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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
That's right.
https://karpathy.ai/lexicap/0005-large.html#00:27:26.120
Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
But aren't you surprised by the beauty of it?
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So not mathematical beauty, but the fact that it works at all or are you criticizing that
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
very beauty, our human desire to interpret, to find our silly interpretations in these
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
constructs?
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Let me ask you this.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Are you surprised and does it inspire you?
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
How do you feel about the success of a system like AlphaGo at beating the game of Go?
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Using neural networks to estimate the quality of a board and the quality of the position.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
That is your interpretation, quality of the board.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Yeah, yes.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Yeah.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So it's not our interpretation.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
The fact is a neural network system, it doesn't matter, a learning system that we don't I
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
think mathematically understand that well, beats the best human player, does something
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
that was thought impossible.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
That means that it's not a very difficult problem.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So you empirically, we've empirically have discovered that this is not a very difficult
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
problem.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Yeah.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
It's true.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So maybe, can't argue.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So even more I would say that if they use deep learning, it is not the most effective
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
way of learning theory.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
And usually when people use deep learning, they're using zillions of training data.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Yeah.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
But you don't need this.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So I describe challenge, can we do some problems which do well deep learning method, this deep
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
net, using hundred times less training data.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Even more, some problems deep learning cannot solve because it's not necessary they create
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
admissible set of function.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
To create deep architecture means to create admissible set of functions.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
You cannot say that you're creating good admissible set of functions.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
You just, it's your fantasy.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
It does not come from us.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
But it is possible to create admissible set of functions because you have your training
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
data.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
That actually for mathematicians, when you consider a variant, you need to use law of
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
large numbers.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
When you're making training in existing algorithm, you need uniform law of large numbers, which
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
is much more difficult, it requires VC dimension and all this stuff.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
But nevertheless, if you use both weak and strong way of convergence, you can decrease
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
a lot of training data.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
You could do the three, the swims like a duck and quacks like a duck.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So let's step back and think about human intelligence in general.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Clearly that has evolved in a non mathematical way.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
It wasn't, as far as we know, God or whoever didn't come up with a model and place in our
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
brain of admissible functions.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
It kind of evolved.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
I don't know, maybe you have a view on this.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So Alan Turing in the 50s, in his paper, asked and rejected the question, can machines think?
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
It's not a very useful question, but can you briefly entertain this useful, useless question?
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Can machines think?
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So talk about intelligence and your view of it.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
I don't know that.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
I know that Turing described imitation.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
If computer can imitate human being, let's call it intelligent.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
And he understands that it is not thinking computer.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
He completely understands what he's doing.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
But he set up problem of imitation.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So now we understand that the problem is not in imitation.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
I'm not sure that intelligence is just inside of us.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
It may be also outside of us.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
I have several observations.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So when I prove some theorem, it's very difficult theorem, in couple of years, in several places,
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
people prove the same theorem, say, Sawyer Lemma, after us was done, then another guys
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
proved the same theorem.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
In the history of science, it's happened all the time.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
For example, geometry, it's happened simultaneously, first it did Lobachevsky and then Gauss and
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Boyai and another guys, and it's approximately in 10 times period, 10 years period of time.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
And I saw a lot of examples like that.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
And many mathematicians think that when they develop something, they develop something
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
in general which affect everybody.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So maybe our model that intelligence is only inside of us is incorrect.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
It's our interpretation.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
It might be there exists some connection with world intelligence.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
I don't know.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
You're almost like plugging in into...
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Yeah, exactly.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
And contributing to this...
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Into a big network.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Into a big, maybe in your own network.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
On the flip side of that, maybe you can comment on big O complexity and how you see classifying
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
algorithms by worst case running time in relation to their input.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So that way of thinking about functions, do you think p equals np, do you think that's
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
an interesting question?
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Yeah, it is an interesting question.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
But let me talk about complexity in about worst case scenario.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
There is a mathematical setting.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
When I came to United States in 1990, people did not know, they did not know statistical
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
learning theory.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
So in Russia, it was published to monographs, our monographs, but in America they didn't
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
know.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Then they learned and somebody told me that it is worst case theory and they will create
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
real case theory, but till now it did not.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
Because it is mathematical too.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
You can do only what you can do using mathematics.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
And which has a clear understanding and clear description.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
And for this reason, we introduce complexity.
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Vladimir Vapnik: Statistical Learning | Lex Fridman Podcast #5
And we need this because using, actually it is diversity, I like this one more.
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