CS_441_2023_Spring_February_28,_2023.vtt

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NOTE
Created on 2024-02-07T21:01:05.3475172Z by ClassTranscribe

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Hello.

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Hey, good morning, everybody.

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Hope you had a good weekend.

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Alright, so today we're going to talk

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about Language.

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And there's like three kind of major

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concepts that I'm going to introduce.

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So a lot of, a lot of.

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Content.

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And the first is, the first is like how

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we can represent language as integers

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using Subword tokenization.

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The second is being able to represent

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text as continuous vectors.

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And the Oregon words as continuous

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vectors.

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And the third is a new kind of

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processing called Attention or

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Transformers.

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These are kind of also in order of

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increasing impact or?

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So like when I first learned about

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WordPiece or the bite pair Encoding,

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which is a way that you can represent

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any text with like a fixed size

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Vocabulary, I was like that's a really

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cool idea.

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And then when I first learned about

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Word2Vec, which is a way of

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representing words in a high

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dimensional continuous space instead of

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as like different integers or different

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discrete tokens, it kind of like blew

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my mind.

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I was like, that's crazy.

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Like you'll see that you can add words

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together and then like.

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Some of the words leads to another Word

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which makes sense.

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And then Transformers just kind of

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changed the world.

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So there's a lot of impact in these

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ideas.

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So in the last lecture we talked about

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vision.

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And with vision, you kind of build up

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this representation from pixels to

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texture to essentially groups of groups

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of groups of pixels, right?

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You have a compositional model, and

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that's modeled with.

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With Convolution often.

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So for example if you look at this is

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just a couple of pixels blown up.

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You probably have no idea what it is.

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When you zoom into just a few pixels,

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you can't identify anything.

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If you zoom out a little bit then you

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can probably see some kind of edge and

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a little bit of features.

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Does anyone who doesn't have the slides

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can you recognize what that is?

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No, not yet.

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What eyes?

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Then if you.

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If you zoom out, do you have the slide

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or no?

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Yeah, I said if you don't have the

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slides, if you have the whole slide,

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it's pretty easy because you can see

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the one.

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So you zoom out a little bit more then

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you can kind of you can see it's

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obviously a nose.

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Now you can see it's a raccoon and then

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you can see the whole thing.

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So when we build up, the visual

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representation is building up from

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little little elements raised pixels

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into bigger patterns and bigger

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patterns until it finally makes sense.

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And that's what the convolutional

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networks that we learned about are

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doing you.

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This is Alex net in the early layers

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just correspond to edges and colors,

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and then the next layer, the

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activations correspond to textures, and

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then little subparts, and then parts

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and then eventually objects in scenes.

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And so the deep learning process is

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like a compositional process of putting

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together small elements into bigger

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elements and recognizing patterns out

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of them, and then bringing together

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those patterns and recognizing larger

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patterns and so on.

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So, but now we're going to talk about

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Language.

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And you might think like in language,

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the meaning is already in the words,

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right?

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So if I say cat or dog or running or

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something like that, it evokes like a

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big evokes like a lot of meaning to you

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where a pixel doesn't evolve very evoke

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very much meaning or even a small

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patch.

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And so it might appear that language is

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going to be very easy, that we can use

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straightforward Representations very

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effectively.

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But it's not totally true.

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I mean, it's a little bit true and

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that's, but as you'll see, it's a bit

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more complicated than that.

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So, for example, if we consider this

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sentence on the left, he sat on the

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chair and it broke.

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Which of these is more similar?

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The chair says the department is broke.

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It's option number one or option #2.

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After sitting the seat is broken.

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2nd.

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So probably most of you would say, at

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least semantically, the second one is a

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lot more similar, right?

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But in terms of the words, the first

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one is a lot more similar.

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So in the first one it says includes

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chair, the broke.

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So all the keywords or most of the

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keywords in the sentence are.

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In this first sentence, the chair says

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the department is broke.

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Where the second sentence is only has

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in common the Word the which isn't very

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meaningful.

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So if you were to represent these

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sentences with if you represent the

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words as different integers and then

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you try to compare the similarities of

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these sentences, and especially if you

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also consider the frequency of the

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words in general, then these sentences

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would not match at all.

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They'd be like totally dissimilar

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because they don't have any keywords in

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common where these sentences would be

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pretty similar.

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So it's not that it's not, it's not

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super simple.

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We have to be a little bit careful.

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So one one thing that we have to be

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aware of is that the same Word, and by

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Word I mean a character sequence can

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mean different things.

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So for example chair in the first in

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the sentence on top and chair on the

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second one are different and one case

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it's like something you sit on and the

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other case it's a person that leads the

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department.

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Broke.

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It's either the divided the chair into

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different pieces or out of money,

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right?

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They're totally different meanings.

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You can also have different words that

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mean similar things, so.

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As so for example you could have.

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Sitting and set right, they're very

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different letter sequences, but they're

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both like referring to the same thing,

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or broken broken.

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They're different words, but they are

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very closely related.

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And importantly, the meaning of the

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word depends on the surrounding Word.

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So nobody has any trouble like

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interpreting any of these sentences.

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The third one is like a bit awkward,

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but everyone can interpret them and you

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instantly, you don't have to think

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about it when he's somebody says he sat

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on the chair and it broke you

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immediately.

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When you think of chair, you think of

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something you sit on, and if somebody

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says the chair says the department is

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broke, you don't think of a chair that

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you sit on, you immediately think of a

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person like saying that the

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department's out of money.

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So we reflexively like understand these

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words based on the surrounding words.

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And this simple idea that the Word

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meaning depends on the surrounding

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words is one of the.

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Underlying like key concepts for Word

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Representations.

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So if we want to analyze text, then the

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first thing that we need to do is to

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convert the text into tokens so that

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we're token is going to come up a lot.

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I token is just basically a unit of

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data.

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And so it can be an integer or it can

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be a vector that represents a data

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element.

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It's a unit of processing.

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So you can say that a document, you can

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divide up a document into chunks of

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data and then each of those chunks is a

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token.

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So token is can be used to mean many

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things, but it just means like the

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atomic data element essentially.

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So if you have integer tokens, then the

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values are not continuous.

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So for example, five is no closer to 10

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than it is to 5000.

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They're just different labels.

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They're just separate, separate

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elements.

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If you have Vector tokens, then usually

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those are done in a way so that

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similarity is meaningful.

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So if you take the L2 distance between

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tokens, that gives you a sense of how

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similar that the information is that's

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represented by those tokens, if they're

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vectors, or if or.

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It's also common to do dot Product or

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cosine question.

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Token is an atomic element.

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Smallest.

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Integer tokens are not continuous, so

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they cannot integer token be assigned

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to like a Word as well as a phrase in

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some situations?

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Or is it always the Word which I'm

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assuming is like the smallest possible?

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So the question is whether integer can

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be assigned to a phrase or something

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bigger than a Word.

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It could potentially.

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So that's all.

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In your first you typically have like 3

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layers of representation in a language

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system.

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The first layer is that you take a text

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sequence and you break it up into

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integers.

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And as I'll discuss, there's like many

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ways of doing that.

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One way is called Cent piece, in which

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case you can actually have tokens or

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integers that.

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Bridge common words, so like I am,

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might be represented with a single

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token.

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And the then from those integers, then

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you have a mapping to continuous

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vectors that's called the Embedding.

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And then from that Embedding you have

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like a bunch of processing usually,

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usually now using Transformers or

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Attention models, that is then

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producing your final representation and

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prediction.

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So let's look at the different ways.

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So first we're going to talk about how

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we can map words into integers.

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So we'll mention three ways of doing

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that.

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So one way is that we just.

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We dulaney each word with a space

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South.

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We divide characters according to like

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spaces.

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And for each unique character string,

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after doing that to some document, we

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assign it to a different integer.

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And usually when we do this, we would

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say that we're going to represent up to

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say 30,000 or 50,000 words.

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And we're only going to assign the most

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frequent words to integers, and

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anything else will be like have a

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special token, unk or unknown.

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So in this case chair would be assigned

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to 1 integer though would be assigned

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to another integer, says would be

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assigned to another integer and so on.

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What is one advantage of this method?

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Yeah, it's pretty simple.

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That's a big advantage.

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What's another advantage?

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Maybe, yeah.

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Memory saving, yeah, could be.

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Maybe the other advantages won't be so

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clear unless I make them in comparison

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to others, but what's one disadvantage?

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It's hard to tell.

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Alright, sorry, go ahead.

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All the other ones, because they're the

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large variation of what others are

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considered, they're all bunch of

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important.

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So that might be more like I guess, on

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Accuracy, because you bundle all

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unknowns into one.

00:13:54.150 --> 00:13:56.270
A lot of them could be nouns, only a

00:13:56.270 --> 00:13:58.580
small could be very than the adjectives

00:13:58.580 --> 00:13:59.240
and whatnot.

00:13:59.240 --> 00:14:01.910
That's what like affective or excluded.

00:14:02.360 --> 00:14:05.200
So that's one big disadvantage is that

00:14:05.200 --> 00:14:06.280
you might end up with a bunch of

00:14:06.280 --> 00:14:09.140
unknowns and there could be lots of

00:14:09.140 --> 00:14:10.160
those potentially.

00:14:10.160 --> 00:14:10.930
What was yours?

00:14:11.040 --> 00:14:11.510
Another.

00:14:13.390 --> 00:14:15.410
This Word have different integers and

00:14:15.410 --> 00:14:17.320
they're comparing this Norm will not

00:14:17.320 --> 00:14:18.250
making any sense.

00:14:19.620 --> 00:14:20.590
Comparing what?

00:14:20.590 --> 00:14:22.590
The integers?

00:14:22.590 --> 00:14:24.110
You can't compare the integers to each

00:14:24.110 --> 00:14:24.400
other.

00:14:25.610 --> 00:14:26.780
That's true.

00:14:26.780 --> 00:14:30.280
So here's what here's what I have in

00:14:30.280 --> 00:14:32.430
terms of just pure as a strategy of

00:14:32.430 --> 00:14:33.730
mapping words to integers.

00:14:33.730 --> 00:14:36.160
So that problem of that the integers

00:14:36.160 --> 00:14:37.990
are not comparable will be the case for

00:14:37.990 --> 00:14:39.553
all three of these methods, but it will

00:14:39.553 --> 00:14:41.750
be fixed in the next section.

00:14:42.830 --> 00:14:44.960
So Pros simple.

00:14:46.250 --> 00:14:49.290
Another Pro is that words do have like

00:14:49.290 --> 00:14:50.940
a fair amount of meaning in them, so

00:14:50.940 --> 00:14:53.380
you can, for example, if you have full

00:14:53.380 --> 00:14:55.700
documents, you can represent them as

00:14:55.700 --> 00:14:56.970
counts of the different words.

00:14:57.830 --> 00:14:59.520
And then you can use those counts to

00:14:59.520 --> 00:15:02.420
retrieve other documents or to try to

00:15:02.420 --> 00:15:04.410
classify a spam or something like that,

00:15:04.410 --> 00:15:05.750
and it will work fairly well.

00:15:05.750 --> 00:15:06.530
It's not terrible.

00:15:07.610 --> 00:15:09.860
So a Word by a Word on its own, often

00:15:09.860 --> 00:15:10.370
as a meaning.

00:15:10.370 --> 00:15:12.090
Now, sometimes it can have more than

00:15:12.090 --> 00:15:14.325
one meaning, but for the most, for the

00:15:14.325 --> 00:15:15.630
most part, it's pretty meaningful.

00:15:17.640 --> 00:15:19.405
There's also some big disadvantages.

00:15:19.405 --> 00:15:22.755
So as one was raised that many words

00:15:22.755 --> 00:15:25.347
will map to unknown and you might not

00:15:25.347 --> 00:15:28.078
like if you say I have a 30,000 word

00:15:28.078 --> 00:15:29.380
dictionary, you might think that's

00:15:29.380 --> 00:15:31.350
quite a lot, but it's not that much

00:15:31.350 --> 00:15:35.220
because all the different forms of each

00:15:35.220 --> 00:15:36.640
Word will be mapped to different

00:15:36.640 --> 00:15:37.450
tokens.

00:15:37.450 --> 00:15:39.830
And so you actually have like a huge

00:15:39.830 --> 00:15:42.470
potential dictionary if there's names,

00:15:42.470 --> 00:15:45.690
unusual words like anachronism.

00:15:45.740 --> 00:15:46.700
Or numbers.

00:15:46.700 --> 00:15:48.210
All of those will get mapped to

00:15:48.210 --> 00:15:48.820
unknown.

00:15:49.840 --> 00:15:51.790
So that can create some problems.

00:15:51.790 --> 00:15:54.220
You need a really large vocabulary, so

00:15:54.220 --> 00:15:56.420
if you want to try to have not too many

00:15:56.420 --> 00:15:57.490
unknowns, then you need.

00:15:57.490 --> 00:15:58.860
You might even need like hundreds of

00:15:58.860 --> 00:16:01.470
thousands of dictionary elements.

00:16:02.430 --> 00:16:04.000
And Vocabulary.

00:16:04.000 --> 00:16:06.010
That's basically the set of things that

00:16:06.010 --> 00:16:07.930
you're representing.

00:16:07.930 --> 00:16:10.380
So it's like this set of like character

00:16:10.380 --> 00:16:11.880
combinations that you'll map to

00:16:11.880 --> 00:16:12.820
different integers.

00:16:14.040 --> 00:16:15.710
And then and then.

00:16:15.710 --> 00:16:17.430
It also doesn't model the similarity of

00:16:17.430 --> 00:16:18.390
related words.

00:16:18.390 --> 00:16:20.820
Broken, broken, which was another point

00:16:20.820 --> 00:16:22.440
brought up.

00:16:22.440 --> 00:16:25.340
So very similar strings get mapped to

00:16:25.340 --> 00:16:26.650
different integers, and there are no

00:16:26.650 --> 00:16:28.260
more similar than any other integers.

00:16:30.530 --> 00:16:32.990
Another extreme that we could do is to

00:16:32.990 --> 00:16:35.180
map each character to an integer.

00:16:36.520 --> 00:16:38.660
So it's as simple as that.

00:16:38.660 --> 00:16:42.230
There's 256 bytes and each Byte is

00:16:42.230 --> 00:16:44.346
represented as a different number.

00:16:44.346 --> 00:16:47.370
And you could like use a reduced

00:16:47.370 --> 00:16:49.670
Vocabulary of justice, like of letters

00:16:49.670 --> 00:16:51.730
and numbers and punctuation, but at

00:16:51.730 --> 00:16:53.140
most you have 256.

00:16:53.920 --> 00:16:56.330
So what is the upside of this idea?

00:16:59.190 --> 00:16:59.900
That that's not.

00:17:02.560 --> 00:17:04.080
So this is even simpler.

00:17:04.080 --> 00:17:05.550
This is like the simplest thing you can

00:17:05.550 --> 00:17:05.705
do.

00:17:05.705 --> 00:17:07.040
You don't even have to look at

00:17:07.040 --> 00:17:09.140
frequencies to select your Vocabulary.

00:17:10.960 --> 00:17:11.380
What else?

00:17:11.380 --> 00:17:13.040
What's another big advantage?

00:17:13.040 --> 00:17:14.160
Can anyone think of another one?

00:17:16.630 --> 00:17:18.760
I really words into a.

00:17:21.340 --> 00:17:24.670
So every single, yeah, like any text

00:17:24.670 --> 00:17:25.500
can be mapped.

00:17:25.500 --> 00:17:27.090
With this, you'll have no unknowns,

00:17:27.090 --> 00:17:27.410
right?

00:17:27.410 --> 00:17:28.700
Because it's covering, because

00:17:28.700 --> 00:17:30.390
everything basically maps to bytes.

00:17:30.390 --> 00:17:32.850
So you can represent anything this way,

00:17:32.850 --> 00:17:34.530
and in fact you can represent other

00:17:34.530 --> 00:17:37.030
modalities as well, yeah.

00:17:37.660 --> 00:17:40.250
Like you said, broken, broken Example.

00:17:40.250 --> 00:17:41.950
Those two were just similar and now

00:17:41.950 --> 00:17:44.100
they'll be actually similar.

00:17:44.100 --> 00:17:45.140
That's right.

00:17:45.140 --> 00:17:47.040
So if you have words that are have

00:17:47.040 --> 00:17:48.930
similar meanings and similar sequences

00:17:48.930 --> 00:17:51.440
of strings, then they'll be like more

00:17:51.440 --> 00:17:52.610
similarly represented.

00:17:53.480 --> 00:17:54.910
What's the disadvantage of this

00:17:54.910 --> 00:17:55.610
approach?

00:17:59.510 --> 00:18:01.340
So the.

00:18:01.740 --> 00:18:03.810
So it's too long, so there's, so that's

00:18:03.810 --> 00:18:06.690
the main disadvantage and also that

00:18:06.690 --> 00:18:07.830
the.

00:18:08.600 --> 00:18:10.390
That I token by itself isn't very

00:18:10.390 --> 00:18:12.320
meaningful, which means that it takes a

00:18:12.320 --> 00:18:14.526
lot more like processing or kind of

00:18:14.526 --> 00:18:16.666
like understanding to make use of this

00:18:16.666 --> 00:18:17.800
kind of representation.

00:18:17.800 --> 00:18:20.030
So if I give you a document and I say

00:18:20.030 --> 00:18:22.251
it has like this many S's and this many

00:18:22.251 --> 00:18:24.218
A's and this many B's like you're going

00:18:24.218 --> 00:18:25.530
to, you're not going to have any idea

00:18:25.530 --> 00:18:26.808
what that means.

00:18:26.808 --> 00:18:29.570
And in general like you need to, then

00:18:29.570 --> 00:18:31.410
you need to consider like jointly

00:18:31.410 --> 00:18:33.180
sequences of characters in order to

00:18:33.180 --> 00:18:34.606
make any sense of it, which means that

00:18:34.606 --> 00:18:36.970
you need like a much more complicated

00:18:36.970 --> 00:18:38.720
kind of processing and representation.

00:18:40.180 --> 00:18:42.650
So I think everything was basically

00:18:42.650 --> 00:18:43.360
mentioned.

00:18:43.360 --> 00:18:46.420
Small Vocabulary, so you could probably

00:18:46.420 --> 00:18:48.925
do less than 100 integers, but at most

00:18:48.925 --> 00:18:52.190
256 simple you can represent any

00:18:52.190 --> 00:18:52.920
document.

00:18:55.210 --> 00:18:58.980
Similar words with will have similar

00:18:58.980 --> 00:19:01.140
sequences, but the count of tokens

00:19:01.140 --> 00:19:02.420
isn't meaningful, and the character

00:19:02.420 --> 00:19:03.380
sequences are long.

00:19:04.770 --> 00:19:06.310
So now finally we've reached the middle

00:19:06.310 --> 00:19:09.300
ground, which is Subword tokenization,

00:19:09.300 --> 00:19:11.980
so mapping each Subword to an integer.

00:19:12.220 --> 00:19:16.300
And so now basically it means that you

00:19:16.300 --> 00:19:20.210
map blocks of frequent characters to

00:19:20.210 --> 00:19:22.340
integers, but those don't necessarily

00:19:22.340 --> 00:19:23.633
need to be a full Word.

00:19:23.633 --> 00:19:25.840
That can be, and with something like

00:19:25.840 --> 00:19:27.290
centerpiece, they can even be more than

00:19:27.290 --> 00:19:29.420
one word that are commonly like put

00:19:29.420 --> 00:19:29.870
together.

00:19:31.430 --> 00:19:32.120
Question.

00:19:34.410 --> 00:19:35.770
If we were mapping based on.

00:19:39.320 --> 00:19:43.815
So at could be 1 integer and then CMB

00:19:43.815 --> 00:19:45.820
could would be another in that case.

00:19:46.700 --> 00:19:47.370
Like 1 Word.

00:19:49.130 --> 00:19:51.630
So Word gets like spread divided into

00:19:51.630 --> 00:19:53.300
multiple integers potentially.

00:19:55.470 --> 00:19:58.460
So for this you can model.

00:19:58.940 --> 00:20:01.490
You can again model any document

00:20:01.490 --> 00:20:03.640
because this will start out as just as

00:20:03.640 --> 00:20:05.220
the Byte representation and then you

00:20:05.220 --> 00:20:07.611
form like groups of bytes and you keep

00:20:07.611 --> 00:20:09.553
you keep like your leaf node

00:20:09.553 --> 00:20:11.507
Representations as well or your Byte

00:20:11.507 --> 00:20:11.830
Representations.

00:20:12.550 --> 00:20:15.220
So you can represent any Word this way,

00:20:15.220 --> 00:20:16.720
but then common words will be

00:20:16.720 --> 00:20:19.960
represented as whole integers and less

00:20:19.960 --> 00:20:22.030
common words will be broken up into a

00:20:22.030 --> 00:20:25.130
set of chunks and also like parts of

00:20:25.130 --> 00:20:26.340
different parts of speech.

00:20:26.340 --> 00:20:29.782
So jump jumped and jumps might be like

00:20:29.782 --> 00:20:33.420
jump followed by Ed or S or.

00:20:34.340 --> 00:20:37.110
Or just the end of the Word.

00:20:39.080 --> 00:20:41.220
Now, the only disadvantage of this is

00:20:41.220 --> 00:20:42.650
that you need to solve for the good

00:20:42.650 --> 00:20:44.290
Subword tokenization, and it's a little

00:20:44.290 --> 00:20:46.070
bit more complicated than just counting

00:20:46.070 --> 00:20:49.550
words or just using characters straight

00:20:49.550 --> 00:20:49.650
up.

00:20:51.500 --> 00:20:53.530
So if we compare these Representations,

00:20:53.530 --> 00:20:55.130
I'll talk about the algorithm for it in

00:20:55.130 --> 00:20:55.470
a minute.

00:20:55.470 --> 00:20:56.880
It's actually pretty simple Algorithm.

00:20:58.040 --> 00:20:59.480
So we if we look at these

00:20:59.480 --> 00:21:02.400
Representations, we can compare them in

00:21:02.400 --> 00:21:03.670
different ways.

00:21:03.670 --> 00:21:05.830
So first, just in terms of

00:21:05.830 --> 00:21:07.670
representation, if we take the chairs

00:21:07.670 --> 00:21:09.880
broken, the character representation

00:21:09.880 --> 00:21:11.480
will just divide it into all the

00:21:11.480 --> 00:21:12.390
characters.

00:21:12.390 --> 00:21:14.817
Subword might represent it as Ch.

00:21:14.817 --> 00:21:17.442
That means that there's Ch and

00:21:17.442 --> 00:21:18.446
something after it.

00:21:18.446 --> 00:21:20.126
And the compound error means that

00:21:20.126 --> 00:21:21.970
there's something before the air.

00:21:21.970 --> 00:21:24.440
So chair is broken.

00:21:25.480 --> 00:21:27.460
So it's divided into 4 sub words here.

00:21:28.100 --> 00:21:29.780
And the Word representation is just

00:21:29.780 --> 00:21:31.460
that you'd have a different integer for

00:21:31.460 --> 00:21:31.980
each word.

00:21:31.980 --> 00:21:33.466
So what I mean by these is that for

00:21:33.466 --> 00:21:34.940
each of these things, between a comma

00:21:34.940 --> 00:21:36.310
there would be a different integer.

00:21:38.100 --> 00:21:40.130
The Vocabulary Size for characters

00:21:40.130 --> 00:21:41.370
would be up to 256.

00:21:41.370 --> 00:21:44.222
For Sub words it typically be 4K to

00:21:44.222 --> 00:21:44.640
50K.

00:21:44.640 --> 00:21:47.390
So GPT for example is 50K.

00:21:48.390 --> 00:21:51.140
But if I remember is like 30 or 40K.

00:21:52.740 --> 00:21:55.670
And Word Representations.

00:21:56.380 --> 00:22:00.470
Are usually you do at least 30 K so

00:22:00.470 --> 00:22:04.700
generally like GPT being 50K is because

00:22:04.700 --> 00:22:05.800
they're trying to model all the

00:22:05.800 --> 00:22:07.050
languages in the world.

00:22:07.620 --> 00:22:10.010
And even if you're modeling English,

00:22:10.010 --> 00:22:11.620
you would usually need a Vocabulary of

00:22:11.620 --> 00:22:13.730
at least 30 K to do the Word

00:22:13.730 --> 00:22:14.710
representation.

00:22:15.400 --> 00:22:18.530
So the so the green means that it's an

00:22:18.530 --> 00:22:20.190
advantage, red is a disadvantage.

00:22:21.950 --> 00:22:23.500
Then if we look at the Completeness.

00:22:24.140 --> 00:22:27.310
So the character in Subword are perfect

00:22:27.310 --> 00:22:28.480
because they can represent all

00:22:28.480 --> 00:22:32.070
Language, but the word is the word

00:22:32.070 --> 00:22:33.320
representation is Incomplete.

00:22:33.320 --> 00:22:34.880
There'll be lots of things marked to

00:22:34.880 --> 00:22:35.820
map to unknown.

00:22:38.140 --> 00:22:39.570
If we think about the independent

00:22:39.570 --> 00:22:42.530
meaningfulness, the characters are bad

00:22:42.530 --> 00:22:44.200
because the letters by themselves don't

00:22:44.200 --> 00:22:45.040
mean anything.

00:22:45.040 --> 00:22:46.410
They're kind of like pixels.

00:22:46.410 --> 00:22:50.060
The Subword is pretty good, so often it

00:22:50.060 --> 00:22:53.000
will be mapped to like single words,

00:22:53.000 --> 00:22:54.710
but some words will be broken up.

00:22:55.460 --> 00:22:57.950
And the word is pretty good.

00:23:00.030 --> 00:23:01.820
And then if we look at sequence length

00:23:01.820 --> 00:23:03.710
then the characters gives you the

00:23:03.710 --> 00:23:05.570
longest sequence so it represent a

00:23:05.570 --> 00:23:06.140
document.

00:23:06.140 --> 00:23:08.780
It will be 1 integer per character.

00:23:08.780 --> 00:23:12.170
Sub words are medium on average when in

00:23:12.170 --> 00:23:14.860
practice people have about 1.4 tokens

00:23:14.860 --> 00:23:17.590
per Word, so many common words will be

00:23:17.590 --> 00:23:19.960
represented with a single token, but

00:23:19.960 --> 00:23:22.645
some words will be broken up and the

00:23:22.645 --> 00:23:26.130
word is the shortest sequence shorter

00:23:26.130 --> 00:23:28.030
than a Subword tokenization.

00:23:30.260 --> 00:23:32.740
And in terms of Encoding Word

00:23:32.740 --> 00:23:35.020
similarity, the characters encodes it

00:23:35.020 --> 00:23:35.610
somewhat.

00:23:35.610 --> 00:23:37.260
Subword I would say is a little better

00:23:37.260 --> 00:23:38.850
because something like broke and broken

00:23:38.850 --> 00:23:42.220
would be like the same, include the

00:23:42.220 --> 00:23:44.310
same Subword plus one more.

00:23:44.310 --> 00:23:46.887
So it's like a shorter way that encodes

00:23:46.887 --> 00:23:50.030
that common the common elements and the

00:23:50.030 --> 00:23:51.890
Word doesn't Encode it at all.

00:23:55.940 --> 00:24:00.520
Now let's see how we can how we can

00:24:00.520 --> 00:24:01.724
learn this Subword Tokenizer.

00:24:01.724 --> 00:24:04.236
So how do we break up chunks of

00:24:04.236 --> 00:24:04.550
characters?

00:24:04.550 --> 00:24:07.270
How do we break up like a text

00:24:07.270 --> 00:24:09.040
documents into chunks of characters so

00:24:09.040 --> 00:24:10.500
that we can represent each chunk with

00:24:10.500 --> 00:24:11.070
an integer?

00:24:11.860 --> 00:24:13.705
The algorithm is really simple.

00:24:13.705 --> 00:24:15.728
It's basically called byte pair

00:24:15.728 --> 00:24:18.800
encoding and all the other like Subword

00:24:18.800 --> 00:24:21.240
tokenization ONS are just like kind of

00:24:21.240 --> 00:24:23.120
tweaks on this idea.

00:24:23.120 --> 00:24:25.810
For example whether you whether you

00:24:25.810 --> 00:24:27.780
first like divide into words using

00:24:27.780 --> 00:24:29.810
spaces or whether you like force

00:24:29.810 --> 00:24:32.360
punctuation to be its own thing.

00:24:32.360 --> 00:24:34.750
But they all use despite pair Encoding.

00:24:34.750 --> 00:24:37.720
The basic idea is that you start with a

00:24:37.720 --> 00:24:39.490
character, assigned it to a unique

00:24:39.490 --> 00:24:41.730
token, so you'll start with 256.

00:24:41.790 --> 00:24:44.930
Tokens, and then you iteratively assign

00:24:44.930 --> 00:24:46.910
a token to the most common pair of

00:24:46.910 --> 00:24:49.490
consecutive tokens until you reach your

00:24:49.490 --> 00:24:50.540
maximum size.

00:24:51.310 --> 00:24:55.760
So as an example, if I have these if my

00:24:55.760 --> 00:24:57.720
initial array of characters is this

00:24:57.720 --> 00:24:59.580
aaabdaaabac?

00:24:59.630 --> 00:25:00.500
PAC.

00:25:01.340 --> 00:25:05.010
Then my most common pair is just a EI

00:25:05.010 --> 00:25:05.578
mean AA.

00:25:05.578 --> 00:25:09.190
So I just replace that by another new

00:25:09.190 --> 00:25:09.940
integer.

00:25:09.940 --> 00:25:11.610
I'm just Representing that by Z.

00:25:11.610 --> 00:25:14.390
So I say aha is.

00:25:14.390 --> 00:25:16.520
Now I'm going to replace all my ahas

00:25:16.520 --> 00:25:17.370
with Z's.

00:25:17.370 --> 00:25:19.498
So this AA becomes Z.

00:25:19.498 --> 00:25:21.199
This AA becomes Z.

00:25:22.670 --> 00:25:26.320
My most common pair is AB.

00:25:26.320 --> 00:25:27.650
There's two abs.

00:25:28.770 --> 00:25:30.300
And sometimes there's ties, and then

00:25:30.300 --> 00:25:31.800
you just like arbitrarily break the

00:25:31.800 --> 00:25:32.130
tie.

00:25:33.030 --> 00:25:35.720
But now I can Replace AB by Y and so

00:25:35.720 --> 00:25:38.186
now I say Y is equal to AB, Z is equal

00:25:38.186 --> 00:25:40.970
to A and I replace all the ABS by's.

00:25:42.290 --> 00:25:46.310
And then my most common pair is ZY and

00:25:46.310 --> 00:25:49.230
so I can replace Y by X and I say X

00:25:49.230 --> 00:25:53.040
equals ZY and now I have this like

00:25:53.040 --> 00:25:53.930
shorter sequence.

00:25:55.560 --> 00:25:56.860
So you can use this for.

00:25:56.860 --> 00:25:58.540
I think it was first proposed for

00:25:58.540 --> 00:26:01.360
justice compression, but here we

00:26:01.360 --> 00:26:02.470
actually want to.

00:26:02.470 --> 00:26:04.500
We care about this dictionary as like a

00:26:04.500 --> 00:26:05.780
way of representing the text.

00:26:08.190 --> 00:26:10.200
Question even though.

00:26:13.650 --> 00:26:15.540
Painter finding is not that easy.

00:26:22.850 --> 00:26:25.860
And it's actually even easier for

00:26:25.860 --> 00:26:28.470
computers I would say, because as

00:26:28.470 --> 00:26:30.030
humans we can do it with a character

00:26:30.030 --> 00:26:30.905
string this long.

00:26:30.905 --> 00:26:33.070
But if you have like a 100 billion

00:26:33.070 --> 00:26:34.790
length character string, then trying to

00:26:34.790 --> 00:26:37.450
find the most common 2 character pairs

00:26:37.450 --> 00:26:38.396
would be hard.

00:26:38.396 --> 00:26:40.605
But for I'll show you the algorithm in

00:26:40.605 --> 00:26:40.890
a minute.

00:26:40.890 --> 00:26:42.520
It's actually not complicated.

00:26:42.520 --> 00:26:44.850
You just iterate through the characters

00:26:44.850 --> 00:26:45.830
and you Count.

00:26:45.830 --> 00:26:48.340
You create a dictionary for each unique

00:26:48.340 --> 00:26:48.930
pair.

00:26:49.030 --> 00:26:51.370
And you count them and then you do

00:26:51.370 --> 00:26:52.910
argmax, so.

00:26:53.620 --> 00:26:57.590
And then so then if I have some string

00:26:57.590 --> 00:26:59.330
like this So what would this represent

00:26:59.330 --> 00:27:00.810
here X ZD?

00:27:11.190 --> 00:27:13.600
So first, what X maps to what?

00:27:15.140 --> 00:27:15.720
OK.

00:27:15.720 --> 00:27:20.850
And then, so I'll have zyzz D and then.

00:27:21.710 --> 00:27:22.550
So.

00:27:25.270 --> 00:27:28.160
Yeah, so right.

00:27:28.160 --> 00:27:28.630
Yep.

00:27:28.630 --> 00:27:32.622
So this becomes a, this becomes AB, and

00:27:32.622 --> 00:27:33.708
this becomes a.

00:27:33.708 --> 00:27:35.560
So AA BA ad.

00:27:36.900 --> 00:27:37.750
So it's easy.

00:27:37.750 --> 00:27:39.845
It's pretty fast to like go.

00:27:39.845 --> 00:27:42.040
So Learning this tokenization takes

00:27:42.040 --> 00:27:42.500
some time.

00:27:42.500 --> 00:27:44.840
But then once you have it, it's fast to

00:27:44.840 --> 00:27:46.690
map into it, and then it's also fast to

00:27:46.690 --> 00:27:48.300
decompress spec into the original

00:27:48.300 --> 00:27:48.870
characters.

00:27:51.560 --> 00:27:55.140
So this is the basic idea of what's

00:27:55.140 --> 00:27:57.210
called the WordPiece Tokenizer.

00:27:57.210 --> 00:28:00.455
So this was first proposed by Sennrich

00:28:00.455 --> 00:28:02.450
and then I think it was wood all that

00:28:02.450 --> 00:28:04.120
gave it the name WordPiece.

00:28:04.120 --> 00:28:05.896
But they just say we did what Sennrich

00:28:05.896 --> 00:28:08.390
did and these papers are both from

00:28:08.390 --> 00:28:09.300
2016.

00:28:10.750 --> 00:28:12.890
So this is like the Algorithm from the

00:28:12.890 --> 00:28:15.731
Sennrich paper, and basically the

00:28:15.731 --> 00:28:18.198
algorithm is just you just go.

00:28:18.198 --> 00:28:20.603
You have like this get stats, which is

00:28:20.603 --> 00:28:22.960
that you create a dictionary, a hash

00:28:22.960 --> 00:28:25.835
table of all pairs of characters.

00:28:25.835 --> 00:28:28.755
For each you go through for each word,

00:28:28.755 --> 00:28:31.572
and for each character and your Word

00:28:31.572 --> 00:28:34.610
you add account for each pair of your

00:28:34.610 --> 00:28:36.170
of characters that you see.

00:28:37.080 --> 00:28:39.720
And then you do best is you get the

00:28:39.720 --> 00:28:42.980
most common pair that you saw in your

00:28:42.980 --> 00:28:45.800
in your in your document or your set of

00:28:45.800 --> 00:28:46.400
documents.

00:28:47.120 --> 00:28:49.652
And then you Merge, which merging means

00:28:49.652 --> 00:28:50.740
that you Replace.

00:28:50.740 --> 00:28:53.180
Anytime you see that pair, you replace

00:28:53.180 --> 00:28:54.760
it by the new token.

00:28:55.800 --> 00:28:57.530
And.

00:28:58.340 --> 00:29:00.230
And then you repeat so then you keep on

00:29:00.230 --> 00:29:00.956
doing that.

00:29:00.956 --> 00:29:02.880
So it takes some time because you have

00:29:02.880 --> 00:29:04.600
to keep looping through your document

00:29:04.600 --> 00:29:07.580
for every single every token that you

00:29:07.580 --> 00:29:08.530
want to add.

00:29:08.530 --> 00:29:10.540
And it's not usually just by document.

00:29:10.540 --> 00:29:12.130
I don't mean that it's like a Word

00:29:12.130 --> 00:29:14.510
document, it's often Wikipedia or

00:29:14.510 --> 00:29:16.640
something like it's a big set of text.

00:29:17.550 --> 00:29:20.273
But it's a pretty simple algorithm, and

00:29:20.273 --> 00:29:22.989
it's not like you do it once and then

00:29:22.990 --> 00:29:24.280
you're done, and then other people can

00:29:24.280 --> 00:29:25.560
use this representation.

00:29:27.760 --> 00:29:28.510
So.

00:29:29.540 --> 00:29:31.060
So you can try it.

00:29:31.060 --> 00:29:33.750
So in this sentence, your cat cannot do

00:29:33.750 --> 00:29:35.130
the, can he?

00:29:36.100 --> 00:29:37.880
What is the?

00:29:37.880 --> 00:29:40.930
What's the first pair that you would

00:29:40.930 --> 00:29:42.450
add a new token for?

00:29:45.520 --> 00:29:47.485
So it could be CA.

00:29:47.485 --> 00:29:48.470
So then.

00:29:49.190 --> 00:29:50.810
So CA would.

00:29:50.810 --> 00:29:54.710
Then I would Replace say CA by I'll

00:29:54.710 --> 00:29:54.920
just.

00:29:55.800 --> 00:29:56.390
Whoops.

00:29:58.190 --> 00:30:00.300
It didn't do any advance, but I'll type

00:30:00.300 --> 00:30:00.680
it here.

00:30:01.710 --> 00:30:03.600
So let's try CAI think there's actually

00:30:03.600 --> 00:30:05.270
2 correct answers, but.

00:30:06.400 --> 00:30:09.890
XTX Xnnot.

00:30:10.680 --> 00:30:15.543
Do the X and this is a little tricky.

00:30:15.543 --> 00:30:17.630
This would it depends how you delimit,

00:30:17.630 --> 00:30:20.660
but assuming that if you do not if you

00:30:20.660 --> 00:30:23.030
delimited by spaces then this would

00:30:23.030 --> 00:30:25.240
this would be fine.

00:30:26.300 --> 00:30:30.130
So here's the here's the did you say

00:30:30.130 --> 00:30:30.680
CA?

00:30:30.680 --> 00:30:31.260
Is that what you said?

00:30:32.780 --> 00:30:35.050
OK, so it depends on.

00:30:35.050 --> 00:30:35.973
It depends.

00:30:35.973 --> 00:30:37.819
So often I forgot.

00:30:37.820 --> 00:30:42.490
One detail that I forgot is that you

00:30:42.490 --> 00:30:45.176
often represent like the start of the

00:30:45.176 --> 00:30:46.370
word or the end of the Word.

00:30:47.250 --> 00:30:50.210
So in the case of like Jet makers, feud

00:30:50.210 --> 00:30:52.240
over seat width with big orders at

00:30:52.240 --> 00:30:52.640
stake.

00:30:53.500 --> 00:30:56.700
It breaks it up into J, but this

00:30:56.700 --> 00:30:58.895
leading character means that J is at

00:30:58.895 --> 00:31:00.127
the start of a Word.

00:31:00.127 --> 00:31:01.950
So you represent like whether a letter

00:31:01.950 --> 00:31:03.480
is at the start of a word or not, so

00:31:03.480 --> 00:31:05.140
that you can tell whether you're like

00:31:05.140 --> 00:31:06.200
going into a new Word.

00:31:07.450 --> 00:31:10.980
So this is like JT under score makers,

00:31:10.980 --> 00:31:13.565
so that's like a whole Word and then

00:31:13.565 --> 00:31:16.840
under score FEUD under score over under

00:31:16.840 --> 00:31:19.060
score, C width and then all these

00:31:19.060 --> 00:31:20.680
common words get their own tokens.

00:31:21.820 --> 00:31:23.930
And so in this case, if we do it the

00:31:23.930 --> 00:31:26.450
same way then basically.

00:31:27.750 --> 00:31:30.150
We start with the first thing that we

00:31:30.150 --> 00:31:30.540
do.

00:31:31.770 --> 00:31:34.010
Is basically do this.

00:31:36.730 --> 00:31:40.570
Cannot do the can.

00:31:41.520 --> 00:31:43.190
Can he?

00:31:48.010 --> 00:31:48.670
And.

00:31:51.490 --> 00:31:51.860
Yeah.

00:31:56.740 --> 00:32:00.210
So let's do it one more time.

00:32:00.210 --> 00:32:00.963
So let's.

00:32:00.963 --> 00:32:02.790
So what is the most common pair now?

00:32:07.980 --> 00:32:16.210
Let's see, 123451234 OK yeah, it is.

00:32:17.010 --> 00:32:17.920
So now I get.

00:32:18.710 --> 00:32:19.660
Your.

00:32:23.010 --> 00:32:23.600
Ynot.

00:32:29.380 --> 00:32:31.640
It's a special bike, yeah.

00:32:31.640 --> 00:32:33.720
So it's like its own bite to represent

00:32:33.720 --> 00:32:33.970
that.

00:32:33.970 --> 00:32:35.950
Like this is basically start of Word.

00:32:36.580 --> 00:32:38.520
And then you get into the.

00:32:39.310 --> 00:32:41.055
And then you get into the characters of

00:32:41.055 --> 00:32:41.480
the Word.

00:32:49.180 --> 00:32:51.220
We have the special bite and then the.

00:32:52.480 --> 00:32:54.800
This could be a group, yeah?

00:32:54.800 --> 00:32:56.810
So you could Merge that like a Word

00:32:56.810 --> 00:32:58.510
often starts with this, essentially.

00:33:01.420 --> 00:33:04.310
Yeah, X and where?

00:33:06.100 --> 00:33:06.520
So for.

00:33:07.940 --> 00:33:09.240
Yeah.

00:33:09.240 --> 00:33:10.045
What did I mean?

00:33:10.045 --> 00:33:10.440
Yeah.

00:33:10.440 --> 00:33:10.810
Thanks.

00:33:11.570 --> 00:33:11.950
That's.

00:33:13.670 --> 00:33:14.180
OK, good.

00:33:14.910 --> 00:33:16.450
Alright, so what's the next one?

00:33:20.950 --> 00:33:24.330
So let's see, there's 1234.

00:33:27.930 --> 00:33:31.250
I think yeah, so it's a tie, right?

00:33:31.250 --> 00:33:32.290
But let's go with XN.

00:33:32.290 --> 00:33:34.610
So it looks like it could be Xnnot or

00:33:34.610 --> 00:33:35.930
it could be under score X.

00:33:36.790 --> 00:33:39.860
But let's do XN and I'll call it a.

00:33:41.300 --> 00:33:46.130
Y so Y not do the.

00:33:47.810 --> 00:33:48.450
Why?

00:33:52.780 --> 00:33:53.650
Yeah.

00:33:55.280 --> 00:33:55.780
Early morning.

00:33:59.040 --> 00:34:00.210
Why?

00:34:01.950 --> 00:34:06.600
Why he OK?

00:34:07.950 --> 00:34:09.530
So I think you get the idea.

00:34:09.530 --> 00:34:10.740
And then you keep doing that.

00:34:10.740 --> 00:34:12.140
Now I'm just doing it with one

00:34:12.140 --> 00:34:14.023
sentence, but again, you'd usually be

00:34:14.023 --> 00:34:16.929
doing it with like a GB of text, so it

00:34:16.930 --> 00:34:19.059
wouldn't be like so.

00:34:20.320 --> 00:34:20.970
Contrived.

00:34:25.260 --> 00:34:26.110
So the main.

00:34:26.190 --> 00:34:30.865
The so this is the basic Algorithm.

00:34:30.865 --> 00:34:32.880
In practice there's often like tweaks

00:34:32.880 --> 00:34:33.260
to it.

00:34:33.260 --> 00:34:35.560
So for example in cent piece you allow

00:34:35.560 --> 00:34:37.720
like different words to be merged

00:34:37.720 --> 00:34:39.770
together because you don't like

00:34:39.770 --> 00:34:41.200
delimited by spaces first.

00:34:42.160 --> 00:34:44.290
Often another thing that's often done

00:34:44.290 --> 00:34:46.700
is that you say that the punctuation

00:34:46.700 --> 00:34:49.560
has to be separate, so that dog with a

00:34:49.560 --> 00:34:51.630
period, dog with a question mark, and

00:34:51.630 --> 00:34:53.350
dog with a comma don't get all mapped

00:34:53.350 --> 00:34:54.330
to different tokens.

00:34:55.200 --> 00:34:58.410
And then there's also sometimes people

00:34:58.410 --> 00:35:00.020
do like a forward and backward pass.

00:35:00.020 --> 00:35:01.110
See Merge.

00:35:02.160 --> 00:35:03.690
And then you.

00:35:04.530 --> 00:35:06.480
And then you can check to see it's a

00:35:06.480 --> 00:35:08.230
greedy algorithm, so you can check to

00:35:08.230 --> 00:35:10.040
see if like some pairs are like not

00:35:10.040 --> 00:35:12.260
needed anymore, and then you can remove

00:35:12.260 --> 00:35:14.060
them and then fill in those tokens.

00:35:14.060 --> 00:35:15.930
But those are all kind of like

00:35:15.930 --> 00:35:17.720
implementation details that are not too

00:35:17.720 --> 00:35:19.240
critical question.

00:35:21.880 --> 00:35:25.360
So if you start with 256 and then

00:35:25.360 --> 00:35:27.590
you're going up to 40,000 for example,

00:35:27.590 --> 00:35:28.940
then it would be almost 40,000.

00:35:28.940 --> 00:35:30.020
So it would be.

00:35:30.020 --> 00:35:32.010
You'd do it for everyone, Merge for

00:35:32.010 --> 00:35:33.200
every new token that you need to

00:35:33.200 --> 00:35:33.730
create.

00:35:35.160 --> 00:35:38.220
So for in the literature, typically

00:35:38.220 --> 00:35:40.600
it's like 30,000 to 50,000 is your

00:35:40.600 --> 00:35:41.770
dictionary Size.

00:35:42.970 --> 00:35:43.340


00:35:49.210 --> 00:35:51.000
So that's Subword tokenization.

00:35:51.000 --> 00:35:54.036
So you map groups of characters in

00:35:54.036 --> 00:35:54.830
integers so that.

00:35:54.830 --> 00:35:56.430
Then you can represent any text as a

00:35:56.430 --> 00:35:58.180
sequence of integers, and the text is

00:35:58.180 --> 00:35:59.030
fully represented.

00:35:59.800 --> 00:36:01.240
But there still isn't like a really

00:36:01.240 --> 00:36:02.450
good way to represent the code

00:36:02.450 --> 00:36:03.310
similarity, right?

00:36:03.310 --> 00:36:04.810
Because you'll end up with like these

00:36:04.810 --> 00:36:08.150
30,000 or 40,000 integers, and there's

00:36:08.150 --> 00:36:09.920
no like relationship between those

00:36:09.920 --> 00:36:10.197
integers.

00:36:10.197 --> 00:36:12.610
Like 4 is not anymore similar to five

00:36:12.610 --> 00:36:14.760
than it is to like 6000.

00:36:16.220 --> 00:36:19.402
So the next idea to try to Encode the

00:36:19.402 --> 00:36:21.802
meaning of the word in a continuous

00:36:21.802 --> 00:36:24.230
Vector, or the meaning of Subword in a

00:36:24.230 --> 00:36:24.850
continuous Vector.

00:36:24.850 --> 00:36:26.530
So first we'll just look at it in terms

00:36:26.530 --> 00:36:27.010
of words.

00:36:28.940 --> 00:36:31.290
And the main idea is to try to learn

00:36:31.290 --> 00:36:33.170
these vectors based on the surrounding

00:36:33.170 --> 00:36:33.700
words.

00:36:34.970 --> 00:36:38.760
So this actually this idea first became

00:36:38.760 --> 00:36:41.120
popular before Subword tokenization

00:36:41.120 --> 00:36:42.233
became popular.

00:36:42.233 --> 00:36:44.540
So it was just operating on full words.

00:36:44.540 --> 00:36:47.160
And one of the key papers is this paper

00:36:47.160 --> 00:36:47.970
Word2Vec.

00:36:48.740 --> 00:36:53.440
And in Word2Vec, for each word you

00:36:53.440 --> 00:36:55.020
solve for some kind of continuous

00:36:55.020 --> 00:36:57.110
representation and they have two

00:36:57.110 --> 00:36:58.160
different ways to do that.

00:36:58.160 --> 00:37:00.065
Essentially you're just trying to

00:37:00.065 --> 00:37:02.700
predict either predict the given like

00:37:02.700 --> 00:37:04.054
say 5 words in a row.

00:37:04.054 --> 00:37:05.913
You either predict the center Word

00:37:05.913 --> 00:37:07.280
given the surrounding words.

00:37:07.990 --> 00:37:09.940
Or you try to predict the surrounding

00:37:09.940 --> 00:37:11.460
words given the center words.

00:37:12.460 --> 00:37:15.660
So in this one, the center bag of words

00:37:15.660 --> 00:37:18.390
I think it is you say that the.

00:37:18.970 --> 00:37:20.949
That you've got first you've got for

00:37:20.950 --> 00:37:23.650
each integer you have some projection

00:37:23.650 --> 00:37:25.980
into for example 100 dimensional

00:37:25.980 --> 00:37:26.460
Vector.

00:37:27.550 --> 00:37:29.940
And then you take your training set and

00:37:29.940 --> 00:37:32.417
divide it up into sets of five words.

00:37:32.417 --> 00:37:35.430
If your window size is, if your T is 2,

00:37:35.430 --> 00:37:37.633
so that your window size is 5.

00:37:37.633 --> 00:37:40.290
And then you say that the center Word

00:37:40.290 --> 00:37:44.930
should be as close to the sum of the

00:37:44.930 --> 00:37:47.380
surrounding words as possible in this

00:37:47.380 --> 00:37:48.580
Vector representation.

00:37:49.260 --> 00:37:51.170
And then you just do like some kind of

00:37:51.170 --> 00:37:53.026
like I think these RMS prop, but some

00:37:53.026 --> 00:37:54.290
kind of like gradient descent,

00:37:54.290 --> 00:37:56.410
subgradient descent to optimize your

00:37:56.410 --> 00:37:58.250
Word vectors under this constraint.

00:37:59.740 --> 00:38:01.684
The other method is called Skip gram.

00:38:01.684 --> 00:38:04.960
So in Skip gram you also divide your

00:38:04.960 --> 00:38:07.390
document into like series of some

00:38:07.390 --> 00:38:08.995
number of words.

00:38:08.995 --> 00:38:11.299
But instead you and again you like

00:38:11.300 --> 00:38:12.636
project your center Word.

00:38:12.636 --> 00:38:14.473
But then based on that projection you

00:38:14.473 --> 00:38:16.200
then again have a linear mapping to

00:38:16.200 --> 00:38:18.300
each of your other words that tries to

00:38:18.300 --> 00:38:20.841
predict which other Word comes, like 2

00:38:20.841 --> 00:38:23.479
tokens before 1 token before or one

00:38:23.479 --> 00:38:25.125
token after two tokens after.

00:38:25.125 --> 00:38:26.772
So this is Skip gram.

00:38:26.772 --> 00:38:28.910
So in this case the average of the

00:38:28.910 --> 00:38:30.430
surrounding words in your Vector

00:38:30.430 --> 00:38:32.220
representation should be the same as

00:38:32.220 --> 00:38:32.970
the center Word.

00:38:33.380 --> 00:38:35.010
In this case, the center Word should

00:38:35.010 --> 00:38:37.340
predict what the linear model after

00:38:37.340 --> 00:38:39.130
it's projected into this Vector

00:38:39.130 --> 00:38:40.155
representation.

00:38:40.155 --> 00:38:43.860
The surrounding words and this can also

00:38:43.860 --> 00:38:46.390
be solved using subgradient descent.

00:38:46.390 --> 00:38:50.150
So these take on the order of like a

00:38:50.150 --> 00:38:51.940
day or two to process typically.

00:38:53.840 --> 00:38:54.420
Question.

00:38:55.570 --> 00:38:55.940
Different.

00:38:58.210 --> 00:38:59.490
Complete their values.

00:39:00.640 --> 00:39:02.710
For example like Skip crap like we have

00:39:02.710 --> 00:39:03.110
to work.

00:39:03.110 --> 00:39:04.210
I don't know, like table.

00:39:05.590 --> 00:39:07.420
The first sentence like the last

00:39:07.420 --> 00:39:09.360
sentence but the probability of the

00:39:09.360 --> 00:39:10.770
Word surrounding the Word table in the.

00:39:12.570 --> 00:39:13.270
It would be different.

00:39:16.510 --> 00:39:17.716
Right.

00:39:17.716 --> 00:39:20.129
Yeah, right.

00:39:20.130 --> 00:39:21.400
So the probability of a Word would

00:39:21.400 --> 00:39:26.310
depend on its on its neighbors and what

00:39:26.310 --> 00:39:28.050
we're trying to do here is we're trying

00:39:28.050 --> 00:39:29.190
to essentially.

00:39:30.060 --> 00:39:31.980
Under that model, where we say that the

00:39:31.980 --> 00:39:33.950
probability of a Word depend depends on

00:39:33.950 --> 00:39:36.140
its neighbors, we're trying to find the

00:39:36.140 --> 00:39:38.130
best continuous representation of each

00:39:38.130 --> 00:39:40.630
word so that likelihood is maximized

00:39:40.630 --> 00:39:42.700
for our training documents.

00:39:48.610 --> 00:39:50.820
So at the end of this you replace each

00:39:50.820 --> 00:39:53.000
word by some fixed length continuous

00:39:53.000 --> 00:39:53.775
Vector.

00:39:53.775 --> 00:39:56.590
And these vectors can predict Word

00:39:56.590 --> 00:39:59.850
relationships, so they test like the

00:39:59.850 --> 00:40:04.050
ability to predict different kinds of

00:40:04.050 --> 00:40:06.085
words based on surrounding text or to

00:40:06.085 --> 00:40:08.230
predict different analogies using this

00:40:08.230 --> 00:40:09.320
representation.

00:40:09.320 --> 00:40:12.710
So it's best to just go ahead and share

00:40:12.710 --> 00:40:13.270
that.

00:40:13.430 --> 00:40:16.280
So what I mean is that for example if

00:40:16.280 --> 00:40:18.865
you take the Word mappings, this is for

00:40:18.865 --> 00:40:22.330
300 dimensional Word vectors for like

00:40:22.330 --> 00:40:23.670
for these different words here.

00:40:24.440 --> 00:40:28.810
And you mathematically do pairs minus

00:40:28.810 --> 00:40:31.350
France plus Italy, then the closest

00:40:31.350 --> 00:40:32.910
Word to that will be Rome.

00:40:33.900 --> 00:40:37.320
Or if you do Paris, if you do Paris

00:40:37.320 --> 00:40:39.806
minus France plus Japan, then the

00:40:39.806 --> 00:40:41.570
closest Word will be Tokyo.

00:40:41.570 --> 00:40:44.119
Or if you do pairs minus France plus

00:40:44.120 --> 00:40:46.459
Florida, then the closest Word will be

00:40:46.460 --> 00:40:47.300
Tallahassee.

00:40:48.690 --> 00:40:50.550
And it works with lots of things.

00:40:50.550 --> 00:40:51.270
So if you do like.

00:40:52.070 --> 00:40:54.889
CU minus copper plus zinc, then you get

00:40:54.890 --> 00:40:55.600
ZN.

00:40:55.600 --> 00:40:58.470
Or if you do France minus Sarkozy plus

00:40:58.470 --> 00:41:00.070
Berlusconi, you get Italy.

00:41:00.770 --> 00:41:02.230
Or Einstein.

00:41:02.230 --> 00:41:04.470
Scientist minus Einstein, plus Messi,

00:41:04.470 --> 00:41:05.560
you get midfielder.

00:41:06.840 --> 00:41:07.920
So it learns.

00:41:07.920 --> 00:41:10.200
It learns the relationships of these

00:41:10.200 --> 00:41:12.230
words in an additive way.

00:41:13.690 --> 00:41:17.860
And there's a cool demo here that I'll

00:41:17.860 --> 00:41:18.085
show.

00:41:18.085 --> 00:41:20.070
There's actually 2 demos, one of them

00:41:20.070 --> 00:41:21.300
I'm not going to do in class.

00:41:22.190 --> 00:41:24.950
But it kind of like explains more like

00:41:24.950 --> 00:41:26.950
how you train the Word Tyvek

00:41:26.950 --> 00:41:27.810
representation.

00:41:28.730 --> 00:41:29.720
And then?

00:41:34.200 --> 00:41:36.240
This one is.

00:41:40.770 --> 00:41:42.550
This one is like visualizing.

00:41:56.170 --> 00:41:58.340
It takes a little bit of time to

00:41:58.340 --> 00:41:59.360
download the model.

00:42:02.190 --> 00:42:04.300
So it's going to show is like.

00:42:04.300 --> 00:42:07.030
It's gonna show initially some set of

00:42:07.030 --> 00:42:09.140
words like represented in a 3D space.

00:42:09.140 --> 00:42:12.350
They projected the Word2Vec dimensions

00:42:12.350 --> 00:42:13.770
down into 3 axes.

00:42:14.690 --> 00:42:16.990
And then you can add additional words

00:42:16.990 --> 00:42:19.410
in that space and see where they lie

00:42:19.410 --> 00:42:22.250
compared to other words, and you can

00:42:22.250 --> 00:42:24.530
create your own analogies.

00:42:36.930 --> 00:42:38.830
So I was going to take a 2 minute break

00:42:38.830 --> 00:42:40.766
after showing you this, but let's take

00:42:40.766 --> 00:42:42.750
a 2 minute break now, and then I'll

00:42:42.750 --> 00:42:44.220
show it to you and you can try to think

00:42:44.220 --> 00:42:45.710
of analogies that you might want to

00:42:45.710 --> 00:42:46.260
see.

00:42:47.790 --> 00:42:50.020
It took like a couple minutes last time

00:42:50.020 --> 00:42:51.630
I downloaded it on my phone, but.

00:42:52.800 --> 00:42:53.980
Maybe it always takes a couple of

00:42:53.980 --> 00:42:54.430
minutes.

00:42:56.130 --> 00:42:58.110
Count ask something involved a back

00:42:58.110 --> 00:42:59.950
that propagate in the.

00:43:01.080 --> 00:43:05.510
In the multi layer perception, I want

00:43:05.510 --> 00:43:07.930
to copy some of functioning of torch.

00:43:07.930 --> 00:43:13.810
So Forward is just putting the vectors

00:43:13.810 --> 00:43:18.480
into the into the weights and getting

00:43:18.480 --> 00:43:22.790
the result by sequential step so.

00:43:23.730 --> 00:43:26.070
How to how do we backtrack some

00:43:26.070 --> 00:43:30.270
something from the Result so the loss

00:43:30.270 --> 00:43:33.350
and update the weight into the

00:43:33.350 --> 00:43:34.120
previously?

00:43:36.040 --> 00:43:36.580
Typically.

00:43:38.790 --> 00:43:40.480
And so the.

00:43:41.080 --> 00:43:46.110
So mathematically it's by the chain

00:43:46.110 --> 00:43:47.510
rule and the partial derivatives.

00:43:49.550 --> 00:43:52.540
Algorithmically, you.

00:43:52.980 --> 00:43:55.300
You compute the gradient for each

00:43:55.300 --> 00:43:57.680
previous layer, and then the gradient

00:43:57.680 --> 00:43:59.995
for the layer below that will be like

00:43:59.995 --> 00:44:01.760
the gradient of the subsequent layer

00:44:01.760 --> 00:44:05.110
times like how much that each weight

00:44:05.110 --> 00:44:06.409
influence that gradient.

00:44:08.090 --> 00:44:08.780


00:44:10.890 --> 00:44:13.510
I go ahead and I can't draw it that

00:44:13.510 --> 00:44:14.060
quickly, but.

00:44:15.780 --> 00:44:17.770
Attention 20 like that just means.

00:44:21.840 --> 00:44:22.750
Simple models.

00:44:22.750 --> 00:44:24.030
So let.

00:44:24.030 --> 00:44:26.430
Let's say that we use Radu.

00:44:26.430 --> 00:44:28.320
So this will.

00:44:28.320 --> 00:44:30.350
This will work as.

00:44:31.720 --> 00:44:32.670
Loss here.

00:44:33.420 --> 00:44:36.310
And how can we update the weight here?

00:44:38.000 --> 00:44:39.070
This process.

00:44:39.480 --> 00:44:40.340
And.

00:44:41.080 --> 00:44:41.530
Kind of.

00:44:41.860 --> 00:44:42.390
Connected.

00:44:44.240 --> 00:44:44.610
90.

00:44:45.310 --> 00:44:47.690
So here you would compute the gradient

00:44:47.690 --> 00:44:52.370
of the error with respect to the output

00:44:52.370 --> 00:44:54.976
here and then you can compute the

00:44:54.976 --> 00:44:56.676
partial derivative of that with respect

00:44:56.676 --> 00:44:57.567
to this weight.

00:44:57.567 --> 00:45:00.540
And then you take like you subtract

00:45:00.540 --> 00:45:02.450
that partial derivative time some step

00:45:02.450 --> 00:45:03.540
size from the weight.

00:45:05.410 --> 00:45:07.489
I'm sorry, this usually takes like 20

00:45:07.490 --> 00:45:09.360
or 30 minutes to explain, so it's hard

00:45:09.360 --> 00:45:11.790
to cover it really quickly.

00:45:11.790 --> 00:45:13.896
That's OK alright, I'm going to let

00:45:13.896 --> 00:45:16.220
this keep Downloading I guess, and go

00:45:16.220 --> 00:45:17.603
on and I'll try to keep.

00:45:17.603 --> 00:45:18.737
I'll come back to it.

00:45:18.737 --> 00:45:20.130
I don't know, it's taking even longer

00:45:20.130 --> 00:45:21.555
than it took on my phone, but it did.

00:45:21.555 --> 00:45:23.160
I did test that it works, so hopefully

00:45:23.160 --> 00:45:25.770
it will wait, there's something.

00:45:25.770 --> 00:45:27.370
No, it's still downloading the model.

00:45:27.370 --> 00:45:29.060
Let me just check.

00:45:31.390 --> 00:45:32.140
Relationship.

00:45:35.210 --> 00:45:36.340
That doesn't look good.

00:45:38.470 --> 00:45:40.020
Let's try refreshing.

00:45:42.200 --> 00:45:43.850
No, come on.

00:45:47.890 --> 00:45:48.820
Maybe if I go here.

00:45:49.520 --> 00:45:50.270
12.

00:45:51.890 --> 00:45:53.860
No, that's not what I wanted.

00:45:55.190 --> 00:45:56.470
Let me Experiments.

00:46:06.930 --> 00:46:08.150
No, I used.

00:46:08.150 --> 00:46:10.300
I did use my phone before.

00:46:12.680 --> 00:46:14.810
You can try it if I have one.

00:46:18.790 --> 00:46:21.320
If I cannot get this to work soon, I

00:46:21.320 --> 00:46:21.910
will just.

00:46:23.260 --> 00:46:23.980
Move on.

00:46:50.910 --> 00:46:51.720
That doesn't look good.

00:46:51.720 --> 00:46:54.300
OK, I think I might have to move on.

00:46:54.300 --> 00:46:55.730
Sorry, I'm not sure why it's not

00:46:55.730 --> 00:46:56.340
working.

00:47:00.760 --> 00:47:03.200
But maybe you can get that to work.

00:47:03.200 --> 00:47:05.097
Basically it shows all the points and

00:47:05.097 --> 00:47:07.112
then you can add additional words and

00:47:07.112 --> 00:47:08.337
then you can create your own analogies

00:47:08.337 --> 00:47:10.830
and then it will show like the vectors

00:47:10.830 --> 00:47:13.620
and show how it compared how it which

00:47:13.620 --> 00:47:15.080
word is most similar in your

00:47:15.080 --> 00:47:15.690
dictionary.

00:47:17.090 --> 00:47:20.926
So the so the really amazing thing

00:47:20.926 --> 00:47:23.642
about this to me is that it's just like

00:47:23.642 --> 00:47:25.200
the idea about thinking of words in a

00:47:25.200 --> 00:47:27.352
continuous space instead of thinking of

00:47:27.352 --> 00:47:28.860
words as like a discrete thing.

00:47:28.860 --> 00:47:31.140
And the idea that you can like add and

00:47:31.140 --> 00:47:33.000
subtract and perform mathematical

00:47:33.000 --> 00:47:34.950
operations on words and then it makes

00:47:34.950 --> 00:47:37.140
sense like that the corresponding, it

00:47:37.140 --> 00:47:39.050
performs analogies that way like pretty

00:47:39.050 --> 00:47:39.770
accurately.

00:47:39.770 --> 00:47:42.650
That was all like kind of crazy.

00:47:42.650 --> 00:47:46.420
And so this Word2Vec representation or.

00:47:46.470 --> 00:47:48.980
And similar kinds of Word embeddings

00:47:48.980 --> 00:47:51.136
represent that language is really in a

00:47:51.136 --> 00:47:52.010
continuous space.

00:47:52.010 --> 00:47:53.955
Words don't have a discrete meaning,

00:47:53.955 --> 00:47:55.500
they actually have like a lot of

00:47:55.500 --> 00:47:56.200
different meanings.

00:47:56.200 --> 00:47:58.260
And they have like some similarity to

00:47:58.260 --> 00:48:02.125
other words and differences in that

00:48:02.125 --> 00:48:03.820
words can be combined to mean new

00:48:03.820 --> 00:48:04.490
things.

00:48:04.490 --> 00:48:06.490
And so all of this is represented

00:48:06.490 --> 00:48:09.245
mathematically just by mapping the

00:48:09.245 --> 00:48:10.920
words into these big continuous

00:48:10.920 --> 00:48:11.790
vectors.

00:48:11.790 --> 00:48:15.290
So in such a way that you can either

00:48:15.290 --> 00:48:17.150
predict words by averaging.

00:48:17.210 --> 00:48:18.710
The surrounding words, or you can

00:48:18.710 --> 00:48:20.550
predict them through linear models.

00:48:26.460 --> 00:48:27.990
So.

00:48:28.110 --> 00:48:33.065
So it's like they trained the model on

00:48:33.065 --> 00:48:34.660
783,000,000 words with the other

00:48:34.660 --> 00:48:35.050
dimension.

00:48:39.360 --> 00:48:40.910
Like where these books that they were

00:48:40.910 --> 00:48:41.800
training on or?

00:48:43.020 --> 00:48:46.569
It may be I forget now, but it may have

00:48:46.569 --> 00:48:47.864
been the books corpus.

00:48:47.864 --> 00:48:49.830
The books corpus is one thing that's

00:48:49.830 --> 00:48:52.584
commonly used, which is just a bunch of

00:48:52.584 --> 00:48:54.980
books, but some there's a lot of

00:48:54.980 --> 00:48:56.922
there's a bunch of big repositories of

00:48:56.922 --> 00:48:59.270
data, like the Wall Street Journal

00:48:59.270 --> 00:49:01.410
books, Wikipedia.

00:49:01.410 --> 00:49:04.213
So there's like a lot of data sets that

00:49:04.213 --> 00:49:06.920
have been created and like packaged up

00:49:06.920 --> 00:49:08.189
nicely for this kind of thing.

00:49:11.520 --> 00:49:12.140
Question.

00:49:13.530 --> 00:49:14.680
You got it open.

00:49:14.680 --> 00:49:15.600
OK, cool.

00:49:17.380 --> 00:49:21.070
Do you are you able to connect to HDMI?

00:49:34.070 --> 00:49:34.640
All right.

00:49:39.100 --> 00:49:40.080
Alright, thanks.

00:49:40.080 --> 00:49:43.560
So yeah, so you can see that it's

00:49:43.560 --> 00:49:46.400
Representing like it's a bunch of

00:49:46.400 --> 00:49:49.980
mainly mother, wife, husband, daughter,

00:49:49.980 --> 00:49:51.320
Princess, so.

00:49:52.030 --> 00:49:53.360
Different genders.

00:49:53.360 --> 00:49:56.070
They're plotting it on gender, age and

00:49:56.070 --> 00:49:56.700
residual.

00:49:56.700 --> 00:49:57.610
So a difference.

00:49:58.910 --> 00:50:01.030
Another third Vector that everything

00:50:01.030 --> 00:50:03.925
else projects into, and then things

00:50:03.925 --> 00:50:06.510
like chair and computer which are just

00:50:06.510 --> 00:50:07.340
purely residual.

00:50:08.290 --> 00:50:10.180
And then you can see the actual Vector

00:50:10.180 --> 00:50:11.800
Representations here.

00:50:11.800 --> 00:50:14.290
So it's like 300 dimensional Word2Vec

00:50:14.290 --> 00:50:14.840
vectors.

00:50:15.690 --> 00:50:19.150
And then you can add words.

00:50:19.150 --> 00:50:22.060
So for example if I do.

00:50:23.030 --> 00:50:25.260
I can add dog.

00:50:26.830 --> 00:50:28.010
And puppy.

00:50:31.940 --> 00:50:33.280
And then if I.

00:50:34.170 --> 00:50:35.160
Do.

00:50:37.460 --> 00:50:38.420
Scroll down a little bit.

00:50:45.540 --> 00:50:48.240
So if I do for example.

00:50:49.550 --> 00:50:50.410
So this where I type.

00:50:50.410 --> 00:50:50.880
Yeah.

00:50:50.880 --> 00:50:53.840
So if I say man is to.

00:50:56.220 --> 00:50:57.160
Boy.

00:50:58.200 --> 00:51:00.340
As dog is to.

00:51:03.330 --> 00:51:05.690
And I think I understand where I

00:51:05.690 --> 00:51:07.430
pressed submit.

00:51:07.430 --> 00:51:09.040
Come on, don't be such a pain.

00:51:09.040 --> 00:51:10.740
There it goes.

00:51:10.740 --> 00:51:11.456
Just took awhile.

00:51:11.456 --> 00:51:13.550
So then so I said, man is the boy as

00:51:13.550 --> 00:51:14.260
dog is to.

00:51:14.260 --> 00:51:16.510
And then it comes out with puppy and

00:51:16.510 --> 00:51:17.975
you can see the vectors here.

00:51:17.975 --> 00:51:18.350
So.

00:51:19.190 --> 00:51:22.720
Man, the Vector of man to boy is being

00:51:22.720 --> 00:51:23.870
added to dog.

00:51:24.740 --> 00:51:28.570
And then that comes out OK.

00:51:29.370 --> 00:51:32.130
That comes out pretty close to puppy

00:51:32.130 --> 00:51:32.720
this.

00:51:34.440 --> 00:51:36.530
This site seems to be like having some

00:51:36.530 --> 00:51:37.350
problems today.

00:51:37.350 --> 00:51:38.650
It's just kind of slow.

00:51:40.210 --> 00:51:40.580
Data.

00:51:42.520 --> 00:51:44.440
So does anyone else have one to try

00:51:44.440 --> 00:51:45.659
that you'd like me to try?

00:51:46.700 --> 00:51:49.590
This is say, there we go.

00:51:49.590 --> 00:51:53.170
It's just like very having problems.

00:51:55.360 --> 00:51:56.850
I can try one more though, if somebody

00:51:56.850 --> 00:51:57.850
has one.

00:51:57.850 --> 00:51:59.475
Does anyone else have a set of words in

00:51:59.475 --> 00:52:00.310
a analogy?

00:52:02.840 --> 00:52:03.290
OK.

00:52:05.610 --> 00:52:06.180
Kanji.

00:52:06.590 --> 00:52:07.660
Let's see if she can.

00:52:10.210 --> 00:52:11.820
Others in but what's yours?

00:52:11.820 --> 00:52:12.145
Said?

00:52:12.145 --> 00:52:12.740
What's your?

00:52:15.810 --> 00:52:17.290
Cockroaches to Mexican.

00:52:21.740 --> 00:52:22.290
OK.

00:52:23.830 --> 00:52:26.270
So I'll Add tackers.

00:52:27.500 --> 00:52:28.910
Mexican.

00:52:33.590 --> 00:52:40.840
Pizza and Italian.

00:52:43.730 --> 00:52:45.540
Tell me.

00:52:50.000 --> 00:52:51.190
Right, so tacos.

00:52:51.330 --> 00:52:51.680
I.

00:52:52.830 --> 00:52:55.440
Tacos is to pizza.

00:52:55.440 --> 00:52:58.630
And I think like when they do this test

00:52:58.630 --> 00:53:00.177
they have like they're not doing it out

00:53:00.177 --> 00:53:02.020
of all 30,000 words or whatever.

00:53:02.020 --> 00:53:03.880
I think they're doing it out of some

00:53:03.880 --> 00:53:05.050
Sub candidates.

00:53:05.050 --> 00:53:06.600
So kind of like what we're doing here.

00:53:07.470 --> 00:53:10.630
As tacos is the pizza as what?

00:53:14.280 --> 00:53:15.830
Talker system Mexican.

00:53:19.930 --> 00:53:20.360
Pizza.

00:53:23.370 --> 00:53:24.460
It should work.

00:53:24.460 --> 00:53:26.309
It's just Add addition, so it should

00:53:26.310 --> 00:53:26.630
be.

00:53:27.450 --> 00:53:29.600
It should be recompose able.

00:53:30.730 --> 00:53:31.670
Alright.

00:53:31.670 --> 00:53:33.480
And then I never understand, like which

00:53:33.480 --> 00:53:36.090
one they're asking me to press them on.

00:53:39.490 --> 00:53:43.820
I'm supposed to do what is it, pizza.

00:53:46.240 --> 00:53:47.450
OK, I'll try it.

00:53:55.780 --> 00:53:57.320
Alright, let me try to fix that.

00:53:58.330 --> 00:53:58.970


00:54:00.730 --> 00:54:02.120
This Demo is killing me.

00:54:06.180 --> 00:54:07.300
There we go.

00:54:07.300 --> 00:54:08.270
All right, pizza.

00:54:17.280 --> 00:54:18.870
I think it's just processing.

00:54:20.970 --> 00:54:21.700
OK, there we go.

00:54:21.700 --> 00:54:22.880
Pizza is 2 Italian.

00:54:25.650 --> 00:54:28.230
I want to I'm going to have to go with

00:54:28.230 --> 00:54:30.310
other things, but do do feel free to

00:54:30.310 --> 00:54:30.940
try.

00:54:36.310 --> 00:54:37.200
Alright, thank you.

00:54:43.600 --> 00:54:44.770
What was your analogy?

00:54:44.770 --> 00:54:47.110
Chicken is to basketball as what?

00:54:49.690 --> 00:54:51.130
It just like makes something up and see

00:54:51.130 --> 00:54:52.890
what it comes up with, yeah.

00:55:08.580 --> 00:55:10.890
So now we're going to talk about

00:55:10.890 --> 00:55:11.560
Attention.

00:55:12.310 --> 00:55:16.395
And so far we've talked about linear

00:55:16.395 --> 00:55:18.260
linear processing.

00:55:18.260 --> 00:55:20.180
You just take some set of features and

00:55:20.180 --> 00:55:22.220
you multiply it by weights and sum up

00:55:22.220 --> 00:55:24.850
the sum of the product.

00:55:25.710 --> 00:55:28.520
We talked about Convolution, which is

00:55:28.520 --> 00:55:30.421
basically just when you apply a linear

00:55:30.421 --> 00:55:31.440
operator over Windows.

00:55:31.440 --> 00:55:33.340
So you can even do this in text as

00:55:33.340 --> 00:55:33.650
well.

00:55:33.650 --> 00:55:36.250
But for images you Apply within like

00:55:36.250 --> 00:55:39.009
little pixel patches, you apply the

00:55:39.010 --> 00:55:41.290
same linear operator to each patch and

00:55:41.290 --> 00:55:42.700
return the result, and then you get

00:55:42.700 --> 00:55:44.600
back like a new map of features.

00:55:45.940 --> 00:55:47.570
So now we're going to introduce a brand

00:55:47.570 --> 00:55:51.860
new type of kind of processing, which

00:55:51.860 --> 00:55:54.086
is called Attention and the basic idea

00:55:54.086 --> 00:55:54.759
of Attention.

00:55:55.660 --> 00:55:58.310
Is that you're given a set of key value

00:55:58.310 --> 00:56:01.650
pairs, and I'll explain what that means

00:56:01.650 --> 00:56:04.150
in the next slide and a query, and then

00:56:04.150 --> 00:56:07.145
the output of the Attention model or of

00:56:07.145 --> 00:56:09.400
the Attention function is a sum of the

00:56:09.400 --> 00:56:11.260
values weighted by the key query

00:56:11.260 --> 00:56:11.960
similarity.

00:56:14.930 --> 00:56:15.960
So.

00:56:17.530 --> 00:56:21.920
The in Cross Attention you have like a

00:56:21.920 --> 00:56:23.060
key value pair.

00:56:23.060 --> 00:56:25.540
So the where the key is used for

00:56:25.540 --> 00:56:27.109
matching and the value is used to

00:56:27.110 --> 00:56:27.840
output.

00:56:27.840 --> 00:56:30.109
So one example is that the key could be

00:56:30.110 --> 00:56:31.780
your features and the value could be

00:56:31.780 --> 00:56:33.170
the thing that you want to predict.

00:56:34.130 --> 00:56:36.140
And then you have some query which is

00:56:36.140 --> 00:56:37.950
something that you want to compute a

00:56:37.950 --> 00:56:38.750
value for.

00:56:39.620 --> 00:56:42.052
And you use the query, you match the

00:56:42.052 --> 00:56:44.920
query to the keys, and then you sum the

00:56:44.920 --> 00:56:47.800
values based on those similarities to

00:56:47.800 --> 00:56:50.700
get your value for the query.

00:56:50.700 --> 00:56:52.410
So mathematically, it's kind of like

00:56:52.410 --> 00:56:54.010
simpler mathematically than it is

00:56:54.010 --> 00:56:54.520
verbally.

00:56:55.260 --> 00:56:58.140
So mathematically you have some

00:56:58.140 --> 00:56:59.810
similarity function that says how

00:56:59.810 --> 00:57:02.150
similar some key is to some query.

00:57:02.150 --> 00:57:03.820
So this could be like a dot Product for

00:57:03.820 --> 00:57:04.390
example.

00:57:05.900 --> 00:57:08.800
Or you can distance or 1 divided by

00:57:08.800 --> 00:57:10.760
Euclidean distance and then you have

00:57:10.760 --> 00:57:14.915
your values and you take this sum over

00:57:14.915 --> 00:57:17.580
the similarity of each key times the

00:57:17.580 --> 00:57:19.920
query and multiply it by the value.

00:57:20.810 --> 00:57:22.570
And then you normalize it or divide it

00:57:22.570 --> 00:57:24.530
by the sum of all those similarities,

00:57:24.530 --> 00:57:26.640
which is like equivalent to making

00:57:26.640 --> 00:57:28.320
these similarities sum to one.

00:57:29.130 --> 00:57:33.950
So the output value for Q will just be

00:57:33.950 --> 00:57:37.240
a weighted average of the input values,

00:57:37.240 --> 00:57:39.315
where the weights are proportional to

00:57:39.315 --> 00:57:40.150
the similarity.

00:57:44.090 --> 00:57:46.030
So let's see it for some simple

00:57:46.030 --> 00:57:46.960
examples.

00:57:48.140 --> 00:57:49.830
So let's say that our similarity

00:57:49.830 --> 00:57:52.900
function is just 1 / K -, Q ^2.

00:57:54.890 --> 00:57:57.280
And I've got these key value pairs.

00:57:57.280 --> 00:57:59.976
So here maybe this is a label like one

00:57:59.976 --> 00:58:00.907
-, 1.

00:58:00.907 --> 00:58:03.991
And I've got one Feature here 175.

00:58:03.991 --> 00:58:07.487
So this is like one data element, this

00:58:07.487 --> 00:58:09.836
is the key and this is the value.

00:58:09.836 --> 00:58:11.692
And then this is another key and its

00:58:11.692 --> 00:58:13.339
value and another key and its value.

00:58:14.580 --> 00:58:17.550
And then I've got some query which is

00:58:17.550 --> 00:58:18.350
4.

00:58:19.330 --> 00:58:22.560
So I'm going to compare query to each

00:58:22.560 --> 00:58:26.736
of these keys 175, so the distance K -,

00:58:26.736 --> 00:58:30.443
Q for the first one is 3, so K 1 / K -,

00:58:30.443 --> 00:58:32.600
Q ^2 is 1 / 3 ^2.

00:58:33.370 --> 00:58:35.190
Then I multiply it by the value.

00:58:36.390 --> 00:58:38.810
Then I have 7 -, 4 ^2.

00:58:40.360 --> 00:58:43.400
Multiply that by the value -, 1, and

00:58:43.400 --> 00:58:45.680
then 5 -, 4, ^2, 1.

00:58:45.680 --> 00:58:48.720
Over that, multiply it by the value -,

00:58:48.720 --> 00:58:51.730
1 and then I divide it by each of these

00:58:51.730 --> 00:58:54.891
like similarities 1 / 3 ^2 1 / 3, ^2, 1

00:58:54.891 --> 00:58:59.019
/ 1 ^2 and then the output is -, 8.18.

00:58:59.020 --> 00:59:01.536
So this query was closer to the

00:59:01.536 --> 00:59:02.420
negative numbers.

00:59:03.750 --> 00:59:05.260
Then or at least closer to this

00:59:05.260 --> 00:59:08.050
negative, then there's five number then

00:59:08.050 --> 00:59:10.260
it was to the positive number.

00:59:11.090 --> 00:59:13.670
And so the output is negative of

00:59:13.670 --> 00:59:15.440
corresponding to the value here.

00:59:15.440 --> 00:59:17.760
So these two end up canceling out

00:59:17.760 --> 00:59:19.514
because they're equally far away, and

00:59:19.514 --> 00:59:21.261
one has a value of 1 and one has a

00:59:21.261 --> 00:59:21.959
value of -, 1.

00:59:22.570 --> 00:59:26.065
And then this one has more influence.

00:59:26.065 --> 00:59:27.750
They sort of cancel, they cancel out

00:59:27.750 --> 00:59:29.620
and the numerator, but they still get

00:59:29.620 --> 00:59:31.190
wait, so they still appear in the

00:59:31.190 --> 00:59:31.720
denominator.

00:59:34.550 --> 00:59:37.330
As another example, if my input is 0,

00:59:37.330 --> 00:59:40.290
then the distance to this is 1 / 1 ^2.

00:59:40.290 --> 00:59:41.090
For this it's.

00:59:42.440 --> 00:59:43.610
OK, did that wrong.

00:59:43.610 --> 00:59:47.109
Should be 1 / 7 squared and for this it

00:59:47.109 --> 00:59:47.523
should be.

00:59:47.523 --> 00:59:49.210
For some reason I change it to A1 when

00:59:49.210 --> 00:59:50.793
I was calculating here, but this should

00:59:50.793 --> 00:59:51.800
be 1 / 5 ^2.

00:59:52.510 --> 00:59:55.200
And then I so I compute the similarity

00:59:55.200 --> 00:59:58.200
to each of these, so it's, so it's

00:59:58.200 --> 00:59:59.637
11140 nine 125th.

00:59:59.637 --> 01:00:02.125
And then the value is one negative one

01:00:02.125 --> 01:00:02.567
-, 1.

01:00:02.567 --> 01:00:04.405
So I made a mistake here when I did it

01:00:04.405 --> 01:00:06.980
by hand, but you get the idea I hope.

01:00:06.980 --> 01:00:08.370
And then I divide by the sum of

01:00:08.370 --> 01:00:11.055
similarities and then the output is

01:00:11.055 --> 01:00:12.130
.834.

01:00:13.100 --> 01:00:14.630
Which makes sense, because it's closer

01:00:14.630 --> 01:00:16.160
to this one than it is to the negative

01:00:16.160 --> 01:00:16.500
ones.

01:00:23.780 --> 01:00:24.890
If the query.

01:00:24.890 --> 01:00:28.020
So my similarity function was not the

01:00:28.020 --> 01:00:29.660
best similarity function for that

01:00:29.660 --> 01:00:32.510
reason, so I change it and when I do

01:00:32.510 --> 01:00:34.610
Self Attention I change the similarity

01:00:34.610 --> 01:00:36.380
function to plus one on the bottom so I

01:00:36.380 --> 01:00:37.690
don't have to divide by zero.

01:00:37.690 --> 01:00:38.570
But yeah.

01:00:39.470 --> 01:00:40.810
And here I'm just using.

01:00:40.810 --> 01:00:42.840
You'll see in practice a different

01:00:42.840 --> 01:00:44.450
similarity function is usually used,

01:00:44.450 --> 01:00:46.110
but it's hard to like manually compute,

01:00:46.110 --> 01:00:48.130
so I am using a very simple one here.

01:00:49.510 --> 01:00:52.160
So this is Cross Attention is basically

01:00:52.160 --> 01:00:55.280
that to get the.

01:00:55.360 --> 01:00:57.680
To get the value of some query, you

01:00:57.680 --> 01:01:00.159
compute the similarity of the query to

01:01:00.160 --> 01:01:02.170
each of the keys, and then you take a

01:01:02.170 --> 01:01:04.065
weighted average of the values that's

01:01:04.065 --> 01:01:05.870
weighted by the key query similarity.

01:01:07.360 --> 01:01:11.240
Self Attention is that the key is equal

01:01:11.240 --> 01:01:14.060
to the value and each key is also a

01:01:14.060 --> 01:01:14.710
query.

01:01:14.710 --> 01:01:16.920
So in other words, you just have like a

01:01:16.920 --> 01:01:19.557
group, you just have like a bunch of

01:01:19.557 --> 01:01:21.912
values and you match those values to

01:01:21.912 --> 01:01:23.430
each other and you take a weighted

01:01:23.430 --> 01:01:24.840
average of those values according to

01:01:24.840 --> 01:01:25.740
how similar they are.

01:01:26.630 --> 01:01:28.110
And as you'll see, it's like a kind of

01:01:28.110 --> 01:01:28.890
clustering.

01:01:29.920 --> 01:01:31.620
Here are my Input.

01:01:31.620 --> 01:01:35.450
Can just be 3 numbers and each of these

01:01:35.450 --> 01:01:38.190
I will treat as a key and a query pair

01:01:38.190 --> 01:01:42.150
so I'll have like 117755 and I also

01:01:42.150 --> 01:01:45.047
have three queries which are like 1-7

01:01:45.047 --> 01:01:45.876
and five.

01:01:45.876 --> 01:01:48.810
So here I did the computation out for

01:01:48.810 --> 01:01:51.270
the query one so I get one.

01:01:51.380 --> 01:01:59.662
So I get 1 / 1 * 1 + 1 / 6 ^2 + 1 * 7 +

01:01:59.662 --> 01:02:03.450
1 / 4 ^2 * + 1 * 5.

01:02:04.140 --> 01:02:06.210
And then divide by the similarities.

01:02:06.800 --> 01:02:12.174
And I get 1.11 point 3-7 and then if I

01:02:12.174 --> 01:02:14.616
do it for seven I get 6.54 and if I do

01:02:14.616 --> 01:02:15.060
it for.

01:02:16.470 --> 01:02:18.180
Five, I get 5.13.

01:02:19.510 --> 01:02:21.120
And I can apply iteratively.

01:02:21.120 --> 01:02:23.480
So if I apply it again the same exact

01:02:23.480 --> 01:02:26.132
operation but now on these values of

01:02:26.132 --> 01:02:28.210
1.376 point 545.13.

01:02:28.850 --> 01:02:30.900
Then I get this, and then I do it again

01:02:30.900 --> 01:02:33.420
and you can see that it's like quickly

01:02:33.420 --> 01:02:35.330
bringing the seven and the five close

01:02:35.330 --> 01:02:35.760
together.

01:02:35.760 --> 01:02:38.387
And it's also in the case of the

01:02:38.387 --> 01:02:39.642
similarity function, like bringing

01:02:39.642 --> 01:02:40.270
everything together.

01:02:40.270 --> 01:02:42.660
So it's kind of doing a clustering, but

01:02:42.660 --> 01:02:44.620
where it brings it depends on my

01:02:44.620 --> 01:02:46.360
similarity function, but it brings like

01:02:46.360 --> 01:02:49.106
very similar things very close

01:02:49.106 --> 01:02:49.788
together.

01:02:49.788 --> 01:02:52.340
And over time if I do enough of it will

01:02:52.340 --> 01:02:53.980
bring like everything close together.

01:02:55.170 --> 01:02:56.770
So here's another example where my

01:02:56.770 --> 01:03:01.329
input is 1982 and here's after one

01:03:01.330 --> 01:03:04.118
iteration, 2 iterations, 3 iterations,

01:03:04.118 --> 01:03:05.152
4 iterations.

01:03:05.152 --> 01:03:07.395
So you can see that after just two

01:03:07.395 --> 01:03:09.000
iterations, it's essentially brought

01:03:09.000 --> 01:03:11.189
the nine and the eight to be the same

01:03:11.189 --> 01:03:13.623
value and the one and the two to be the

01:03:13.623 --> 01:03:14.109
same value.

01:03:15.000 --> 01:03:18.840
And then if I keep doing it, will it'll

01:03:18.840 --> 01:03:20.220
like bring them closer?

01:03:20.220 --> 01:03:21.820
Yeah, eventually they'll all be the

01:03:21.820 --> 01:03:22.070
same.

01:03:23.860 --> 01:03:25.730
But if I had other kinds of similarity

01:03:25.730 --> 01:03:28.015
functions, an exponential function, it

01:03:28.015 --> 01:03:30.390
would take a lot longer to bring them

01:03:30.390 --> 01:03:32.480
all together because the IT would be a

01:03:32.480 --> 01:03:34.050
lot more Peaky, and in fact that's

01:03:34.050 --> 01:03:35.020
what's used in practice.

01:03:35.770 --> 01:03:37.394
So you can think about this.

01:03:37.394 --> 01:03:39.289
You can think about this Attention as

01:03:39.290 --> 01:03:40.580
doing like two different things.

01:03:40.580 --> 01:03:43.140
If you apply as Cross Attention, then

01:03:43.140 --> 01:03:44.610
you're basically transferring the

01:03:44.610 --> 01:03:47.080
associations of 1 set of data elements

01:03:47.080 --> 01:03:49.860
to a new data element.

01:03:49.860 --> 01:03:53.686
So you had the association of 1 maps to

01:03:53.686 --> 01:03:57.645
17 maps to -, 1, five maps to -, 1, and

01:03:57.645 --> 01:04:00.780
so my expected value of four is some

01:04:00.780 --> 01:04:03.260
weighted average of these of these

01:04:03.260 --> 01:04:06.100
values, and it's -, .8, or my expected

01:04:06.100 --> 01:04:07.180
value of 0.

01:04:07.440 --> 01:04:09.020
Is a weighted average of these by

01:04:09.020 --> 01:04:12.190
similarity and it's positive point.

01:04:13.700 --> 01:04:15.270
So it's a kind of like near weighted

01:04:15.270 --> 01:04:16.600
nearest neighbor essentially?

01:04:18.330 --> 01:04:20.540
Or in the case of Self Attention, it's

01:04:20.540 --> 01:04:22.740
a kind of like clustering where you're

01:04:22.740 --> 01:04:26.255
grouping together similar elements and

01:04:26.255 --> 01:04:29.010
like aggregating information across

01:04:29.010 --> 01:04:30.040
these tokens.

01:04:33.480 --> 01:04:35.970
So Cross Attention is an instance based

01:04:35.970 --> 01:04:36.750
regression.

01:04:36.750 --> 01:04:38.750
Your computer you're averaging a value

01:04:38.750 --> 01:04:41.330
based on the nearby other nearby.

01:04:41.460 --> 01:04:41.890
I.

01:04:43.750 --> 01:04:44.240
Keys.

01:04:45.340 --> 01:04:48.080
And Self Attention is a soft cluster

01:04:48.080 --> 01:04:50.570
aggregator and it's important to note

01:04:50.570 --> 01:04:52.620
that in this case, like for simplicity,

01:04:52.620 --> 01:04:54.890
I'm just saying that their values are

01:04:54.890 --> 01:04:55.630
scalars.

01:04:56.480 --> 01:04:58.940
And so it looks like the value it's

01:04:58.940 --> 01:05:00.880
just like replacing it and everything

01:05:00.880 --> 01:05:02.400
will eventually merge to one.

01:05:02.400 --> 01:05:04.790
But in practice you're applying this to

01:05:04.790 --> 01:05:06.510
large vectors, large continuous

01:05:06.510 --> 01:05:09.410
vectors, and so the distances can be

01:05:09.410 --> 01:05:10.370
much bigger.

01:05:10.370 --> 01:05:13.830
And the and you can when you add

01:05:13.830 --> 01:05:15.907
multiple dimensional multidimensional

01:05:15.907 --> 01:05:18.590
vectors you can overlay information.

01:05:18.590 --> 01:05:22.230
So similar to if different, you could

01:05:22.230 --> 01:05:25.210
have like a an audio stream where

01:05:25.210 --> 01:05:26.520
you've got music playing in the

01:05:26.520 --> 01:05:28.390
background and two people are talking

01:05:28.390 --> 01:05:28.490
at.

01:05:28.540 --> 01:05:31.280
Months, and you can separate that into

01:05:31.280 --> 01:05:33.140
each person talking in the audio

01:05:33.140 --> 01:05:33.508
stream.

01:05:33.508 --> 01:05:36.216
All of those signals are overlaid on

01:05:36.216 --> 01:05:38.070
each other, but the signals are all

01:05:38.070 --> 01:05:38.590
still there.

01:05:38.590 --> 01:05:40.148
They don't completely interfere with

01:05:40.148 --> 01:05:40.877
each other.

01:05:40.877 --> 01:05:43.314
And in the same way, when you have high

01:05:43.314 --> 01:05:45.410
dimensional vectors, when you're

01:05:45.410 --> 01:05:47.620
averaging those vectors, like with this

01:05:47.620 --> 01:05:49.710
operation, you're not necessarily

01:05:49.710 --> 01:05:51.629
replacing information, you're actually

01:05:51.630 --> 01:05:52.790
adding information.

01:05:52.790 --> 01:05:54.140
So you end up with some high

01:05:54.140 --> 01:05:55.720
dimensional vector that actually

01:05:55.720 --> 01:05:57.698
contains the information in each of

01:05:57.698 --> 01:05:58.009
those.

01:05:58.240 --> 01:05:59.840
Each of those vectors that you were

01:05:59.840 --> 01:06:00.810
adding into it.

01:06:02.880 --> 01:06:06.370
And so it's not just a pure clustering

01:06:06.370 --> 01:06:08.445
where you're like simplifying, it's

01:06:08.445 --> 01:06:10.345
Adding you're adding information,

01:06:10.345 --> 01:06:13.210
you're aggregating information across

01:06:13.210 --> 01:06:14.470
your different tokens.

01:06:16.500 --> 01:06:19.120
So this becomes extremely powerful as

01:06:19.120 --> 01:06:20.440
represented by trogdor.

01:06:21.280 --> 01:06:24.140
And in general, when you combine it

01:06:24.140 --> 01:06:26.340
with learned similarity functions and

01:06:26.340 --> 01:06:28.570
nonlinear Feature transformations.

01:06:30.240 --> 01:06:32.260
So this finally brings us to the

01:06:32.260 --> 01:06:33.270
transformer.

01:06:34.500 --> 01:06:37.430
And the transformer is just an

01:06:37.430 --> 01:06:40.090
application of this Attention idea

01:06:40.090 --> 01:06:43.520
where you define the similarity is.

01:06:45.440 --> 01:06:46.580
Really wonder what is like.

01:06:46.580 --> 01:06:48.240
Always screwing up there where you

01:06:48.240 --> 01:06:50.460
define the similarity as each of the

01:06:50.460 --> 01:06:51.075
dot Product.

01:06:51.075 --> 01:06:53.600
So it's basically a softmax operation

01:06:53.600 --> 01:06:55.000
to get your weighted similarities.

01:06:55.000 --> 01:06:57.130
So when you do the softmax, you divide

01:06:57.130 --> 01:06:58.670
by the sum of these similarities to

01:06:58.670 --> 01:07:00.020
make it sum to one.

01:07:00.980 --> 01:07:04.700
So it's your key dot query E to the key

01:07:04.700 --> 01:07:06.250
dot query is your similarity.

01:07:06.890 --> 01:07:08.260
And then they also have some

01:07:08.260 --> 01:07:10.410
normalization by the dimensionality of

01:07:10.410 --> 01:07:11.980
the keys, because otherwise, like if

01:07:11.980 --> 01:07:13.257
you have really long vectors, then

01:07:13.257 --> 01:07:14.600
you'll always tend to be like pretty

01:07:14.600 --> 01:07:15.230
far away.

01:07:15.230 --> 01:07:17.190
And so this normalizes it so that for

01:07:17.190 --> 01:07:18.700
different length vectors you'll still

01:07:18.700 --> 01:07:20.594
have like a unit Norm kind of

01:07:20.594 --> 01:07:22.229
similarity, a unit length similarity

01:07:22.230 --> 01:07:22.630
typically.

01:07:24.730 --> 01:07:26.720
And then you multiply it by the value.

01:07:26.720 --> 01:07:28.590
So here it's represented in matrix

01:07:28.590 --> 01:07:30.252
operation, so you have an outer product

01:07:30.252 --> 01:07:32.170
of all your queries times all your

01:07:32.170 --> 01:07:32.650
keys.

01:07:32.650 --> 01:07:34.230
So that gives you a matrix of the

01:07:34.230 --> 01:07:36.380
similarity of each query to each key.

01:07:37.340 --> 01:07:38.840
And you take a softmax.

01:07:39.420 --> 01:07:42.210
So then you are normalizing, you're

01:07:42.210 --> 01:07:42.970
competing those.

01:07:44.060 --> 01:07:46.420
The similarity score for each key in

01:07:46.420 --> 01:07:48.100
query, so this will still be a matrix.

01:07:48.790 --> 01:07:51.400
You multiply it by your values and now

01:07:51.400 --> 01:07:55.755
you have a new value Vector for each of

01:07:55.755 --> 01:07:56.780
your queries.

01:07:58.130 --> 01:07:59.740
So it's just doing the same thing, but

01:07:59.740 --> 01:08:01.800
with matrix operations for efficiency.

01:08:01.800 --> 01:08:04.780
And this is like very great for GPUs.

01:08:04.780 --> 01:08:08.400
GPUs can do this super fast and tpus

01:08:08.400 --> 01:08:09.430
can do it even faster.

01:08:11.040 --> 01:08:12.630
There's our tensor processing units.

01:08:14.110 --> 01:08:16.000
And then this is just that represented

01:08:16.000 --> 01:08:16.720
as a diagram.

01:08:16.720 --> 01:08:19.160
So key and query comes in, you get

01:08:19.160 --> 01:08:21.410
matrix multiplied Scaled by this thing.

01:08:22.070 --> 01:08:24.350
Then softmax and then another matrix

01:08:24.350 --> 01:08:25.000
multiply.

01:08:26.840 --> 01:08:29.800
And you can learn the similarity

01:08:29.800 --> 01:08:32.207
function with a linear layer, and you

01:08:32.207 --> 01:08:34.220
can even learn multiple similarity

01:08:34.220 --> 01:08:35.110
functions.

01:08:35.110 --> 01:08:36.600
So first, let's say we're doing a

01:08:36.600 --> 01:08:38.210
single head transformer.

01:08:38.210 --> 01:08:41.755
So that means that basically we pass in

01:08:41.755 --> 01:08:43.480
our value, our key in our query.

01:08:44.300 --> 01:08:46.480
We pass them through some linear layer

01:08:46.480 --> 01:08:48.310
that transforms them into a new

01:08:48.310 --> 01:08:48.800
Embedding.

01:08:49.530 --> 01:08:51.420
And then we take the dot Product, do

01:08:51.420 --> 01:08:53.240
the same dot Product detention that I

01:08:53.240 --> 01:08:53.980
just showed.

01:08:53.980 --> 01:08:56.750
So this allows it to learn like you can

01:08:56.750 --> 01:08:58.920
pass in like the same values as value,

01:08:58.920 --> 01:08:59.460
key and query.

01:08:59.460 --> 01:09:00.650
And it can say, well, I'm going to use

01:09:00.650 --> 01:09:02.320
like this aspect of the data to compute

01:09:02.320 --> 01:09:04.310
the similarity and then I'm going to

01:09:04.310 --> 01:09:07.204
sum over this other aspect of the data

01:09:07.204 --> 01:09:08.550
to produce my output.

01:09:10.220 --> 01:09:12.550
And then to make it like just a little

01:09:12.550 --> 01:09:14.980
bit more complicated they do, you can

01:09:14.980 --> 01:09:17.453
do a Multi head Attention which is when

01:09:17.453 --> 01:09:21.040
you have multiple linear models and if

01:09:21.040 --> 01:09:23.878
you're Input say has 100 dimensions and

01:09:23.878 --> 01:09:26.450
you have ten of these heads, then each

01:09:26.450 --> 01:09:28.693
of these linear models maps from 100 to

01:09:28.693 --> 01:09:30.770
10 so it maps into a 10 dimensional

01:09:30.770 --> 01:09:31.750
similarity space.

01:09:32.490 --> 01:09:34.665
And then you do the same operation and

01:09:34.665 --> 01:09:36.630
then you concatenate at the end to get

01:09:36.630 --> 01:09:39.440
back 100 dimensional Vector.

01:09:40.810 --> 01:09:43.330
So this allows the transformer to

01:09:43.330 --> 01:09:46.230
compare these like continuous vectors

01:09:46.230 --> 01:09:48.850
in different learned ways and then

01:09:48.850 --> 01:09:51.130
aggregate, aggregate like different

01:09:51.130 --> 01:09:52.470
aspects of the values and then

01:09:52.470 --> 01:09:54.670
recombine it into the original length

01:09:54.670 --> 01:09:55.190
Vector.

01:09:59.680 --> 01:10:01.570
So putting these together, we get

01:10:01.570 --> 01:10:03.890
what's called the transformer.

01:10:03.890 --> 01:10:05.820
Transformer is a general data

01:10:05.820 --> 01:10:08.680
processor, so you have some kind of

01:10:08.680 --> 01:10:10.630
Vector set of vectors coming in.

01:10:10.630 --> 01:10:11.990
These could be like your Word2Vec

01:10:11.990 --> 01:10:13.030
Representations.

01:10:14.500 --> 01:10:16.380
So you just have a bunch of these Word

01:10:16.380 --> 01:10:17.580
vectors coming in.

01:10:17.580 --> 01:10:19.250
It could also be as we'll see in the

01:10:19.250 --> 01:10:21.440
next class, like image patches or other

01:10:21.440 --> 01:10:22.450
kinds of data.

01:10:23.580 --> 01:10:24.140
This.

01:10:24.140 --> 01:10:26.090
Note that all of these operations are

01:10:26.090 --> 01:10:28.810
position invariant, so when I'm taking

01:10:28.810 --> 01:10:29.810
the.

01:10:30.460 --> 01:10:32.450
Like it doesn't when I when I do these

01:10:32.450 --> 01:10:33.390
kinds of operations.

01:10:33.390 --> 01:10:35.330
It doesn't matter what order I store

01:10:35.330 --> 01:10:36.860
these pairs in, the output for the

01:10:36.860 --> 01:10:38.070
query is going to be the same.

01:10:38.980 --> 01:10:41.010
And so often you add what's called a

01:10:41.010 --> 01:10:45.600
Positional Embedding to your input, so

01:10:45.600 --> 01:10:48.222
that the position is stored as part of

01:10:48.222 --> 01:10:50.170
your like value or as part of the

01:10:50.170 --> 01:10:50.640
Vector.

01:10:53.120 --> 01:10:55.230
And that allows it to know like whether

01:10:55.230 --> 01:10:56.820
2 words are next to each other or not.

01:10:59.650 --> 01:11:01.760
Positional Embedding is.

01:11:02.430 --> 01:11:05.629
In practice, you take like a in

01:11:05.630 --> 01:11:07.183
language for example, you would have

01:11:07.183 --> 01:11:09.390
like a floating point or some number to

01:11:09.390 --> 01:11:10.890
represent where the Word appears in a

01:11:10.890 --> 01:11:11.380
sequence.

01:11:12.100 --> 01:11:13.890
And then you process it through, pass

01:11:13.890 --> 01:11:16.819
it through sines and cosines of

01:11:16.820 --> 01:11:20.530
different frequencies to create like a

01:11:20.530 --> 01:11:22.400
Vector that's the same size as the

01:11:22.400 --> 01:11:24.334
original like Word Vector.

01:11:24.334 --> 01:11:27.574
And then you add it to the Word Vector.

01:11:27.574 --> 01:11:29.705
And the reason for using the signs and

01:11:29.705 --> 01:11:31.410
cosines is because if you take the dot

01:11:31.410 --> 01:11:33.280
product of these Positional embeddings.

01:11:33.900 --> 01:11:36.376
Then the similarity corresponds to

01:11:36.376 --> 01:11:38.400
their distance to their.

01:11:38.400 --> 01:11:41.019
It's like monotonic with their like

01:11:41.020 --> 01:11:41.940
Euclidean distance.

01:11:42.650 --> 01:11:45.191
So normally if you take a position X

01:11:45.191 --> 01:11:47.560
and you take the dot product of another

01:11:47.560 --> 01:11:51.120
X, then that doesn't tell you that

01:11:51.120 --> 01:11:52.520
doesn't correspond to similarity,

01:11:52.520 --> 01:11:52.720
right?

01:11:52.720 --> 01:11:54.075
Because if either one of them gets

01:11:54.075 --> 01:11:55.935
bigger than that dot Product just gets

01:11:55.935 --> 01:11:56.410
bigger.

01:11:56.410 --> 01:11:57.997
But if you take the sine and cosines of

01:11:57.997 --> 01:11:59.969
X and then you take the dot product of

01:11:59.970 --> 01:12:02.234
those sines and cosines, then if the

01:12:02.234 --> 01:12:04.360
2X's are close together then their

01:12:04.360 --> 01:12:05.910
similarity will be higher and that

01:12:05.910 --> 01:12:06.680
representation.

01:12:09.650 --> 01:12:12.920
And so you have this transformer block,

01:12:12.920 --> 01:12:14.946
so you apply the multi head attention.

01:12:14.946 --> 01:12:18.790
Then you apply a two layer MLP multi

01:12:18.790 --> 01:12:19.636
linear perceptron.

01:12:19.636 --> 01:12:22.250
You have Skip connections around each

01:12:22.250 --> 01:12:22.770
of them.

01:12:22.770 --> 01:12:24.460
That's like these errors here.

01:12:24.460 --> 01:12:26.570
And then there's what's called a layer

01:12:26.570 --> 01:12:27.720
Norm, which is just.

01:12:29.070 --> 01:12:31.130
Subtracting the mean and dividing the

01:12:31.130 --> 01:12:33.710
steering deviation of all the tokens

01:12:33.710 --> 01:12:34.600
within each layer.

01:12:35.580 --> 01:12:37.320
And you can just stack these on top of

01:12:37.320 --> 01:12:39.310
each other to do like multiple layers

01:12:39.310 --> 01:12:40.270
of processing.

01:12:43.670 --> 01:12:45.330
So this is a little more about the

01:12:45.330 --> 01:12:46.025
Positional embeddings.

01:12:46.025 --> 01:12:48.080
I forgot that I had this detail here.

01:12:49.230 --> 01:12:50.920
So this is how you compute the

01:12:50.920 --> 01:12:51.657
Positional embeddings.

01:12:51.657 --> 01:12:54.110
So you just Define these like sines and

01:12:54.110 --> 01:12:55.382
cosines of different frequencies.

01:12:55.382 --> 01:12:57.368
This is like the two to the I thing.

01:12:57.368 --> 01:13:01.718
So this is just dividing by mapping it

01:13:01.718 --> 01:13:05.380
into like a smaller the original

01:13:05.380 --> 01:13:07.350
integer position into a smaller value

01:13:07.350 --> 01:13:08.380
before computing that.

01:13:11.800 --> 01:13:12.910
And.

01:13:14.680 --> 01:13:17.900
So the transformer processing is a

01:13:17.900 --> 01:13:21.910
little bit like it's it can act kind of

01:13:21.910 --> 01:13:22.810
like Convolution.

01:13:22.810 --> 01:13:25.510
So in Convolution you're comparing like

01:13:25.510 --> 01:13:27.450
each pixel for example to the

01:13:27.450 --> 01:13:29.040
surrounding pixels and then computing

01:13:29.040 --> 01:13:30.450
some output based on that.

01:13:30.450 --> 01:13:33.145
And Transformers you're also you're

01:13:33.145 --> 01:13:34.990
comparing like each patch to the

01:13:34.990 --> 01:13:36.140
surrounding patches if you're in

01:13:36.140 --> 01:13:38.199
images, but it's not limited to the

01:13:38.200 --> 01:13:40.630
nearby ones, it's actually can operates

01:13:40.630 --> 01:13:42.700
over everything, all the other data

01:13:42.700 --> 01:13:43.160
that's being.

01:13:43.220 --> 01:13:44.760
Processed at the same time.

01:13:49.830 --> 01:13:51.950
So here's the Complete language

01:13:51.950 --> 01:13:53.850
transformer that's in this Attention is

01:13:53.850 --> 01:13:55.040
all you need paper.

01:13:55.790 --> 01:13:58.320
So you have WordPiece tokens which we

01:13:58.320 --> 01:14:00.790
talked about that are mapped to 512

01:14:00.790 --> 01:14:03.510
dimensional vectors, and in this case

01:14:03.510 --> 01:14:05.460
these vectors are not learned by

01:14:05.460 --> 01:14:08.370
Word2Vec, they're instead just learned

01:14:08.370 --> 01:14:10.170
as part of the total transformer

01:14:10.170 --> 01:14:10.750
Training.

01:14:11.500 --> 01:14:13.380
You add a Positional Encoding to each

01:14:13.380 --> 01:14:14.150
Vector.

01:14:14.150 --> 01:14:17.176
Then you have a bunch of these Self

01:14:17.176 --> 01:14:18.830
Attention blocks that are added on top

01:14:18.830 --> 01:14:19.370
of each other.

01:14:19.370 --> 01:14:21.837
So the data the Inputs go through these

01:14:21.837 --> 01:14:22.850
Self Attention blocks.

01:14:23.650 --> 01:14:29.035
And then you also have like your output

01:14:29.035 --> 01:14:29.940
is added.

01:14:29.940 --> 01:14:32.230
So for example, first if you're trying

01:14:32.230 --> 01:14:34.980
to say what is the color of a banana.

01:14:36.170 --> 01:14:38.527
Then you process your what is the color

01:14:38.527 --> 01:14:40.790
of a banana here and then you generate

01:14:40.790 --> 01:14:43.150
the most likely output and then so

01:14:43.150 --> 01:14:44.580
maybe that the output then will be

01:14:44.580 --> 01:14:45.236
yellow.

01:14:45.236 --> 01:14:48.555
And then next you Feed yellow in here

01:14:48.555 --> 01:14:50.377
and again you take like the output of

01:14:50.377 --> 01:14:51.632
what is the color of a banana.

01:14:51.632 --> 01:14:53.392
And then you do Cross Attention with

01:14:53.392 --> 01:14:55.250
yellow and then hopefully it will

01:14:55.250 --> 01:14:56.972
output like N of sequence so it'll just

01:14:56.972 --> 01:14:59.049
say yellow or it could say like yellow,

01:14:59.050 --> 01:15:00.280
green or whatever.

01:15:00.280 --> 01:15:03.265
And so every time you output a new Word

01:15:03.265 --> 01:15:05.380
you consider all the words that were

01:15:05.380 --> 01:15:05.770
Input.

01:15:05.820 --> 01:15:07.230
As well as all the words that have been

01:15:07.230 --> 01:15:08.013
output so far.

01:15:08.013 --> 01:15:10.355
And then you output the next word, and

01:15:10.355 --> 01:15:12.380
then you keep on outputting one word at

01:15:12.380 --> 01:15:14.570
a time until you get to the end of

01:15:14.570 --> 01:15:17.510
sequence token, which means that you're

01:15:17.510 --> 01:15:17.780
done.

01:15:24.950 --> 01:15:28.310
So I'm pretty much done, but I'm going

01:15:28.310 --> 01:15:30.790
to wrap this up at the start of the

01:15:30.790 --> 01:15:31.230
next class.

01:15:31.230 --> 01:15:32.870
I'll talk about how you apply this to

01:15:32.870 --> 01:15:33.630
Translation.

01:15:34.300 --> 01:15:35.930
And I'll show these Attention

01:15:35.930 --> 01:15:39.274
Visualizations then, so we can see just

01:15:39.274 --> 01:15:41.435
I'll show you just one briefly.

01:15:41.435 --> 01:15:45.350
So for example, in this sentence, it is

01:15:45.350 --> 01:15:46.860
in this spirit that a majority of

01:15:46.860 --> 01:15:48.410
American governments have passed new

01:15:48.410 --> 01:15:49.889
laws since 2009, making the

01:15:49.890 --> 01:15:51.750
registration of voting process more

01:15:51.750 --> 01:15:52.160
difficult.

01:15:52.160 --> 01:15:52.570
EOS.

01:15:52.570 --> 01:15:56.060
Hubad it's like after you do these

01:15:56.060 --> 01:15:58.260
Transformers, you can see that there's

01:15:58.260 --> 01:16:00.640
like more the make the representation

01:16:00.640 --> 01:16:03.005
of making draws its meaning or draws

01:16:03.005 --> 01:16:05.200
it's like additional values from more

01:16:05.200 --> 01:16:05.790
difficult.

01:16:06.390 --> 01:16:10.062
Because making more difficult is like

01:16:10.062 --> 01:16:10.344
the.

01:16:10.344 --> 01:16:12.070
It's like the Syntactic like

01:16:12.070 --> 01:16:13.146
Relationship, right?

01:16:13.146 --> 01:16:15.160
It's making more difficult so it's able

01:16:15.160 --> 01:16:17.570
to like jump words and draw similarity,

01:16:17.570 --> 01:16:19.270
draw meaning from other words that are

01:16:19.270 --> 01:16:21.196
related to this Word in terms of the

01:16:21.196 --> 01:16:23.020
meaning or in terms of the syntax.

01:16:26.240 --> 01:16:26.930
Yeah.

01:16:28.600 --> 01:16:30.650
So I will show you some of these on

01:16:30.650 --> 01:16:32.810
Thursday and talk about how it's used

01:16:32.810 --> 01:16:33.850
for Translation.

01:16:33.850 --> 01:16:35.510
So that'll just take a little bit of

01:16:35.510 --> 01:16:36.100
time.

01:16:36.100 --> 01:16:39.110
And then I'm going to talk about the

01:16:39.110 --> 01:16:42.170
application of the Transformers using

01:16:42.170 --> 01:16:45.141
Bert, which is a very popular language

01:16:45.141 --> 01:16:47.863
model, as well as visit, which is a

01:16:47.863 --> 01:16:49.990
very popular vision model and Unified

01:16:49.990 --> 01:16:52.854
IO which is a vision language model.

01:16:52.854 --> 01:16:55.850
And once you once you like, these are

01:16:55.850 --> 01:16:57.640
all just basically Transformers like

01:16:57.640 --> 01:16:58.950
they're Architecture sections.

01:16:59.010 --> 01:17:01.450
Are and we use Transformers from

01:17:01.450 --> 01:17:04.780
Vaswani Idol like basically like doing

01:17:04.780 --> 01:17:07.020
nothing else like they have like all of

01:17:07.020 --> 01:17:08.170
these papers that are using

01:17:08.170 --> 01:17:09.963
Transformers have Architecture sections

01:17:09.963 --> 01:17:12.400
like that big because this single

01:17:12.400 --> 01:17:16.050
transformer block can do like any kind

01:17:16.050 --> 01:17:17.970
of processing.

01:17:17.970 --> 01:17:18.865
So.

01:17:18.865 --> 01:17:19.950
All right.

01:17:19.950 --> 01:17:21.340
So I'll pick it up next Thursday.

01:17:21.340 --> 01:17:22.110
Thank you.

01:17:25.840 --> 01:17:26.440
Office hours.