The following is a conversation with Vladimir Vapnik.
He's the coinventor of the Support Vector Machines,
Support Vector Clustering, VC Theory,
and many foundational ideas in statistical learning.
He was born in the Soviet Union and worked
at the Institute of Control Sciences in Moscow.
Then in the United States, he worked at AT&T, NEC Labs,
Facebook Research, and now as a professor at Columbia
University.
His work has been cited over 170,000 times.
He has some very interesting ideas
about artificial intelligence and the nature of learning,
especially on the limits of our current approaches
and the open problems in the field.
This conversation is part of MIT course
on artificial general intelligence
and the Artificial Intelligence Podcast.
If you enjoy it, please subscribe on YouTube
or rate it on iTunes or your podcast provider of choice
or simply connect with me on Twitter
or other social networks at Lex Friedman, spelled F R I D.
And now here's my conversation with Vladimir Vapnik.
Einstein famously said that God doesn't play dice.
Yeah.
You have studied the world through the eyes of statistics.
So let me ask you, in terms of the nature of reality,
fundamental nature of reality, does God play dice?
We don't know some factors, and because we
don't know some factors, which could be important,
it looks like God play dice, but we should describe it.
In philosophy, they distinguish between two positions,
positions of instrumentalism, where
you're creating theory for prediction
and position of realism, where you're
trying to understand what God's big.
Can you describe instrumentalism and realism
a little bit?
For example, if you have some mechanical laws, what is that?
Is it law which is true always and everywhere?
Or it is law which allows you to predict
the position of moving element, what you believe.
You believe that it is God's law, that God created the world,
which obeyed to this physical law,
or it is just law for predictions?
And which one is instrumentalism?
For predictions.
If you believe that this is law of God, and it's always
true everywhere, that means that you're a realist.
So you're trying to really understand that God's thought.
So the way you see the world as an instrumentalist?
You know, I'm working for some models,
model of machine learning.
So in this model, we can see setting,
and we try to solve, resolve the setting,
to solve the problem.
And you can do it in two different ways,
from the point of view of instrumentalists.
And that's what everybody does now,
because they say that the goal of machine learning
is to find the rule for classification.
That is true, but it is an instrument for prediction.
But I can say the goal of machine learning
is to learn about conditional probability.
So how God played use, and is He play?
What is probability for one?
What is probability for another given situation?
But for prediction, I don't need this.
I need the rule.
But for understanding, I need conditional probability.
So let me just step back a little bit first to talk about.
You mentioned, which I read last night,
the parts of the 1960 paper by Eugene Wigner,
unreasonable effectiveness of mathematics
and natural sciences.
Such a beautiful paper, by the way.
It made me feel, to be honest, to confess my own work
in the past few years on deep learning, heavily applied.
It made me feel that I was missing out
on some of the beauty of nature in the way
that math can uncover.
So let me just step away from the poetry of that for a second.
How do you see the role of math in your life?
Is it a tool?
Is it poetry?
Where does it sit?
And does math for you have limits of what it can describe?
Some people saying that math is language which use God.
So I believe in that.
Speak to God or use God.
Or use God.
Use God.
Yeah.
So I believe that this article about unreasonable
effectiveness of math is that if you're
looking in mathematical structures,
they know something about reality.
And the most scientists from natural science,
they're looking on equation and trying to understand reality.
So the same in machine learning.
If you're trying very carefully look on all equations
which define conditional probability,
you can understand something about reality more
than from your fantasy.
So math can reveal the simple underlying principles
of reality, perhaps.
You know, what means simple?
It is very hard to discover them.
But then when you discover them and look at them,
you see how beautiful they are.
And it is surprising why people did not see that before.
You're looking on equation and derive it from equations.
For example, I talked yesterday about least squirmated.
And people had a lot of fantasy have to improve least squirmated.
But if you're going step by step by solving some equations,
you suddenly will get some term which,
after thinking, you understand that it described
position of observation point.
In least squirmated, we throw out a lot of information.
We don't look in composition of point of observations.
We're looking only on residuals.
But when you understood that, that's a very simple idea.
But it's not too simple to understand.
And you can derive this just from equations.
So some simple algebra, a few steps
will take you to something surprising
that when you think about, you understand.
And that is proof that human intuition not to reach
and very primitive.
And it does not see very simple situations.
So let me take a step back in general.
Yes, right?
But what about human as opposed to intuition and ingenuity?
Moments of brilliance.
So do you have to be so hard on human intuition?
Are there moments of brilliance in human intuition?
They can leap ahead of math, and then the math will catch up?
I don't think so.
I think that the best human intuition,
it is putting in axioms.
And then it is technical.
See where the axioms take you.
But if they correctly take axioms,
but it axiom polished during generations of scientists.
And this is integral wisdom.
So that's beautifully put.
But if you maybe look at when you think of Einstein
and special relativity, what is the role of imagination
coming first there in the moment of discovery of an idea?
So there is obviously a mix of math
and out of the box imagination there.
That I don't know.
Whatever I did, I exclude any imagination.
Because whatever I saw in machine learning that
come from imagination, like features, like deep learning,
they are not relevant to the problem.
When you're looking very carefully
for mathematical equations, you're
deriving very simple theory, which goes far by
no theory at school than whatever people can imagine.
Because it is not good fantasy.
It is just interpretation.
It is just fantasy.
But it is not what you need.
You don't need any imagination to derive, say,
main principle of machine learning.
When you think about learning and intelligence,
maybe thinking about the human brain
and trying to describe mathematically the process of learning
that is something like what happens in the human brain,
do you think we have the tools currently?
Do you think we will ever have the tools
to try to describe that process of learning?
It is not description of what's going on.
It is interpretation.
It is your interpretation.
Your vision can be wrong.
You know, when a guy invent microscope,
Levin Cook for the first time, only he got this instrument
and nobody, he kept secrets about microscope.
But he wrote reports in London Academy of Science.
In his report, when he looked into the blood,
he looked everywhere, on the water, on the blood,
on the spin.
But he described blood like fight between queen and king.
So he saw blood cells, red cells,
and he imagines that it is army fighting each other.
And it was his interpretation of situation.
And he sent this report in Academy of Science.
They very carefully looked because they believed
that he is right, he saw something.
But he gave wrong interpretation.
And I believe the same can happen with brain.
Because the most important part, you know,
I believe in human language.
In some proverb, it's so much wisdom.
For example, people say that it is better than 1,000 days
of diligent studies one day with great teacher.
But if I will ask you what teacher does, nobody knows.
And that is intelligence.
And what we know from history, and now from mass
and machine learning, that teacher can do a lot.
So what, from a mathematical point of view,
is the great teacher?
I don't know.
That's an awful question.
Now, what we can say what teacher can do,
he can introduce some invariance, some predicate
for creating invariance.
How he doing it?
I don't know.
Because teacher knows reality and can describe
from this reality a predicate invariance.
But he knows that when you're using invariant,
he can decrease number of observations 100 times.
But maybe try to pull that apart a little bit.
I think you mentioned a piano teacher saying to the student,
play like a butterfly.
I played piano, I played guitar for a long time.
Yeah, maybe it's romantic, poetic.
But it feels like there's a lot of truth in that statement.
There is a lot of instruction in that statement.
And so can you pull that apart?
What is that?
The language itself may not contain this information.
It's not blah, blah, blah.
It does not blah, blah, blah, yeah.
It affects you.
It's what?
It affects you.
It affects your playing.
Yes, it does.
But it's not the language.
It feels like what is the information being exchanged there?
What is the nature of information?
What is the representation of that information?
I believe that it is sort of predicate.
But I don't know.
That is exactly what intelligence in machine learning
should be.
Because the rest is just mathematical technique.
I think that what was discovered recently
is that there is two mechanisms of learning.
One called strong convergence mechanism
and weak convergence mechanism.
Before, people use only one convergence.
In weak convergence mechanism, you can use predicate.
That's what play like butterfly.
And it will immediately affect your playing.
You know, there is English proverb.
Great.
If it looks like a duck, swims like a duck,
and quack like a duck, then it is probably duck.
Yes.
But this is exact about predicate.
Looks like a duck, what it means.
So you saw many ducks that you're training data.
So you have description of how looks integral looks ducks.
Yeah, the visual characteristics of a duck.
Yeah, but you won't.
And you have model for the cognition ducks.
So you would like that theoretical description
from model coincide with empirical description, which
you saw on Territax there.
So about looks like a duck, it is general.
But what about swims like a duck?
You should know that duck swims.
You can say it play chess like a duck, OK?
Duck doesn't play chess.
And it is completely legal predicate, but it is useless.
So half teacher can recognize not useless predicate.
So up to now, we don't use this predicate
in existing machine learning.
And you think that's not so useful?
So why we need billions of data?
But in this English proverb, they use only three predicate.
Looks like a duck, swims like a duck, and quack like a duck.
So you can't deny the fact that swims like a duck
and quacks like a duck has humor in it, has ambiguity.
Let's talk about swim like a duck.
It does not say jumps like a duck.
Why?
Because it's not relevant.
But that means that you know ducks, you know different birds,
you know animals.
And you derive from this that it is relevant to say swim like a duck.
So underneath, in order for us to understand swims like a duck,
it feels like we need to know millions of other little pieces
of information.
We pick up along the way.
You don't think so.
There doesn't need to be this knowledge base.
In those statements, carries some rich information
that helps us understand the essence of duck.
How far are we from integrating predicates?
You know that when you consider complete theory,
machine learning, so what it does,
you have a lot of functions.
And then you're talking, it looks like a duck.
You see your training data.
From training data, you recognize like expected duck should look.
Then you remove all functions, which does not look like you think
it should look from training data.
So you decrease amount of function from which you pick up one.
Then you give a second predicate.
And then, again, decrease the set of function.
And after that, you pick up the best function you can find.
It is standard machine learning.
So why you need not too many examples?
Because your predicates aren't very good, or you're not.
That means that predicate very good.
Because every predicate is invented
to decrease a divisible set of functions.
So you talk about admissible set of functions,
and you talk about good functions.
So what makes a good function?
So admissible set of function is set of function
which has small capacity, or small diversity,
small VC dimension example, which contain good function.
So by the way, for people who don't know,
VC, you're the V in the VC.
So how would you describe to a lay person what VC theory is?
How would you describe VC?
So when you have a machine, so a machine
capable to pick up one function from the admissible set
of function.
But set of admissibles function can be big.
They contain all continuous functions and it's useless.
You don't have so many examples to pick up function.
But it can be small.
Small, we call it capacity, but maybe better called diversity.
So not very different function in the set
is infinite set of function, but not very diverse.
So it is small VC dimension.
When VC dimension is small, you need small amount
of training data.
So the goal is to create admissible set of functions
which have small VC dimension and contain good function.
Then you will be able to pick up the function
using small amount of observations.
So that is the task of learning.
It is creating a set of admissible functions
that has a small VC dimension.
And then you've figured out a clever way of picking up.
No, that is goal of learning, which I formulated yesterday.
Statistical learning theory does not
involve in creating admissible set of function.
In classical learning theory, everywhere, 100% in textbook,
the set of function admissible set of function is given.
But this is science about nothing,
because the most difficult problem
to create admissible set of functions, given, say,
a lot of functions, continuum set of functions,
create admissible set of functions,
that means that it has finite VC dimension,
small VC dimension, and contain good function.
So this was out of consideration.
So what's the process of doing that?
I mean, it's fascinating.
What is the process of creating this admissible set of functions?
That is invariant.
That's invariance.
Can you describe invariance?
Yeah, you're looking of properties of training data.
And properties means that you have some function,
and you just count what is the average value of function
on training data.
You have a model, and what is the expectation
of this function on the model.
And they should coincide.
So the problem is about how to pick up functions.
It can be any function.
In fact, it is true for all functions.
But because when I talking set, say,
duck does not jumping, so you don't ask question, jump like a duck.
Because it is trivial, it does not jumping,
it doesn't help you to recognize jump.
But you know something, which question to ask,
when you're asking, it swims like a jump, like a duck.
But looks like a duck, it is general situation.
Looks like, say, guy who have this illness, this disease,
it is legal, so there is a general type of predicate
looks like, and special type of predicate,
which related to this specific problem.
And that is intelligence part of all this business.
And that we are teachers in world.
Incorporating those specialized predicates.
What do you think about deep learning as neural networks,
these arbitrary architectures as helping accomplish some of the tasks
you're thinking about, their effectiveness or lack thereof,
what are the weaknesses and what are the possible strengths?
You know, I think that this is fantasy.
Everything which like deep learning, like features.
Let me give you this example.
One of the greatest book, this Churchill book about history of Second World War.
And he's starting this book describing that in all time, when war is over,
so the great kings, they gathered together,
almost all of them were relatives,
and they discussed what should be done, how to create peace.
And they came to agreement.
And when happens First World War, the general public came in power.
And they were so greedy that robbed Germany.
And it was clear for everybody that it is not peace.
That peace will last only 20 years, because they were not professionals.
It's the same I see in machine learning.
There are mathematicians who are looking for the problem from a very deep point of view,
a mathematical point of view.
And there are computer scientists who mostly does not know mathematics.
They just have interpretation of that.
And they invented a lot of blah, blah, blah interpretations like deep learning.
Why you need deep learning?
Mathematics does not know deep learning.
Mathematics does not know neurons.
It is just function.
If you like to say piecewise linear function, say that,
and do it in class of piecewise linear function.
But they invent something.
And then they try to prove the advantage of that through interpretations,
which mostly wrong.
And when not enough they appeal to brain,
which they know nothing about that.
Nobody knows what's going on in the brain.
So I think that more reliable look on maths.
This is a mathematical problem.
Do your best to solve this problem.
Try to understand that there is not only one way of convergence,
which is strong way of convergence.
There is a weak way of convergence, which requires predicate.
And if you will go through all this stuff,
you will see that you don't need deep learning.
Even more, I would say one of the theorem,
which is called representor theorem.
It says that optimal solution of mathematical problem,
which described learning, is on shadow network, not on deep learning.
And a shallow network, yeah.
The ultimate problem is there.
Absolutely.
So in the end, what you're saying is exactly right.
The question is, you have no value for throwing something on the table,
playing with it, not math.
It's like in your old network where you said throwing something in the bucket
or the biological example and looking at kings and queens
or the cells or the microscope.
You don't see value in imagining the cells or kings and queens
and using that as inspiration and imagination
for where the math will eventually lead you.
You think that interpretation basically deceives you in a way that's not productive.
I think that if you're trying to analyze this business of learning
and especially discussion about deep learning,
it is discussion about interpretation.
It's discussion about things, about what you can say about things.
That's right, but aren't you surprised by the beauty of it?
Not mathematical beauty, but the fact that it works at all.
Or are you criticizing that very beauty,
our human desire to interpret,
to find our silly interpretations in these constructs?
Let me ask you this.
Are you surprised?
Does it inspire you?
How do you feel about the success of a system like AlphaGo
at beating the game of Go?
Using neural networks to estimate the quality of a board
and the quality of the board?
That is your interpretation quality of the board.
Yes.
It's not our interpretation.
The fact is, a neural network system doesn't matter.
A learning system that we don't mathematically understand
that beats the best human player.
It does something that was thought impossible.
That means that it's not very difficult problem.
We've empirically discovered that this is not a very difficult problem.
That's true.
Maybe I can't argue.
Even more, I would say,
that if they use deep learning,
it is not the most effective way of learning theory.
Usually, when people use deep learning,
they're using zillions of training data.
But you don't need this.
I describe the challenge.
Can we do some problems with deep learning method
with deep net using 100 times less training data?
Even more, some problems deep learning cannot solve
because it's not necessary.
They create admissible set of functions.
Deep architecture means to create admissible set of functions.
You cannot say that you're creating good admissible set of functions.
It's your fantasy.
It does not come from mass.
But it is possible to create admissible set of functions
because you have your training data.
Actually, for mathematicians, when you consider a variant,
you need to use law of large numbers.
When you're making training in existing algorithm,
you need uniform law of large numbers,
which is much more difficult.
You see dimension and all this stuff.
Nevertheless, if you use both weak and strong way of convergence,
you can decrease a lot of training data.
You could do the three, the Swims like a duck and Quacks like a duck.
Let's step back and think about human intelligence in general.
Clearly, that has evolved in a nonmathematical way.
As far as we know, God, or whoever,
didn't come up with a model in place in our brain of admissible functions.
It kind of evolved.
I don't know.
Maybe you have a view on this.
Alan Turing in the 50s in his paper asked and rejected the question,
can machines think?
It's not a very useful question.
But can you briefly entertain this useless question?
Can machines think?
So talk about intelligence and your view of it.
I don't know that.
I know that Turing described imitation.
If computer can imitate human being, let's call it intelligent.
And he understands that it is not thinking computer.
Yes.
He completely understands what he's doing.
But he's set up a problem of imitation.
So now we understand that the problem is not in imitation.
I'm not sure that intelligence is just inside of us.
It may be also outside of us.
I have several observations.
So when I prove some theorem, it's a very difficult theorem.
But in a couple of years, in several places, people proved the same theorem.
Say, soil lemma after us was done.
Then another guy proved the same theorem.
In the history of science, it's happened all the time.
For example, geometry.
It's happened simultaneously.
First it did Lobachevsky and then Gauss and Boyai and other guys.
It happened simultaneously in 10 years period of time.
And I saw a lot of examples like that.
And many mathematicians think that when they develop something,
they develop something in general which affects everybody.
So maybe our model that intelligence is only inside of us is incorrect.
It's our interpretation.
Maybe there exists some connection with world intelligence.
I don't know.
You're almost like plugging in into...
Yeah, exactly.
...and contributing to this...
Into a big network.
...into a big, maybe in your own network.
No, no, no.
On the flip side of that, maybe you can comment on big O complexity
and how you see classifying algorithms by worst case running time
in relation to their input.
So that way of thinking about functions.
Do you think P equals NP?
Do you think that's an interesting question?
Yeah, it is an interesting question.
But let me talk about complexity and about worst case scenario.
There is a mathematical setting.
When I came to the United States in 1990,
people did not know this theory.
They did not know statistical learning theory.
So in Russia it was published to monographs or monographs,
but in America they didn't know.
Then they learned.
And somebody told me that if it's worst case theory,
and they will create real case theory,
but till now it did not.
Because it is a mathematical tool.
You can do only what you can do using mathematics,
which has a clear understanding and clear description.
And for this reason we introduced complexity.
And we need this.
Because actually it is diverse, I like this one more.
This dimension you can prove some theorems.
But we also create theory for case when you know probability measure.
And that is the best case which can happen.
It is entropy theory.
So from a mathematical point of view,
you know the best possible case and the worst possible case.
You can derive different model in medium.
But it's not so interesting.
You think the edges are interesting?
The edges are interesting.
Because it is not so easy to get a good bound, exact bound.
It's not many cases where you have.
The bound is not exact.
But interesting principles which discover the mass.
Do you think it's interesting because it's challenging
and reveals interesting principles that allow you to get those bounds?
Or do you think it's interesting because it's actually very useful
for understanding the essence of a function of an algorithm?
So it's like me judging your life as a human being
by the worst thing you did and the best thing you did
versus all the stuff in the middle.
It seems not productive.
I don't think so because you cannot describe situation in the middle.
Or it will be not general.
So you can describe edges cases.
And it is clear it has some model.
But you cannot describe model for every new case.
So you will be never accurate when you're using model.
But from a statistical point of view,
the way you've studied functions and the nature of learning
and the world, don't you think that the real world has a very long tail
that the edge cases are very far away from the mean,
the stuff in the middle, or no?
I don't know that.
I think that from my point of view,
if you will use formal statistic, uniform law of large numbers,
if you will use this invariance business,
you will need just law of large numbers.
And there's a huge difference between uniform law of large numbers
and large numbers.
Can you describe that a little more?
Or should we just take it to...
No, for example, when I'm talking about duck,
I gave three predicates and it was enough.
But if you will try to do formal distinguish,
you will need a lot of observations.
I got you.
And so that means that information about looks like a duck
contain a lot of bits of information,
formal bits of information.
So we don't know that how much bit of information
contain things from artificial intelligence.
And that is the subject of analysis.
Till now, old business,
I don't like how people consider artificial intelligence.
They consider us some codes which imitate activity of human being.
It is not science.
It is applications.
You would like to imitate God.
It is very useful and we have good problem.
But you need to learn something more.
How people can to develop predicates,
swims like a duck,
or play like butterfly or something like that.
Not the teacher tells you how it came in his mind.
How he choose this image.
That is problem of intelligence.
That is the problem of intelligence.
And you see that connected to the problem of learning?
Absolutely.
Because you immediately give this predicate
like specific predicate, swims like a duck,
or quack like a duck.
It was chosen somehow.
So what is the line of work, would you say?
If you were to formulate as a set of open problems,
that will take us there.
Play like a butterfly.
We will get a system to be able to...
Let's separate two stories.
One mathematical story.
That if you have predicate, you can do something.
And another story you have to get predicate.
It is intelligence problem.
And people even did not start understanding intelligence.
Because to understand intelligence, first of all,
try to understand what doing teachers.
How teacher teach.
Why one teacher better than another one?
Yeah.
So you think we really even haven't started on the journey
of generating the predicate?
No.
We don't understand.
We even don't understand that this problem exists.
Because did you hear?
You do.
No, I just know name.
I want to understand why one teacher better than another.
And how affect teacher student.
It is not because he repeating the problem which is in textbook.
Yes.
He make some remarks.
He make some philosophy of reasoning.
Yeah, that's a beautiful...
So it is a formulation of a question that is the open problem.
Why is one teacher better than another?
Right.
What he does better.
Yeah.
What...
Why at every level?
How do they get better?
What does it mean to be better?
The whole...
Yeah.
From whatever model I have.
One teacher can give a very good predicate.
One teacher can say swims like a dog.
And another can say jump like a dog.
And jump like a dog.
Car is zero information.
Yeah.
So what is the most exciting problem in statistical learning you've ever worked on?
Or are working on now?
I just finished this invariant story.
And I'm happy that...
I believe that it is ultimate learning story.
At least I can show that there are no another mechanism, only two mechanisms.
But they separate statistical part from intelligent part.
And I know nothing about intelligent part.
And if we will know this intelligent part,
so it will help us a lot in teaching, in learning.
You don't know it when we see it?
So for example, in my talk, the last slide was the challenge.
So you have, say, NIST digital recognition problem.
And deep learning claims that they did it very well.
Say 99.5% of correct answers.
But they use 60,000 observations.
Can you do the same?
100 times less.
But incorporating invariants.
What it means, you know, digit one, two, three.
Yeah.
Just looking at that.
Explain to me which invariant I should keep.
To use 100 examples.
Or say 100 times less examples to do the same job.
Yeah.
That last slide, unfortunately, you talk ended quickly.
The last slide was a powerful open challenge
and a formulation of the essence here.
That is the exact problem of intelligence.
Because everybody, when machine learning started,
it was developed by mathematicians,
they immediately recognized that we use much more
training data than humans needed.
But now again, we came to the same story.
Have to decrease.
That is the problem of learning.
It is not like in deep learning,
they use zealons of training data.
Because maybe zealons are not enough
if you have a good invariance.
Maybe you'll never collect some number of observations.
But now it is a question to intelligence.
Have to do that.
Because statistical part is ready.
As soon as you supply us with predicate,
we can do good job with small amount of observations.
And the very first challenges will know digit recognition.
And you know digits.
And please tell me invariance.
I think about that.
I can say for digit 3, I would introduce
concept of horizontal symmetry.
So the digit 3 has horizontal symmetry
more than say digit 2 or something like that.
But as soon as I get the idea of horizontal symmetry,
I can mathematically invent a lot of
measure of horizontal symmetry
on vertical symmetry or diagonal symmetry,
whatever, if I have a day of symmetry.
But what else?
Looking on digit, I see that it is metapredicate,
which is not shape.
It is something like symmetry,
like how dark is whole picture, something like that.
Which can self rise up predicate.
You think such a predicate could rise
out of something that is not general.
Meaning it feels like for me to be able to
understand the difference between a 2 and a 3,
I would need to have had a childhood
of 10 to 15 years playing with kids,
going to school, being yelled by parents.
All of that, walking, jumping, looking at ducks.
And now then I would be able to generate
the right predicate for telling the difference
between 2 and a 3.
Or do you think there is a more efficient way?
I know for sure that you must know
something more than digits.
That's a powerful statement.
But maybe there are several languages
of description, these elements of digits.
So I'm talking about symmetry,
about some properties of geometry,
I'm talking about something abstract.
But this is a problem of intelligence.
So in one of our articles, it is trivial to show
that every example can carry
not more than one bit of information in real.
Because when you show example
and you say this is one, you can remove, say,
a function which does not tell you one, say,
the best strategy, if you can do it perfectly,
it's remove half of the functions.
But when you use one predicate, which looks like a duck,
you can remove much more functions than half.
And that means that it contains
a lot of bit of information from a formal point of view.
But when you have a general picture
of what you want to recognize,
a general picture of the world,
can you invent this predicate?
And that predicate carries a lot of information.
Beautifully put, maybe just me,
but in all the math you show, in your work,
which is some of the most profound mathematical work
in the field of learning AI and just math in general.
I hear a lot of poetry and philosophy.
You really kind of talk about philosophy of science.
There's a poetry and music to a lot of the work you're doing
and the way you're thinking about it.
So where does that come from?
Do you escape to poetry? Do you escape to music?
I think that there exists ground truth.
There exists ground truth?
Yeah, and that can be seen everywhere.
The smart guy, philosopher,
sometimes I surprise how they deep see.
Sometimes I see that some of them are completely out of subject.
But the ground truth I see in music.
Music is the ground truth?
Yeah.
And in poetry, many poets, they believe they take dictation.
So what piece of music,
as a piece of empirical evidence,
gave you a sense that they are touching something in the ground truth?
It is structure.
The structure with the math of music.
Because when you're listening to Bach,
you see this structure.
Very clear, very classic, very simple.
And the same in Bach, when you have axioms in geometry,
you have the same feeling.
And in poetry, sometimes you see the same.
And if you look back at your childhood,
you grew up in Russia,
you maybe were born as a researcher in Russia,
you developed as a researcher in Russia,
you came to the United States in a few places.
If you look back,
what were some of your happiest moments as a researcher?
Some of the most profound moments.
Not in terms of their impact on society,
but in terms of their impact on how damn good you feel that day,
and you remember that moment.
You know, every time when you found something,
it is great.
It's a life.
Every simple thing.
But my general feeling that most of my time was wrong.
You should go again and again and again
and try to be honest in front of yourself.
Not to make interpretation,
but try to understand that it's related to ground truth.
It is not my blah, blah, blah interpretation or something like that.
But you're allowed to get excited at the possibility of discovery.
You have to double check it, but...
No, but how it's related to the other ground truth
is it just temporary or it is forever?
You know, you always have a feeling
when you found something,
how big is that?
So, 20 years ago, when we discovered statistical learning,
so nobody believed.
Except for one guy, Dudley from MIT.
And then in 20 years, it became fashion.
And the same with support vector machines.
That's kernel machines.
So with support vector machines and learning theory,
when you were working on it,
you had a sense that you had a sense of the profundity of it,
how this seems to be right.
It seems to be powerful.
Right, absolutely, immediately.
I recognize that it will last forever.
And now, when I found this invariance story,
I have a feeling that it is completely wrong.
Because I have proved that there are no different mechanisms.
Some say cosmetic improvement you can do,
but in terms of invariance,
you need both invariance and statistical learning
and they should work together.
But also, I'm happy that we can formulate
what is intelligence from that
and to separate from technical part.
And that is completely different.
Absolutely.
Well, Vladimir, thank you so much for talking today.
Thank you.
Thank you very much.