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	WEBVTT

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	The following is a conversation with Vladimir Vapnik.

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	He's the coinventor of the Support Vector Machines,

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	Support Vector Clustering, VC Theory,

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	and many foundational ideas in statistical learning.

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	He was born in the Soviet Union and worked

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	at the Institute of Control Sciences in Moscow.

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	Then in the United States, he worked at AT&T, NEC Labs,

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	Facebook Research, and now as a professor at Columbia

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	University.

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	His work has been cited over 170,000 times.

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	He has some very interesting ideas

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	about artificial intelligence and the nature of learning,

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	especially on the limits of our current approaches

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	and the open problems in the field.

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	This conversation is part of MIT course

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	on artificial general intelligence

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	and the Artificial Intelligence Podcast.

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	If you enjoy it, please subscribe on YouTube

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	or rate it on iTunes or your podcast provider of choice

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	or simply connect with me on Twitter

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	or other social networks at Lex Friedman, spelled F R I D.

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	And now here's my conversation with Vladimir Vapnik.

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	Einstein famously said that God doesn't play dice.

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	Yeah.

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	You have studied the world through the eyes of statistics.

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	So let me ask you, in terms of the nature of reality,

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	fundamental nature of reality, does God play dice?

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	We don't know some factors, and because we

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	don't know some factors, which could be important,

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	it looks like God play dice, but we should describe it.

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	In philosophy, they distinguish between two positions,

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	positions of instrumentalism, where

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	you're creating theory for prediction

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	and position of realism, where you're

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	trying to understand what God's big.

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	Can you describe instrumentalism and realism

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	a little bit?

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	For example, if you have some mechanical laws, what is that?

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	Is it law which is true always and everywhere?

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	Or it is law which allows you to predict

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	the position of moving element, what you believe.

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	You believe that it is God's law, that God created the world,

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	which obeyed to this physical law,

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	or it is just law for predictions?

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	And which one is instrumentalism?

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	For predictions.

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	If you believe that this is law of God, and it's always

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	true everywhere, that means that you're a realist.

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	So you're trying to really understand that God's thought.

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	So the way you see the world as an instrumentalist?

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	You know, I'm working for some models,

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	model of machine learning.

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	So in this model, we can see setting,

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	and we try to solve, resolve the setting,

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	to solve the problem.

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	And you can do it in two different ways,

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	from the point of view of instrumentalists.

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	And that's what everybody does now,

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	because they say that the goal of machine learning

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	is to find the rule for classification.

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	That is true, but it is an instrument for prediction.

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	But I can say the goal of machine learning

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	is to learn about conditional probability.

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	So how God played use, and is He play?

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	What is probability for one?

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	What is probability for another given situation?

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	But for prediction, I don't need this.

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	I need the rule.

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	But for understanding, I need conditional probability.

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	So let me just step back a little bit first to talk about.

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	You mentioned, which I read last night,

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	the parts of the 1960 paper by Eugene Wigner,

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	unreasonable effectiveness of mathematics

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	and natural sciences.

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	Such a beautiful paper, by the way.

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	It made me feel, to be honest, to confess my own work

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	in the past few years on deep learning, heavily applied.

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	It made me feel that I was missing out

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	on some of the beauty of nature in the way

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	that math can uncover.

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	So let me just step away from the poetry of that for a second.

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	How do you see the role of math in your life?

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	Is it a tool?

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	Is it poetry?

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	Where does it sit?

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	And does math for you have limits of what it can describe?

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	Some people saying that math is language which use God.

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	So I believe in that.

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	Speak to God or use God.

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	Or use God.

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	Use God.

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	Yeah.

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	So I believe that this article about unreasonable

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	effectiveness of math is that if you're

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	looking in mathematical structures,

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	they know something about reality.

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	And the most scientists from natural science,

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	they're looking on equation and trying to understand reality.

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	So the same in machine learning.

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	If you're trying very carefully look on all equations

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	which define conditional probability,

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	you can understand something about reality more

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	than from your fantasy.

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	So math can reveal the simple underlying principles

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	of reality, perhaps.

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	You know, what means simple?

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	It is very hard to discover them.

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	But then when you discover them and look at them,

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	you see how beautiful they are.

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	And it is surprising why people did not see that before.

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	You're looking on equation and derive it from equations.

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	For example, I talked yesterday about least squirmated.

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	And people had a lot of fantasy have to improve least squirmated.

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	But if you're going step by step by solving some equations,

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	you suddenly will get some term which,

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	after thinking, you understand that it described

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	position of observation point.

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	In least squirmated, we throw out a lot of information.

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	We don't look in composition of point of observations.

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	We're looking only on residuals.

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	But when you understood that, that's a very simple idea.

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	But it's not too simple to understand.

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	And you can derive this just from equations.

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	So some simple algebra, a few steps

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	will take you to something surprising

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	that when you think about, you understand.

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	And that is proof that human intuition not to reach

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	and very primitive.

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	And it does not see very simple situations.

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	So let me take a step back in general.

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	Yes, right?

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	But what about human as opposed to intuition and ingenuity?

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	Moments of brilliance.

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	So do you have to be so hard on human intuition?

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	Are there moments of brilliance in human intuition?

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	They can leap ahead of math, and then the math will catch up?

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	I don't think so.

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	I think that the best human intuition,

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	it is putting in axioms.

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	And then it is technical.

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	See where the axioms take you.

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	But if they correctly take axioms,

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	but it axiom polished during generations of scientists.

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	And this is integral wisdom.

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	So that's beautifully put.

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	But if you maybe look at when you think of Einstein

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	and special relativity, what is the role of imagination

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	coming first there in the moment of discovery of an idea?

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	So there is obviously a mix of math

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	and out of the box imagination there.

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	That I don't know.

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	Whatever I did, I exclude any imagination.

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	Because whatever I saw in machine learning that

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	come from imagination, like features, like deep learning,

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	they are not relevant to the problem.

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	When you're looking very carefully

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	for mathematical equations, you're

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	deriving very simple theory, which goes far by

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	no theory at school than whatever people can imagine.

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	Because it is not good fantasy.

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	It is just interpretation.

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	It is just fantasy.

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	But it is not what you need.

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	You don't need any imagination to derive, say,

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	main principle of machine learning.

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	When you think about learning and intelligence,

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	maybe thinking about the human brain

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	and trying to describe mathematically the process of learning

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	that is something like what happens in the human brain,

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	do you think we have the tools currently?

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	Do you think we will ever have the tools

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	to try to describe that process of learning?

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	It is not description of what's going on.

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	It is interpretation.

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	It is your interpretation.

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	Your vision can be wrong.

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	You know, when a guy invent microscope,

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	Levin Cook for the first time, only he got this instrument

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	and nobody, he kept secrets about microscope.

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	But he wrote reports in London Academy of Science.

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	In his report, when he looked into the blood,

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	he looked everywhere, on the water, on the blood,

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	on the spin.

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	But he described blood like fight between queen and king.

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	So he saw blood cells, red cells,

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	and he imagines that it is army fighting each other.

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	And it was his interpretation of situation.

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	And he sent this report in Academy of Science.

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	They very carefully looked because they believed

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	that he is right, he saw something.

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	But he gave wrong interpretation.

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	And I believe the same can happen with brain.

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	Because the most important part, you know,

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	I believe in human language.

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	In some proverb, it's so much wisdom.

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	For example, people say that it is better than 1,000 days

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	of diligent studies one day with great teacher.

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	But if I will ask you what teacher does, nobody knows.

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	And that is intelligence.

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	And what we know from history, and now from mass

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	and machine learning, that teacher can do a lot.

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	So what, from a mathematical point of view,

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	is the great teacher?

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	I don't know.

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	That's an awful question.

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	Now, what we can say what teacher can do,

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	he can introduce some invariance, some predicate

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	for creating invariance.

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	How he doing it?

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	I don't know.

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	Because teacher knows reality and can describe

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	from this reality a predicate invariance.

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	But he knows that when you're using invariant,

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	he can decrease number of observations 100 times.

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	But maybe try to pull that apart a little bit.

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	I think you mentioned a piano teacher saying to the student,

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	play like a butterfly.

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	I played piano, I played guitar for a long time.

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	Yeah, maybe it's romantic, poetic.

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	But it feels like there's a lot of truth in that statement.

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	There is a lot of instruction in that statement.

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	And so can you pull that apart?

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	What is that?

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	The language itself may not contain this information.

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	It's not blah, blah, blah.

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	It does not blah, blah, blah, yeah.

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	It affects you.

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	It's what?

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	It affects you.

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	It affects your playing.

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	Yes, it does.

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	But it's not the language.

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	It feels like what is the information being exchanged there?

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	What is the nature of information?

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	What is the representation of that information?

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	I believe that it is sort of predicate.

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	But I don't know.

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	That is exactly what intelligence in machine learning

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	should be.

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	Because the rest is just mathematical technique.

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	I think that what was discovered recently

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	is that there is two mechanisms of learning.

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	One called strong convergence mechanism

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	and weak convergence mechanism.

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	Before, people use only one convergence.

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	In weak convergence mechanism, you can use predicate.

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	That's what play like butterfly.

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	And it will immediately affect your playing.

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	You know, there is English proverb.

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	Great.

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	If it looks like a duck, swims like a duck,

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	and quack like a duck, then it is probably duck.

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	Yes.

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	But this is exact about predicate.

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	Looks like a duck, what it means.

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	So you saw many ducks that you're training data.

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	So you have description of how looks integral looks ducks.

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	Yeah, the visual characteristics of a duck.

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	Yeah, but you won't.

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	And you have model for the cognition ducks.

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	So you would like that theoretical description

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	from model coincide with empirical description, which

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	you saw on Territax there.

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	So about looks like a duck, it is general.

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	But what about swims like a duck?

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	You should know that duck swims.

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	You can say it play chess like a duck, OK?

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	Duck doesn't play chess.

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	And it is completely legal predicate, but it is useless.

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	So half teacher can recognize not useless predicate.

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	So up to now, we don't use this predicate

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	in existing machine learning.

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	And you think that's not so useful?

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	So why we need billions of data?

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	But in this English proverb, they use only three predicate.

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	Looks like a duck, swims like a duck, and quack like a duck.

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	So you can't deny the fact that swims like a duck

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	and quacks like a duck has humor in it, has ambiguity.

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	Let's talk about swim like a duck.

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	It does not say jumps like a duck.

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	Why?

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	Because it's not relevant.

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	But that means that you know ducks, you know different birds,

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	you know animals.

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	And you derive from this that it is relevant to say swim like a duck.

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	So underneath, in order for us to understand swims like a duck,

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	it feels like we need to know millions of other little pieces

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	of information.

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	We pick up along the way.

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	You don't think so.

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	There doesn't need to be this knowledge base.

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	In those statements, carries some rich information

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	that helps us understand the essence of duck.

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	How far are we from integrating predicates?

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	You know that when you consider complete theory,

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	machine learning, so what it does,

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	you have a lot of functions.

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	And then you're talking, it looks like a duck.

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	You see your training data.

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	From training data, you recognize like expected duck should look.

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	Then you remove all functions, which does not look like you think

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	it should look from training data.

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	So you decrease amount of function from which you pick up one.

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	Then you give a second predicate.

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	And then, again, decrease the set of function.

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	And after that, you pick up the best function you can find.

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	It is standard machine learning.

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	So why you need not too many examples?

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	Because your predicates aren't very good, or you're not.

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	That means that predicate very good.

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	Because every predicate is invented

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	to decrease a divisible set of functions.

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	So you talk about admissible set of functions,

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	and you talk about good functions.

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	So what makes a good function?

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	So admissible set of function is set of function

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	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.