, 39:23.440 --> 39:25.440 swims like a duck, 39:25.440 --> 39:28.440 or play like butterfly or something like that. 39:28.440 --> 39:33.440 Not the teacher tells you how it came in his mind. 39:33.440 --> 39:36.440 How he choose this image. 39:36.440 --> 39:39.440 That is problem of intelligence. 39:39.440 --> 39:41.440 That is the problem of intelligence. 39:41.440 --> 39:44.440 And you see that connected to the problem of learning? 39:44.440 --> 39:45.440 Absolutely. 39:45.440 --> 39:48.440 Because you immediately give this predicate 39:48.440 --> 39:52.440 like specific predicate, swims like a duck, 39:52.440 --> 39:54.440 or quack like a duck. 39:54.440 --> 39:57.440 It was chosen somehow. 39:57.440 --> 40:00.440 So what is the line of work, would you say? 40:00.440 --> 40:05.440 If you were to formulate as a set of open problems, 40:05.440 --> 40:07.440 that will take us there. 40:07.440 --> 40:09.440 Play like a butterfly. 40:09.440 --> 40:11.440 We will get a system to be able to... 40:11.440 --> 40:13.440 Let's separate two stories. 40:13.440 --> 40:15.440 One mathematical story. 40:15.440 --> 40:19.440 That if you have predicate, you can do something. 40:19.440 --> 40:22.440 And another story you have to get predicate. 40:22.440 --> 40:26.440 It is intelligence problem. 40:26.440 --> 40:31.440 And people even did not start understanding intelligence. 40:31.440 --> 40:34.440 Because to understand intelligence, first of all, 40:34.440 --> 40:37.440 try to understand what doing teachers. 40:37.440 --> 40:40.440 How teacher teach. 40:40.440 --> 40:43.440 Why one teacher better than another one? 40:43.440 --> 40:44.440 Yeah. 40:44.440 --> 40:48.440 So you think we really even haven't started on the journey 40:48.440 --> 40:50.440 of generating the predicate? 40:50.440 --> 40:51.440 No. 40:51.440 --> 40:52.440 We don't understand. 40:52.440 --> 40:56.440 We even don't understand that this problem exists. 40:56.440 --> 40:58.440 Because did you hear? 40:58.440 --> 40:59.440 You do. 40:59.440 --> 41:02.440 No, I just know name. 41:02.440 --> 41:07.440 I want to understand why one teacher better than another. 41:07.440 --> 41:12.440 And how affect teacher student. 41:12.440 --> 41:17.440 It is not because he repeating the problem which is in textbook. 41:17.440 --> 41:18.440 Yes. 41:18.440 --> 41:20.440 He make some remarks. 41:20.440 --> 41:23.440 He make some philosophy of reasoning. 41:23.440 --> 41:24.440 Yeah, that's a beautiful... 41:24.440 --> 41:31.440 So it is a formulation of a question that is the open problem. 41:31.440 --> 41:33.440 Why is one teacher better than another? 41:33.440 --> 41:34.440 Right. 41:34.440 --> 41:37.440 What he does better. 41:37.440 --> 41:38.440 Yeah. 41:38.440 --> 41:39.440 What... 41:39.440 --> 41:42.440 Why at every level? 41:42.440 --> 41:44.440 How do they get better? 41:44.440 --> 41:47.440 What does it mean to be better? 41:47.440 --> 41:49.440 The whole... 41:49.440 --> 41:50.440 Yeah. 41:50.440 --> 41:53.440 From whatever model I have. 41:53.440 --> 41:56.440 One teacher can give a very good predicate. 41:56.440 --> 42:00.440 One teacher can say swims like a dog. 42:00.440 --> 42:03.440 And another can say jump like a dog. 42:03.440 --> 42:05.440 And jump like a dog. 42:05.440 --> 42:07.440 Car is zero information. 42:07.440 --> 42:08.440 Yeah. 42:08.440 --> 42:13.440 So what is the most exciting problem in statistical learning you've ever worked on? 42:13.440 --> 42:16.440 Or are working on now? 42:16.440 --> 42:22.440 I just finished this invariant story. 42:22.440 --> 42:24.440 And I'm happy that... 42:24.440 --> 42:30.440 I believe that it is ultimate learning story. 42:30.440 --> 42:37.440 At least I can show that there are no another mechanism, only two mechanisms. 42:37.440 --> 42:44.440 But they separate statistical part from intelligent part. 42:44.440 --> 42:48.440 And I know nothing about intelligent part. 42:48.440 --> 42:52.440 And if we will know this intelligent part, 42:52.440 --> 42:59.440 so it will help us a lot in teaching, in learning. 42:59.440 --> 43:02.440 You don't know it when we see it? 43:02.440 --> 43:06.440 So for example, in my talk, the last slide was the challenge. 43:06.440 --> 43:11.440 So you have, say, NIST digital recognition problem. 43:11.440 --> 43:16.440 And deep learning claims that they did it very well. 43:16.440 --> 43:21.440 Say 99.5% of correct answers. 43:21.440 --> 43:24.440 But they use 60,000 observations. 43:24.440 --> 43:26.440 Can you do the same? 43:26.440 --> 43:29.440 100 times less. 43:29.440 --> 43:31.440 But incorporating invariants. 43:31.440 --> 43:34.440 What it means, you know, digit one, two, three. 43:34.440 --> 43:35.440 Yeah. 43:35.440 --> 43:37.440 Just looking at that. 43:37.440 --> 43:40.440 Explain to me which invariant I should keep. 43:40.440 --> 43:43.440 To use 100 examples. 43:43.440 --> 43:48.440 Or say 100 times less examples to do the same job. 43:48.440 --> 43:49.440 Yeah. 43:49.440 --> 43:55.440 That last slide, unfortunately, you talk ended quickly. 43:55.440 --> 43:59.440 The last slide was a powerful open challenge 43:59.440 --> 44:02.440 and a formulation of the essence here. 44:02.440 --> 44:06.440 That is the exact problem of intelligence. 44:06.440 --> 44:12.440 Because everybody, when machine learning started, 44:12.440 --> 44:15.440 it was developed by mathematicians, 44:15.440 --> 44:19.440 they immediately recognized that we use much more 44:19.440 --> 44:22.440 training data than humans needed. 44:22.440 --> 44:25.440 But now again, we came to the same story. 44:25.440 --> 44:27.440 Have to decrease. 44:27.440 --> 44:30.440 That is the problem of learning. 44:30.440 --> 44:32.440 It is not like in deep learning, 44:32.440 --> 44:35.440 they use zealons of training data. 44:35.440 --> 44:38.440 Because maybe zealons are not enough 44:38.440 --> 44:44.440 if you have a good invariance. 44:44.440 --> 44:49.440 Maybe you'll never collect some number of observations. 44:49.440 --> 44:53.440 But now it is a question to intelligence. 44:53.440 --> 44:55.440 Have to do that. 44:55.440 --> 44:58.440 Because statistical part is ready. 44:58.440 --> 45:02.440 As soon as you supply us with predicate, 45:02.440 --> 45:06.440 we can do good job with small amount of observations. 45:06.440 --> 45:10.440 And the very first challenges will know digit recognition. 45:10.440 --> 45:12.440 And you know digits. 45:12.440 --> 45:15.440 And please tell me invariance. 45:15.440 --> 45:16.440 I think about that. 45:16.440 --> 45:20.440 I can say for digit 3, I would introduce 45:20.440 --> 45:24.440 concept of horizontal symmetry. 45:24.440 --> 45:29.440 So the digit 3 has horizontal symmetry 45:29.440 --> 45:33.440 more than say digit 2 or something like that. 45:33.440 --> 45:37.440 But as soon as I get the idea of horizontal symmetry, 45:37.440 --> 45:40.440 I can mathematically invent a lot of 45:40.440 --> 45:43.440 measure of horizontal symmetry 45:43.440 --> 45:46.440 on vertical symmetry or diagonal symmetry, 45:46.440 --> 45:49.440 whatever, if I have a day of symmetry. 45:49.440 --> 45:52.440 But what else? 45:52.440 --> 46:00.440 Looking on digit, I see that it is metapredicate, 46:00.440 --> 46:04.440 which is not shape. 46:04.440 --> 46:07.440 It is something like symmetry, 46:07.440 --> 46:12.440 like how dark is whole picture, something like that. 46:12.440 --> 46:15.440 Which can self rise up predicate. 46:15.440 --> 46:18.440 You think such a predicate could rise 46:18.440 --> 46:26.440 out of something that is not general. 46:26.440 --> 46:31.440 Meaning it feels like for me to be able to 46:31.440 --> 46:34.440 understand the difference between a 2 and a 3, 46:34.440 --> 46:39.440 I would need to have had a childhood 46:39.440 --> 46:45.440 of 10 to 15 years playing with kids, 46:45.440 --> 46:50.440 going to school, being yelled by parents. 46:50.440 --> 46:55.440 All of that, walking, jumping, looking at ducks. 46:55.440 --> 46:58.440 And now then I would be able to generate 46:58.440 --> 47:01.440 the right predicate for telling the difference 47:01.440 --> 47:03.440 between 2 and a 3. 47:03.440 --> 47:06.440 Or do you think there is a more efficient way? 47:06.440 --> 47:10.440 I know for sure that you must know 47:10.440 --> 47:12.440 something more than digits. 47:12.440 --> 47:15.440 That's a powerful statement. 47:15.440 --> 47:19.440 But maybe there are several languages 47:19.440 --> 47:24.440 of description, these elements of digits. 47:24.440 --> 47:27.440 So I'm talking about symmetry, 47:27.440 --> 47:30.440 about some properties of geometry, 47:30.440 --> 47:33.440 I'm talking about something abstract. 47:33.440 --> 47:38.440 But this is a problem of intelligence. 47:38.440 --> 47:42.440 So in one of our articles, it is trivial to show 47:42.440 --> 47:46.440 that every example can carry 47:46.440 --> 47:49.440 not more than one bit of information in real. 47:49.440 --> 47:54.440 Because when you show example 47:54.440 --> 47:59.440 and you say this is one, you can remove, say, 47:59.440 --> 48:03.440 a function which does not tell you one, say, 48:03.440 --> 48:06.440 the best strategy, if you can do it perfectly, 48:06.440 --> 48:09.440 it's remove half of the functions. 48:09.440 --> 48:14.440 But when you use one predicate, which looks like a duck, 48:14.440 --> 48:18.440 you can remove much more functions than half. 48:18.440 --> 48:20.440 And that means that it contains 48:20.440 --> 48:25.440 a lot of bit of information from a formal point of view. 48:25.440 --> 48:31.440 But when you have a general picture 48:31.440 --> 48:33.440 of what you want to recognize, 48:33.440 --> 48:36.440 a general picture of the world, 48:36.440 --> 48:40.440 can you invent this predicate? 48:40.440 --> 48:46.440 And that predicate carries a lot of information. 48:46.440 --> 48:49.440 Beautifully put, maybe just me, 48:49.440 --> 48:53.440 but in all the math you show, in your work, 48:53.440 --> 48:57.440 which is some of the most profound mathematical work 48:57.440 --> 49:01.440 in the field of learning AI and just math in general. 49:01.440 --> 49:04.440 I hear a lot of poetry and philosophy. 49:04.440 --> 49:09.440 You really kind of talk about philosophy of science. 49:09.440 --> 49:12.440 There's a poetry and music to a lot of the work you're doing 49:12.440 --> 49:14.440 and the way you're thinking about it. 49:14.440 --> 49:16.440 So where does that come from? 49:16.440 --> 49:20.440 Do you escape to poetry? Do you escape to music? 49:20.440 --> 49:24.440 I think that there exists ground truth. 49:24.440 --> 49:26.440 There exists ground truth? 49:26.440 --> 49:30.440 Yeah, and that can be seen everywhere. 49:30.440 --> 49:32.440 The smart guy, philosopher, 49:32.440 --> 49:38.440 sometimes I surprise how they deep see. 49:38.440 --> 49:45.440 Sometimes I see that some of them are completely out of subject. 49:45.440 --> 49:50.440 But the ground truth I see in music. 49:50.440 --> 49:52.440 Music is the ground truth? 49:52.440 --> 49:53.440 Yeah. 49:53.440 --> 50:01.440 And in poetry, many poets, they believe they take dictation. 50:01.440 --> 50:06.440 So what piece of music, 50:06.440 --> 50:08.440 as a piece of empirical evidence, 50:08.440 --> 50:14.440 gave you a sense that they are touching something in the ground truth? 50:14.440 --> 50:16.440 It is structure. 50:16.440 --> 50:18.440 The structure with the math of music. 50:18.440 --> 50:20.440 Because when you're listening to Bach, 50:20.440 --> 50:22.440 you see this structure. 50:22.440 --> 50:25.440 Very clear, very classic, very simple. 50:25.440 --> 50:31.440 And the same in Bach, when you have axioms in geometry, 50:31.440 --> 50:33.440 you have the same feeling. 50:33.440 --> 50:36.440 And in poetry, sometimes you see the same. 50:36.440 --> 50:40.440 And if you look back at your childhood, 50:40.440 --> 50:42.440 you grew up in Russia, 50:42.440 --> 50:46.440 you maybe were born as a researcher in Russia, 50:46.440 --> 50:48.440 you developed as a researcher in Russia, 50:48.440 --> 50:51.440 you came to the United States in a few places. 50:51.440 --> 50:53.440 If you look back, 50:53.440 --> 50:59.440 what were some of your happiest moments as a researcher? 50:59.440 --> 51:02.440 Some of the most profound moments. 51:02.440 --> 51:06.440 Not in terms of their impact on society, 51:06.440 --> 51:12.440 but in terms of their impact on how damn good you feel that day, 51:12.440 --> 51:15.440 and you remember that moment. 51:15.440 --> 51:20.440 You know, every time when you found something, 51:20.440 --> 51:22.440 it is great. 51:22.440 --> 51:24.440 It's a life. 51:24.440 --> 51:26.440 Every simple thing. 51:26.440 --> 51:32.440 But my general feeling that most of my time was wrong. 51:32.440 --> 51:35.440 You should go again and again and again 51:35.440 --> 51:39.440 and try to be honest in front of yourself. 51:39.440 --> 51:41.440 Not to make interpretation, 51:41.440 --> 51:46.440 but try to understand that it's related to ground truth. 51:46.440 --> 51:52.440 It is not my blah, blah, blah interpretation or something like that. 51:52.440 --> 51:57.440 But you're allowed to get excited at the possibility of discovery. 51:57.440 --> 52:00.440 You have to double check it, but... 52:00.440 --> 52:04.440 No, but how it's related to the other ground truth 52:04.440 --> 52:10.440 is it just temporary or it is forever? 52:10.440 --> 52:13.440 You know, you always have a feeling 52:13.440 --> 52:17.440 when you found something, 52:17.440 --> 52:19.440 how big is that? 52:19.440 --> 52:23.440 So, 20 years ago, when we discovered statistical learning, 52:23.440 --> 52:25.440 so nobody believed. 52:25.440 --> 52:31.440 Except for one guy, Dudley from MIT. 52:31.440 --> 52:36.440 And then in 20 years, it became fashion. 52:36.440 --> 52:39.440 And the same with support vector machines. 52:39.440 --> 52:41.440 That's kernel machines. 52:41.440 --> 52:44.440 So with support vector machines and learning theory, 52:44.440 --> 52:48.440 when you were working on it, 52:48.440 --> 52:55.440 you had a sense that you had a sense of the profundity of it, 52:55.440 --> 52:59.440 how this seems to be right. 52:59.440 --> 53:01.440 It seems to be powerful. 53:01.440 --> 53:04.440 Right, absolutely, immediately. 53:04.440 --> 53:08.440 I recognize that it will last forever. 53:08.440 --> 53:17.440 And now, when I found this invariance story, 53:17.440 --> 53:21.440 I have a feeling that it is completely wrong. 53:21.440 --> 53:25.440 Because I have proved that there are no different mechanisms. 53:25.440 --> 53:30.440 Some say cosmetic improvement you can do, 53:30.440 --> 53:34.440 but in terms of invariance, 53:34.440 --> 53:38.440 you need both invariance and statistical learning 53:38.440 --> 53:41.440 and they should work together. 53:41.440 --> 53:47.440 But also, I'm happy that we can formulate 53:47.440 --> 53:51.440 what is intelligence from that 53:51.440 --> 53:54.440 and to separate from technical part. 53:54.440 --> 53:56.440 And that is completely different. 53:56.440 --> 53:58.440 Absolutely. 53:58.440 --> 54:00.440 Well, Vladimir, thank you so much for talking today. 54:00.440 --> 54:01.440 Thank you. 54:01.440 --> 54:28.440 Thank you very much.