vtt/episode_005_small.vtt

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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,

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 small VC dimension example, which contain good function.

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 So by the way, for people who don't know,

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 VC, you're the V in the VC.

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 So how would you describe to a lay person what VC theory is?

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 How would you describe VC?

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 So when you have a machine, so a machine

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 capable to pick up one function from the admissible set

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 of function.

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 But set of admissibles function can be big.

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 They contain all continuous functions and it's useless.

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 You don't have so many examples to pick up function.

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 But it can be small.

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 Small, we call it capacity, but maybe better called diversity.

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 So not very different function in the set

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 is infinite set of function, but not very diverse.

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 So it is small VC dimension.

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 When VC dimension is small, you need small amount

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 of training data.

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 So the goal is to create admissible set of functions

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 which have small VC dimension and contain good function.

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 Then you will be able to pick up the function

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 using small amount of observations.

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 So that is the task of learning.

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 It is creating a set of admissible functions

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 that has a small VC dimension.

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 And then you've figured out a clever way of picking up.

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 No, that is goal of learning, which I formulated yesterday.

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 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.