CMU Advanced NLP 2024 (2) Word Representation and Text Classification/transcript.srt

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cool um so this time I'm going to talk

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about word representation and text

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classifiers these are kind of the

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foundations that you need to know uh in

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order to move on to the more complex

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things that we'll be talking in future

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classes uh but actually the in

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particular the word representation part

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is pretty important it's a major uh

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thing that we need to do for all NLP

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models so uh let's go into it

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so last class I talked about the bag of

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words model um and just to review this

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was a model where basically we take each

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word we represent it as a one hot Vector

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uh like

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this and we add all of these vectors

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together we multiply the resulting

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frequency vector by some weights and we

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get a score out of this and we can use

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this score for binary classification or

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if we want to do multiclass

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classification we get you know multiple

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scores for each

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class and the features F were just based

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on our word identities and the weights

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were

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learned and um if we look at what's

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missing in bag of words

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models um we talked about handling of

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conjugated or compound

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words we talked about handling of word

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similarity and we talked about handling

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of combination features and handling of

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sentence structure and so all of these

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are are tricky problems uh we saw that

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you know creating a rule-based system to

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solve these problems is non-trivial and

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at the very least would take a lot of

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time and so now I want to talk about

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some solutions to the problems in this

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class so the first the solution to the

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first problem or a solution to the first

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problem is uh subword or character based

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models and that's what I'll talk about

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first handling of word similarity this

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can be handled uh using Word edings

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and the word embeddings uh will be

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another thing we'll talk about this time

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handling of combination features uh we

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can handle through neural networks which

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we'll also talk about this time and then

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handling of sentence structure uh the

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kind of standard way of handling this

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now is through sequence-based models and

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that will be uh starting in a few

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classes so uh let's jump into

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it so subword models uh as I mentioned

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this is a really really important part

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all of the models that we're building

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nowadays including you know

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state-of-the-art language models and and

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things like this and the basic idea

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behind this is that we want to split uh

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in particular split less common words up

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into multiple subboard tokens so to give

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an example of this uh if we have

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something like the companies are

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expanding uh it might split companies

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into compan

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e and expand in like this and there are

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a few benefits of this uh the first

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benefit is that this allows you to

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parameters between word varieties or

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compound words and the other one is to

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reduce parameter size and save compute

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and meming and both of these are kind of

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like equally important things that we

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need to be uh we need to be considering

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so does anyone know how many words there

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are in

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English any

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ideas

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yeah two

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million pretty good um any other

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ideas

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yeah

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60,000 some models use 60,000 I I think

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60,000 is probably these subword models

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uh when you're talking about this so

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they can use sub models to take the 2

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million which I think is a reasonable

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guess to 6 60,000 any other

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ideas 700,000 okay pretty good um so

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this was a per question it doesn't

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really have a good answer um but two 200

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million's probably pretty good six uh

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700,000 is pretty good the reason why

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this is a trick question is because are

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company and companies different

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words uh maybe maybe not right because

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if we know the word company we can you

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know guess what the word companies means

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um what about automobile is that a

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different word well maybe if we know

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Auto and mobile we can kind of guess

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what automobile means but not really so

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maybe that's a different word there's

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all kinds of Shades of Gray there and

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also we have really frequent words that

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everybody can probably acknowledge our

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words like

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the and

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a and um maybe

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car and then we have words down here

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which are like Miss spellings or

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something like that misspellings of

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actual correct words or

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slay uh or other things like that and

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then it's questionable whether those are

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actual words or not so um there's a

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famous uh law called Zip's

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law um which probably a lot of people

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have heard of it's also the source of

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your zip

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file um which is using Zip's law to

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compress uh compress output by making

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the uh more frequent words have shorter

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bite strings and less frequent words

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have uh you know less frequent bite

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strings but basically like we're going

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to have an infinite number of words or

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at least strings that are separated by

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white space so we need to handle this

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somehow and that's what subword units

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do so um 60,000 was a good guess for the

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number of subword units you might use in

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a model and so uh by using subw units we

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can limit to about that much

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so there's a couple of common uh ways to

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create these subword units and basically

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all of them rely on the fact that you

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want more common strings to become

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subword

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units um or actually sorry I realize

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maybe before doing that I could explain

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an alternative to creating subword units

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so the alternative to creating subword

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units is to treat every character or

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maybe every bite in a string as a single

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thing that you encode in forent so in

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other words instead of trying to model

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the companies are expanding we Model T h

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e space c o m uh etc etc can anyone

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think of any downsides of

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this

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yeah yeah the set of these will be very

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will be very small but that's not

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necessarily a problem

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right yeah um and any other

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ideas

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yeah yeah the resulting sequences will

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be very long um and when you say

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difficult to use it could be difficult

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to use for a couple of reasons there's

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mainly two reasons actually any any IDE

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about

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this any

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yeah yeah that's a little bit of a

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separate problem than the character

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based model so let me get back to that

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but uh let let's finish the discussion

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of the character based models so if it's

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really if it's really long maybe a

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simple thing like uh let's say you have

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a big neural network and it's processing

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a really long sequence any ideas what

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happens basically you run out of memory

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or it takes a really long time right so

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you have computational problems another

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reason why is um think of what a bag of

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words model would look like if it was a

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bag of characters

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model it wouldn't be very informative

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about whether like a sentence is

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positive sentiment or negative sentiment

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right because instead of having uh go o

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you would have uh instead of having good

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you would have go o and that doesn't

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really directly tell you whether it's

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positive sentiment or not so those are

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basically the two problems um compute

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and lack of expressiveness in the

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underlying representations so you need

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to handle both of those yes so if we uh

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move from

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character better expressiveness and we

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assume that if we just get the bigger

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and bigger paragraphs we'll get even

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better

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yeah so a very good question I'll repeat

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it um and actually this also goes back

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to the other question you asked about

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words that look the same but are

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pronounced differently or have different

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meanings and so like let's say we just

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remembered this whole sentence right the

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companies are

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expanding um and that was like a single

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embedding and we somehow embedded it the

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problem would be we're never going to

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see that sentence again um or if we go

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to longer sentences we're never going to

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see the longer sentences again so it

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becomes too sparse so there's kind of a

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sweet spot between

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like long enough to be expressive and

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short enough to occur many times so that

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you can learn appropriately and that's

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kind of what subword models are aiming

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for and if you get longer subwords then

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you'll get things that are more

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expressive but more sparse in shorter

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subwords you'll get things that are like

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uh less expressive but less spice so you

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need to balance between them and then

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once we get into sequence modeling they

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start being able to model like which

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words are next to each other uh which

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tokens are next to each other and stuff

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like that so even if they are less

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expressive the combination between them

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can be expressive so um yeah that's kind

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of a preview of what we're going to be

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doing

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next okay so um let's assume that we

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want to have some subwords that are

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longer than characters but shorter than

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tokens how do we make these in a

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consistent way there's two major ways of

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doing this uh the first one is bite pair

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encoding and this is uh very very simple

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in fact it's so

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simple

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that we can implement

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it in this notebook here which you can

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click through to on the

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slides and it's uh

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about 10 lines of code um and so

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basically what B pair encoding

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does

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is that you start out with um all of the

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vocabulary that you want to process

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where each vocabulary item is split into

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uh the characters and an end of word

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symbol and you have a corresponding

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frequency of

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this you then uh get statistics about

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the most common pairs of tokens that

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occur next to each other and so here the

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most common pairs of tokens that occur

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next to each other are e s because it

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occurs nine times because it occurs in

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newest and wildest also s and t w

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because those occur there too and then

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you have we and other things like that

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so out of all the most frequent ones you

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just merge them together and that gives

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you uh new s new

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EST and wide

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EST and then you do the same thing this

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time now you get EST so now you get this

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uh suffix EST and that looks pretty

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reasonable for English right you know

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EST is a common suffix that we use it

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seems like it should be a single token

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and um so you just do this over and over

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again if you want a vocabulary of 60,000

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for example you would do um 60,000 minus

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00:12:29,279 --> 00:12:33,079
number of characters merge operations

281
00:12:31,120 --> 00:12:37,160
and eventually you would get a B of

282
00:12:33,079 --> 00:12:41,920
60,000 um and yeah very very simple

283
00:12:37,160 --> 00:12:41,920
method to do this um any questions about

284
00:12:43,160 --> 00:12:46,160
that

285
00:12:57,839 --> 00:13:00,839
yeah

286
00:13:15,600 --> 00:13:20,959
yeah so uh just to repeat the the

287
00:13:18,040 --> 00:13:23,560
comment uh this seems like a greedy

288
00:13:20,959 --> 00:13:25,320
version of Huffman encoding which is a

289
00:13:23,560 --> 00:13:28,839
you know similar to what you're using in

290
00:13:25,320 --> 00:13:32,000
your zip file a way to shorten things by

291
00:13:28,839 --> 00:13:36,560
getting longer uh more frequent things

292
00:13:32,000 --> 00:13:39,120
being inced as a single token um I think

293
00:13:36,560 --> 00:13:40,760
B pair encoding did originally start

294
00:13:39,120 --> 00:13:43,720
like that that's part of the reason why

295
00:13:40,760 --> 00:13:45,760
the encoding uh thing is here I think it

296
00:13:43,720 --> 00:13:47,360
originally started there I haven't read

297
00:13:45,760 --> 00:13:49,360
really deeply into this but I can talk

298
00:13:47,360 --> 00:13:53,240
more about how the next one corresponds

299
00:13:49,360 --> 00:13:54,440
to information Theory and Tuesday I'm

300
00:13:53,240 --> 00:13:55,720
going to talk even more about how

301
00:13:54,440 --> 00:13:57,720
language models correspond to

302
00:13:55,720 --> 00:14:00,040
information theories so we can uh we can

303
00:13:57,720 --> 00:14:04,519
discuss maybe in more detail

304
00:14:00,040 --> 00:14:07,639
to um so the the alternative option is

305
00:14:04,519 --> 00:14:10,000
to use unigram models and unigram models

306
00:14:07,639 --> 00:14:12,240
are the simplest type of language model

307
00:14:10,000 --> 00:14:15,079
I'm going to talk more in detail about

308
00:14:12,240 --> 00:14:18,279
them next time but basically uh the way

309
00:14:15,079 --> 00:14:20,759
it works is you create a model that

310
00:14:18,279 --> 00:14:23,600
generates all word uh words in the

311
00:14:20,759 --> 00:14:26,199
sequence independently sorry I thought I

312
00:14:23,600 --> 00:14:26,199
had a

313
00:14:26,320 --> 00:14:31,800
um I thought I had an equation but

314
00:14:28,800 --> 00:14:31,800
basically the

315
00:14:32,240 --> 00:14:35,759
equation looks

316
00:14:38,079 --> 00:14:41,079
like

317
00:14:47,720 --> 00:14:52,120
this so you say the probability of the

318
00:14:50,360 --> 00:14:53,440
sequence is the product of the

319
00:14:52,120 --> 00:14:54,279
probabilities of each of the words in

320
00:14:53,440 --> 00:14:55,959
the

321
00:14:54,279 --> 00:15:00,079
sequence

322
00:14:55,959 --> 00:15:04,079
and uh then you try to pick a vocabulary

323
00:15:00,079 --> 00:15:06,839
that maximizes the probability of the

324
00:15:04,079 --> 00:15:09,320
Corpus given a fixed vocabulary size so

325
00:15:06,839 --> 00:15:10,320
you try to say okay you get a vocabulary

326
00:15:09,320 --> 00:15:14,440
size of

327
00:15:10,320 --> 00:15:16,920
60,000 how do you um how do you pick the

328
00:15:14,440 --> 00:15:19,680
best 60,000 vocabulary to maximize the

329
00:15:16,920 --> 00:15:22,440
probability of the the Corpus and that

330
00:15:19,680 --> 00:15:25,959
will result in something very similar uh

331
00:15:22,440 --> 00:15:27,920
it will also try to give longer uh

332
00:15:25,959 --> 00:15:29,880
vocabulary uh sorry more common

333
00:15:27,920 --> 00:15:32,240
vocabulary long sequences because that

334
00:15:29,880 --> 00:15:35,560
allows you to to maximize this

335
00:15:32,240 --> 00:15:36,959
objective um the optimization for this

336
00:15:35,560 --> 00:15:40,040
is performed using something called the

337
00:15:36,959 --> 00:15:44,440
EM algorithm where basically you uh

338
00:15:40,040 --> 00:15:48,560
predict the uh the probability of each

339
00:15:44,440 --> 00:15:51,600
token showing up and uh then select the

340
00:15:48,560 --> 00:15:53,279
most common tokens and then trim off the

341
00:15:51,600 --> 00:15:54,759
ones that are less common and then just

342
00:15:53,279 --> 00:15:58,120
do this over and over again until you

343
00:15:54,759 --> 00:15:59,839
drop down to the 60,000 token lat so the

344
00:15:58,120 --> 00:16:02,040
details for this are not important for

345
00:15:59,839 --> 00:16:04,160
most people in this class uh because

346
00:16:02,040 --> 00:16:07,480
you're going to just be using a toolkit

347
00:16:04,160 --> 00:16:08,880
that implements this for you um but if

348
00:16:07,480 --> 00:16:10,759
you're interested in this I'm happy to

349
00:16:08,880 --> 00:16:14,199
talk to you about it

350
00:16:10,759 --> 00:16:14,199
yeah is there

351
00:16:14,680 --> 00:16:18,959
problem Oh in unigram models there's a

352
00:16:17,199 --> 00:16:20,959
huge problem with assuming Independence

353
00:16:18,959 --> 00:16:22,720
in language models because then you

354
00:16:20,959 --> 00:16:25,120
could rearrange the order of words in

355
00:16:22,720 --> 00:16:26,600
sentences um that that's something we're

356
00:16:25,120 --> 00:16:27,519
going to talk about in language model

357
00:16:26,600 --> 00:16:30,560
next

358
00:16:27,519 --> 00:16:32,839
time but the the good thing about this

359
00:16:30,560 --> 00:16:34,519
is the EM algorithm requires dynamic

360
00:16:32,839 --> 00:16:36,079
programming in this case and you can't

361
00:16:34,519 --> 00:16:37,800
easily do dynamic programming if you

362
00:16:36,079 --> 00:16:40,160
don't make that

363
00:16:37,800 --> 00:16:41,880
assumptions um and then finally after

364
00:16:40,160 --> 00:16:43,560
you've picked your vocabulary and you've

365
00:16:41,880 --> 00:16:45,720
assigned a probability to each word in

366
00:16:43,560 --> 00:16:47,800
the vocabulary you then find a

367
00:16:45,720 --> 00:16:49,639
segmentation of the input that maximizes

368
00:16:47,800 --> 00:16:52,600
the unigram

369
00:16:49,639 --> 00:16:54,880
probabilities um so this is basically

370
00:16:52,600 --> 00:16:56,519
the idea of what's going on here um I'm

371
00:16:54,880 --> 00:16:58,120
not going to go into a lot of detail

372
00:16:56,519 --> 00:17:00,560
about this because most people are just

373
00:16:58,120 --> 00:17:02,279
going to be users of this algorithm so

374
00:17:00,560 --> 00:17:06,240
it's not super super

375
00:17:02,279 --> 00:17:09,400
important um the one important thing

376
00:17:06,240 --> 00:17:11,240
about this is that there's a library

377
00:17:09,400 --> 00:17:15,520
called sentence piece that's used very

378
00:17:11,240 --> 00:17:19,199
widely in order to build these um in

379
00:17:15,520 --> 00:17:22,000
order to build these subword units and

380
00:17:19,199 --> 00:17:23,720
uh basically what you do is you run the

381
00:17:22,000 --> 00:17:27,600
sentence piece

382
00:17:23,720 --> 00:17:30,200
train uh model or sorry uh program and

383
00:17:27,600 --> 00:17:32,640
that gives you uh you select your vocab

384
00:17:30,200 --> 00:17:34,240
size uh this also this character

385
00:17:32,640 --> 00:17:36,120
coverage is basically how well do you

386
00:17:34,240 --> 00:17:39,760
need to cover all of the characters in

387
00:17:36,120 --> 00:17:41,840
your vocabulary or in your input text um

388
00:17:39,760 --> 00:17:45,240
what model type do you use and then you

389
00:17:41,840 --> 00:17:48,640
run this uh sentence piece en code file

390
00:17:45,240 --> 00:17:51,039
uh to uh encode the output and split the

391
00:17:48,640 --> 00:17:54,799
output and there's also python bindings

392
00:17:51,039 --> 00:17:56,240
available for this and by the one thing

393
00:17:54,799 --> 00:17:57,919
that you should know is by default it

394
00:17:56,240 --> 00:18:00,600
uses the unigram model but it also

395
00:17:57,919 --> 00:18:01,960
supports EP in my experience it doesn't

396
00:18:00,600 --> 00:18:05,159
make a huge difference about which one

397
00:18:01,960 --> 00:18:07,640
you use the bigger thing is how um how

398
00:18:05,159 --> 00:18:10,159
big is your vocabulary size and if your

399
00:18:07,640 --> 00:18:11,880
vocabulary size is smaller then things

400
00:18:10,159 --> 00:18:13,760
will be more efficient but less

401
00:18:11,880 --> 00:18:17,480
expressive if your vocabulary size is

402
00:18:13,760 --> 00:18:21,280
bigger things will be um will

403
00:18:17,480 --> 00:18:23,240
be more expressive but less efficient

404
00:18:21,280 --> 00:18:25,360
and A good rule of thumb is like

405
00:18:23,240 --> 00:18:26,960
something like 60,000 to 80,000 is

406
00:18:25,360 --> 00:18:29,120
pretty reasonable if you're only doing

407
00:18:26,960 --> 00:18:31,320
English if you're spreading out to

408
00:18:29,120 --> 00:18:32,600
things that do other languages um which

409
00:18:31,320 --> 00:18:35,960
I'll talk about in a second then you

410
00:18:32,600 --> 00:18:38,720
need a much bigger B regular

411
00:18:35,960 --> 00:18:40,559
say so there's two considerations here

412
00:18:38,720 --> 00:18:42,440
two important considerations when using

413
00:18:40,559 --> 00:18:46,320
these models uh the first is

414
00:18:42,440 --> 00:18:48,760
multilinguality as I said so when you're

415
00:18:46,320 --> 00:18:50,760
using um subword

416
00:18:48,760 --> 00:18:54,710
models they're hard to use

417
00:18:50,760 --> 00:18:55,840
multilingually because as I said before

418
00:18:54,710 --> 00:18:59,799
[Music]

419
00:18:55,840 --> 00:19:03,799
they give longer strings to more

420
00:18:59,799 --> 00:19:06,520
frequent strings basically so then

421
00:19:03,799 --> 00:19:09,559
imagine what happens if 50% of your

422
00:19:06,520 --> 00:19:11,919
Corpus is English another 30% of your

423
00:19:09,559 --> 00:19:15,400
Corpus is

424
00:19:11,919 --> 00:19:17,200
other languages written in Latin script

425
00:19:15,400 --> 00:19:21,720
10% is

426
00:19:17,200 --> 00:19:25,480
Chinese uh 5% is cerlic script languages

427
00:19:21,720 --> 00:19:27,240
four 4% is 3% is Japanese and then you

428
00:19:25,480 --> 00:19:31,080
have like

429
00:19:27,240 --> 00:19:33,320
0.01% written in like burmes or

430
00:19:31,080 --> 00:19:35,520
something like that suddenly burmes just

431
00:19:33,320 --> 00:19:37,400
gets chunked up really really tiny

432
00:19:35,520 --> 00:19:38,360
really long sequences and it doesn't

433
00:19:37,400 --> 00:19:45,559
work as

434
00:19:38,360 --> 00:19:45,559
well um so one way that people fix this

435
00:19:45,919 --> 00:19:50,520
um and actually there's a really nice uh

436
00:19:48,760 --> 00:19:52,600
blog post about this called exploring

437
00:19:50,520 --> 00:19:53,760
B's vocabulary which I referenced here

438
00:19:52,600 --> 00:19:58,039
if you're interested in learning more

439
00:19:53,760 --> 00:20:02,960
about that um but one way that people

440
00:19:58,039 --> 00:20:05,240
were around this is if your

441
00:20:02,960 --> 00:20:07,960
actual uh data

442
00:20:05,240 --> 00:20:11,559
distribution looks like this like

443
00:20:07,960 --> 00:20:11,559
English uh

444
00:20:17,039 --> 00:20:23,159
Ty we actually sorry I took out the

445
00:20:19,280 --> 00:20:23,159
Indian languages in my example

446
00:20:24,960 --> 00:20:30,159
apologies

447
00:20:27,159 --> 00:20:30,159
so

448
00:20:30,400 --> 00:20:35,919
um what you do is you essentially create

449
00:20:33,640 --> 00:20:40,000
a different distribution that like

450
00:20:35,919 --> 00:20:43,559
downweights English a little bit and up

451
00:20:40,000 --> 00:20:47,000
weights up weights all of the other

452
00:20:43,559 --> 00:20:49,480
languages um so that you get more of

453
00:20:47,000 --> 00:20:53,159
other languages when creating so this is

454
00:20:49,480 --> 00:20:53,159
a common work around that you can do for

455
00:20:54,200 --> 00:20:59,960
this um the

456
00:20:56,799 --> 00:21:03,000
second problem with these is

457
00:20:59,960 --> 00:21:08,000
arbitrariness so as you saw in my

458
00:21:03,000 --> 00:21:11,240
example with bpe e s s and t and of

459
00:21:08,000 --> 00:21:13,520
board symbol all have the same probabil

460
00:21:11,240 --> 00:21:16,960
or have the same frequency right so if

461
00:21:13,520 --> 00:21:21,520
we get to that point do we segment es or

462
00:21:16,960 --> 00:21:25,039
do we seg uh EST or do we segment e

463
00:21:21,520 --> 00:21:26,559
s and so this is also a problem and it

464
00:21:25,039 --> 00:21:29,000
actually can affect your results

465
00:21:26,559 --> 00:21:30,480
especially if you like don't have a

466
00:21:29,000 --> 00:21:31,760
really strong vocabulary for the

467
00:21:30,480 --> 00:21:33,279
language you're working in or you're

468
00:21:31,760 --> 00:21:37,200
working in a new

469
00:21:33,279 --> 00:21:40,159
domain and so there's a few workarounds

470
00:21:37,200 --> 00:21:41,520
for this uh one workaround for this is

471
00:21:40,159 --> 00:21:44,000
uh called subword

472
00:21:41,520 --> 00:21:46,279
regularization and the way it works is

473
00:21:44,000 --> 00:21:49,400
instead

474
00:21:46,279 --> 00:21:51,640
of just having a single segmentation and

475
00:21:49,400 --> 00:21:54,679
getting the kind of

476
00:21:51,640 --> 00:21:56,200
maximally probable segmentation or the

477
00:21:54,679 --> 00:21:58,480
one the greedy one that you get out of

478
00:21:56,200 --> 00:22:01,360
BP instead you sample different

479
00:21:58,480 --> 00:22:03,000
segmentations in training time and use

480
00:22:01,360 --> 00:22:05,720
the different segmentations and that

481
00:22:03,000 --> 00:22:09,200
makes your model more robust to this

482
00:22:05,720 --> 00:22:10,840
kind of variation and that's also

483
00:22:09,200 --> 00:22:15,679
actually the reason why sentence piece

484
00:22:10,840 --> 00:22:17,919
was released was through this um subword

485
00:22:15,679 --> 00:22:19,559
regularization paper so that's also

486
00:22:17,919 --> 00:22:22,720
implemented in sentence piece if that's

487
00:22:19,559 --> 00:22:22,720
something you're interested in

488
00:22:24,919 --> 00:22:32,520
trying cool um are there any questions

489
00:22:28,480 --> 00:22:32,520
or discussions about this

490
00:22:53,279 --> 00:22:56,279
yeah

491
00:22:56,960 --> 00:22:59,960
already

492
00:23:06,799 --> 00:23:11,080
yeah so this is a good question um just

493
00:23:08,960 --> 00:23:12,760
to repeat the question it was like let's

494
00:23:11,080 --> 00:23:16,080
say we have a big

495
00:23:12,760 --> 00:23:19,640
multilingual um subword

496
00:23:16,080 --> 00:23:23,440
model and we want to add a new language

497
00:23:19,640 --> 00:23:26,240
in some way uh how can we reuse the

498
00:23:23,440 --> 00:23:28,880
existing model but add a new

499
00:23:26,240 --> 00:23:31,080
language it's a good question if you're

500
00:23:28,880 --> 00:23:33,679
only using it for subord

501
00:23:31,080 --> 00:23:36,320
segmentation um one one nice thing about

502
00:23:33,679 --> 00:23:36,320
the unigram

503
00:23:36,400 --> 00:23:41,799
model here is this is kind of a

504
00:23:38,880 --> 00:23:43,679
probabilistic model so it's very easy to

505
00:23:41,799 --> 00:23:46,360
do the kind of standard things that we

506
00:23:43,679 --> 00:23:48,240
do with probabilistic models which is

507
00:23:46,360 --> 00:23:50,559
like let's say we had an

508
00:23:48,240 --> 00:23:53,919
old uh an

509
00:23:50,559 --> 00:23:56,880
old vocabulary for

510
00:23:53,919 --> 00:23:59,880
this um we could just

511
00:23:56,880 --> 00:23:59,880
interpolate

512
00:24:07,159 --> 00:24:12,320
um we could interpolate like this and

513
00:24:09,559 --> 00:24:13,840
just you know uh combine the

514
00:24:12,320 --> 00:24:17,080
probabilities of the two and then use

515
00:24:13,840 --> 00:24:19,520
that combine probability in order to

516
00:24:17,080 --> 00:24:21,320
segment the new language um things like

517
00:24:19,520 --> 00:24:24,159
this have been uh done before but I

518
00:24:21,320 --> 00:24:26,159
don't remember the exact preferences uh

519
00:24:24,159 --> 00:24:30,440
for them but that that's what I would do

520
00:24:26,159 --> 00:24:31,960
here another interesting thing is um

521
00:24:30,440 --> 00:24:35,399
this might be getting a little ahead of

522
00:24:31,960 --> 00:24:35,399
myself but there's

523
00:24:48,559 --> 00:24:58,279
a there's a paper that talks about um

524
00:24:55,360 --> 00:25:00,159
how you can take things that or trained

525
00:24:58,279 --> 00:25:03,360
with another

526
00:25:00,159 --> 00:25:05,480
vocabulary and basically the idea is um

527
00:25:03,360 --> 00:25:09,320
you pre-train on whatever languages you

528
00:25:05,480 --> 00:25:10,679
have and then uh you learn embeddings in

529
00:25:09,320 --> 00:25:11,880
the new language you freeze the body of

530
00:25:10,679 --> 00:25:14,360
the model and learn embeddings in the

531
00:25:11,880 --> 00:25:15,880
new language so that's another uh method

532
00:25:14,360 --> 00:25:19,080
that's used it's called on the cross

533
00:25:15,880 --> 00:25:19,080
lingual printability

534
00:25:21,840 --> 00:25:26,159
representations and I'll probably talk

535
00:25:23,840 --> 00:25:28,480
about that in the last class of this uh

536
00:25:26,159 --> 00:25:30,720
thing so you can remember that

537
00:25:28,480 --> 00:25:33,720
then cool any other

538
00:25:30,720 --> 00:25:33,720
questions

539
00:25:38,480 --> 00:25:42,640
yeah is bag of words a first step to

540
00:25:41,039 --> 00:25:46,640
process your data if you want to do

541
00:25:42,640 --> 00:25:49,919
Generation Um do you mean like

542
00:25:46,640 --> 00:25:52,440
uh a word based model or a subword based

543
00:25:49,919 --> 00:25:52,440
model

544
00:25:56,679 --> 00:26:00,480
or like is

545
00:26:02,360 --> 00:26:08,000
this so the subword segmentation is the

546
00:26:05,919 --> 00:26:10,640
first step of creating just about any

547
00:26:08,000 --> 00:26:13,080
model nowadays like every model every

548
00:26:10,640 --> 00:26:16,600
model uses this and they usually use

549
00:26:13,080 --> 00:26:21,520
this either to segment characters or

550
00:26:16,600 --> 00:26:23,559
byes um characters are like Unicode code

551
00:26:21,520 --> 00:26:25,799
points so they actually correspond to an

552
00:26:23,559 --> 00:26:28,279
actual visual character and then bites

553
00:26:25,799 --> 00:26:31,120
are many unicode characters are like

554
00:26:28,279 --> 00:26:35,000
three by like a Chinese character is

555
00:26:31,120 --> 00:26:37,159
three byes if I remember correctly so um

556
00:26:35,000 --> 00:26:38,640
the bbased segmentation is nice because

557
00:26:37,159 --> 00:26:41,240
you don't even need to worry about unic

558
00:26:38,640 --> 00:26:43,880
code you can just do the like you can

559
00:26:41,240 --> 00:26:45,640
just segment the pile like literally as

560
00:26:43,880 --> 00:26:49,440
is and so a lot of people do it that way

561
00:26:45,640 --> 00:26:53,279
too uh llama as far as I know is

562
00:26:49,440 --> 00:26:55,720
bites I believe GPT is also bites um but

563
00:26:53,279 --> 00:26:58,799
pre previous to like three or four years

564
00:26:55,720 --> 00:27:02,799
ago people used SCS I

565
00:26:58,799 --> 00:27:05,000
cool um okay so this is really really

566
00:27:02,799 --> 00:27:05,919
important it's not like super complex

567
00:27:05,000 --> 00:27:09,760
and

568
00:27:05,919 --> 00:27:13,039
practically uh you will just maybe maybe

569
00:27:09,760 --> 00:27:15,840
train or maybe just use a tokenizer um

570
00:27:13,039 --> 00:27:18,559
but uh that that's an important thing to

571
00:27:15,840 --> 00:27:20,760
me cool uh next I'd like to move on to

572
00:27:18,559 --> 00:27:24,399
continuous word eddings

573
00:27:20,760 --> 00:27:26,720
so the basic idea is that previously we

574
00:27:24,399 --> 00:27:28,240
represented words with a sparse Vector

575
00:27:26,720 --> 00:27:30,120
uh with a single one

576
00:27:28,240 --> 00:27:31,960
also known as one poot Vector so it

577
00:27:30,120 --> 00:27:35,720
looked a little bit like

578
00:27:31,960 --> 00:27:37,640
this and instead what continuous word

579
00:27:35,720 --> 00:27:39,640
embeddings do is they look up a dense

580
00:27:37,640 --> 00:27:42,320
vector and so you get a dense

581
00:27:39,640 --> 00:27:45,760
representation where the entire Vector

582
00:27:42,320 --> 00:27:45,760
has continuous values in

583
00:27:46,000 --> 00:27:51,919
it and I talked about a bag of words

584
00:27:49,200 --> 00:27:54,320
model but we could also create a

585
00:27:51,919 --> 00:27:58,360
continuous bag of words model and the

586
00:27:54,320 --> 00:28:01,159
way this works is you look up the

587
00:27:58,360 --> 00:28:03,720
values of each Vector the embeddings of

588
00:28:01,159 --> 00:28:06,320
each Vector this gives you an embedding

589
00:28:03,720 --> 00:28:08,440
Vector for the entire sequence and then

590
00:28:06,320 --> 00:28:15,120
you multiply this by a weight

591
00:28:08,440 --> 00:28:17,559
Matrix uh where the so this is column so

592
00:28:15,120 --> 00:28:19,960
the rows of the weight Matrix uh

593
00:28:17,559 --> 00:28:22,919
correspond to to the size of this

594
00:28:19,960 --> 00:28:24,760
continuous embedding and The Columns of

595
00:28:22,919 --> 00:28:28,320
the weight Matrix would correspond to

596
00:28:24,760 --> 00:28:30,919
the uh overall um

597
00:28:28,320 --> 00:28:32,559
to the overall uh number of labels that

598
00:28:30,919 --> 00:28:36,919
you would have here and then that would

599
00:28:32,559 --> 00:28:40,120
give you sces and so this uh basically

600
00:28:36,919 --> 00:28:41,679
what this is saying is each Vector now

601
00:28:40,120 --> 00:28:43,440
instead of having a single thing that

602
00:28:41,679 --> 00:28:46,799
represents which vocabulary item you're

603
00:28:43,440 --> 00:28:48,679
looking at uh you would kind of hope

604
00:28:46,799 --> 00:28:52,120
that you would get vectors where words

605
00:28:48,679 --> 00:28:54,919
that are similar uh by some mention of

606
00:28:52,120 --> 00:28:57,760
by some concept of similar like syntatic

607
00:28:54,919 --> 00:28:59,679
uh syntax semantics whether they're in

608
00:28:57,760 --> 00:29:03,120
the same language or not are close in

609
00:28:59,679 --> 00:29:06,679
the vector space and each Vector element

610
00:29:03,120 --> 00:29:09,399
is a feature uh so for example each

611
00:29:06,679 --> 00:29:11,519
Vector element corresponds to is this an

612
00:29:09,399 --> 00:29:14,960
animate object or is this a positive

613
00:29:11,519 --> 00:29:17,399
word or other Vector other things like

614
00:29:14,960 --> 00:29:19,399
that so just to give an example here

615
00:29:17,399 --> 00:29:21,760
this is totally made up I just made it

616
00:29:19,399 --> 00:29:24,360
in keynote so it's not natural Vector

617
00:29:21,760 --> 00:29:26,279
space but to Ill illustrate the concept

618
00:29:24,360 --> 00:29:27,960
I showed here what if we had a

619
00:29:26,279 --> 00:29:30,240
two-dimensional vector

620
00:29:27,960 --> 00:29:33,399
space where the two-dimensional Vector

621
00:29:30,240 --> 00:29:36,240
space the xais here is corresponding to

622
00:29:33,399 --> 00:29:38,679
whether it's animate or not and the the

623
00:29:36,240 --> 00:29:41,480
Y AIS here is corresponding to whether

624
00:29:38,679 --> 00:29:44,080
it's like positive sentiment or not and

625
00:29:41,480 --> 00:29:46,399
so this is kind of like our ideal uh

626
00:29:44,080 --> 00:29:49,799
goal

627
00:29:46,399 --> 00:29:52,279
here um so why would we want to do this

628
00:29:49,799 --> 00:29:52,279
yeah sorry

629
00:29:56,320 --> 00:30:03,399
guys what do the like in the one it's

630
00:30:00,919 --> 00:30:06,399
one

631
00:30:03,399 --> 00:30:06,399
yep

632
00:30:07,200 --> 00:30:12,519
like so what would the four entries do

633
00:30:09,880 --> 00:30:14,799
here the four entries here are learned

634
00:30:12,519 --> 00:30:17,039
so they are um they're learned just

635
00:30:14,799 --> 00:30:18,519
together with the model um and I'm going

636
00:30:17,039 --> 00:30:22,120
to talk about exactly how we learn them

637
00:30:18,519 --> 00:30:24,000
soon but the the final goal is that

638
00:30:22,120 --> 00:30:25,399
after learning has happened they look

639
00:30:24,000 --> 00:30:26,799
they have these two properties like

640
00:30:25,399 --> 00:30:28,600
similar words are close together in the

641
00:30:26,799 --> 00:30:30,080
vectorace

642
00:30:28,600 --> 00:30:32,640
and

643
00:30:30,080 --> 00:30:35,679
um that's like number one that's the

644
00:30:32,640 --> 00:30:37,600
most important and then number two is

645
00:30:35,679 --> 00:30:39,279
ideally these uh features would have

646
00:30:37,600 --> 00:30:41,200
some meaning uh maybe human

647
00:30:39,279 --> 00:30:44,720
interpretable meaning maybe not human

648
00:30:41,200 --> 00:30:47,880
interpretable meaning but

649
00:30:44,720 --> 00:30:50,880
yeah so um one thing that I should

650
00:30:47,880 --> 00:30:53,159
mention is I I showed a contrast between

651
00:30:50,880 --> 00:30:55,159
the bag of words uh the one hot

652
00:30:53,159 --> 00:30:57,000
representations here and the dense

653
00:30:55,159 --> 00:31:00,880
representations here and I used this

654
00:30:57,000 --> 00:31:03,880
look look up operation for both of them

655
00:31:00,880 --> 00:31:07,399
and this this lookup

656
00:31:03,880 --> 00:31:09,559
operation actually um can be viewed as

657
00:31:07,399 --> 00:31:11,799
grabbing a single Vector from a big

658
00:31:09,559 --> 00:31:14,919
Matrix of word

659
00:31:11,799 --> 00:31:17,760
embeddings and

660
00:31:14,919 --> 00:31:19,760
so the way it can work is like we have

661
00:31:17,760 --> 00:31:22,919
this big vector and then we look up word

662
00:31:19,760 --> 00:31:25,919
number two in a zero index Matrix and it

663
00:31:22,919 --> 00:31:27,799
would just grab this out of that Matrix

664
00:31:25,919 --> 00:31:29,880
and that's practically what most like

665
00:31:27,799 --> 00:31:32,240
deep learning libraries or or whatever

666
00:31:29,880 --> 00:31:35,840
Library you use are going to be

667
00:31:32,240 --> 00:31:38,000
doing but another uh way you can view it

668
00:31:35,840 --> 00:31:40,880
is you can view it as multiplying by a

669
00:31:38,000 --> 00:31:43,880
one hot vector and so you have this

670
00:31:40,880 --> 00:31:48,679
Vector uh exactly the same Matrix uh but

671
00:31:43,880 --> 00:31:50,799
you just multiply by a vector uh 0 1 z z

672
00:31:48,679 --> 00:31:55,720
and that gives you exactly the same

673
00:31:50,799 --> 00:31:58,200
things um so the Practical imple

674
00:31:55,720 --> 00:31:59,720
implementations of this uh uh tend to be

675
00:31:58,200 --> 00:32:01,279
the first one because the first one's a

676
00:31:59,720 --> 00:32:04,679
lot faster to implement you don't need

677
00:32:01,279 --> 00:32:06,760
to multiply like this big thing by a

678
00:32:04,679 --> 00:32:11,000
huge Vector but there

679
00:32:06,760 --> 00:32:13,880
are advantages of knowing the second one

680
00:32:11,000 --> 00:32:15,519
uh just to give an example what if you

681
00:32:13,880 --> 00:32:19,600
for whatever reason you came up with

682
00:32:15,519 --> 00:32:21,440
like an a crazy model that predicts a

683
00:32:19,600 --> 00:32:24,120
probability distribution over words

684
00:32:21,440 --> 00:32:25,720
instead of just words maybe it's a

685
00:32:24,120 --> 00:32:27,679
language model that has an idea of what

686
00:32:25,720 --> 00:32:30,200
the next word is going to look like

687
00:32:27,679 --> 00:32:32,159
and maybe your um maybe your model

688
00:32:30,200 --> 00:32:35,279
thinks the next word has a 50%

689
00:32:32,159 --> 00:32:36,600
probability of being capped 30%

690
00:32:35,279 --> 00:32:42,279
probability of being

691
00:32:36,600 --> 00:32:44,960
dog and uh 2% probability uh sorry uh

692
00:32:42,279 --> 00:32:47,200
20% probability being

693
00:32:44,960 --> 00:32:50,000
bir you can take this vector and

694
00:32:47,200 --> 00:32:51,480
multiply it by The Matrix and get like a

695
00:32:50,000 --> 00:32:53,639
word embedding that's kind of a mix of

696
00:32:51,480 --> 00:32:55,639
all of those word which might be

697
00:32:53,639 --> 00:32:57,960
interesting and let you do creative

698
00:32:55,639 --> 00:33:02,120
things so um knowing that these two

699
00:32:57,960 --> 00:33:05,360
things are the same are the same is kind

700
00:33:02,120 --> 00:33:05,360
of useful for that kind of

701
00:33:05,919 --> 00:33:11,480
thing um any any questions about this

702
00:33:09,120 --> 00:33:13,919
I'm G to talk about how we train next so

703
00:33:11,480 --> 00:33:18,159
maybe maybe I can goow into

704
00:33:13,919 --> 00:33:23,159
that okay cool so how do we get the

705
00:33:18,159 --> 00:33:25,840
vectors uh like the question uh so up

706
00:33:23,159 --> 00:33:27,519
until now we trained a bag of words

707
00:33:25,840 --> 00:33:29,080
model and the way we trained a bag of

708
00:33:27,519 --> 00:33:31,159
words model was using the structured

709
00:33:29,080 --> 00:33:35,440
perceptron algorithm where if the model

710
00:33:31,159 --> 00:33:39,639
got the answer wrong we would either

711
00:33:35,440 --> 00:33:42,799
increment or decrement the embeddings

712
00:33:39,639 --> 00:33:45,080
based on whether uh whether the label

713
00:33:42,799 --> 00:33:46,559
was positive or negative right so I

714
00:33:45,080 --> 00:33:48,919
showed an example of this very simple

715
00:33:46,559 --> 00:33:51,039
algorithm you don't even uh need to

716
00:33:48,919 --> 00:33:52,480
write any like numpy or anything like

717
00:33:51,039 --> 00:33:55,919
that to implement that

718
00:33:52,480 --> 00:33:59,559
algorithm uh so here here it is so we

719
00:33:55,919 --> 00:34:02,320
have like 4X why in uh data we extract

720
00:33:59,559 --> 00:34:04,639
the features we run the classifier uh we

721
00:34:02,320 --> 00:34:07,440
have the predicted why and then we

722
00:34:04,639 --> 00:34:09,480
increment or decrement

723
00:34:07,440 --> 00:34:12,679
features but how do we train more

724
00:34:09,480 --> 00:34:15,599
complex models so I think most people

725
00:34:12,679 --> 00:34:17,079
here have taken a uh machine learning

726
00:34:15,599 --> 00:34:19,159
class of some kind so this will be

727
00:34:17,079 --> 00:34:21,079
reviewed for a lot of people uh but

728
00:34:19,159 --> 00:34:22,280
basically we do this uh by doing

729
00:34:21,079 --> 00:34:24,839
gradient

730
00:34:22,280 --> 00:34:27,240
descent and in order to do so we write

731
00:34:24,839 --> 00:34:29,919
down a loss function calculate the

732
00:34:27,240 --> 00:34:30,919
derivatives of the L function with

733
00:34:29,919 --> 00:34:35,079
respect to the

734
00:34:30,919 --> 00:34:37,320
parameters and move uh the parameters in

735
00:34:35,079 --> 00:34:40,839
the direction that reduces the loss

736
00:34:37,320 --> 00:34:42,720
mtion and so specifically for this bag

737
00:34:40,839 --> 00:34:45,560
of words or continuous bag of words

738
00:34:42,720 --> 00:34:48,240
model um we want this loss of function

739
00:34:45,560 --> 00:34:50,839
to be a loss function that gets lower as

740
00:34:48,240 --> 00:34:52,240
the model gets better and I'm going to

741
00:34:50,839 --> 00:34:54,000
give two examples from binary

742
00:34:52,240 --> 00:34:57,400
classification both of these are used in

743
00:34:54,000 --> 00:34:58,839
NLP models uh reasonably frequently

744
00:34:57,400 --> 00:35:01,440
uh there's a bunch of other loss

745
00:34:58,839 --> 00:35:02,800
functions but these are kind of the two

746
00:35:01,440 --> 00:35:05,480
major

747
00:35:02,800 --> 00:35:08,160
ones so the first one um which is

748
00:35:05,480 --> 00:35:10,160
actually less frequent is the hinge loss

749
00:35:08,160 --> 00:35:13,400
and then the second one is taking a

750
00:35:10,160 --> 00:35:15,800
sigmoid and then doing negative log

751
00:35:13,400 --> 00:35:19,760
likelyhood so the hinge loss basically

752
00:35:15,800 --> 00:35:22,760
what we do is we uh take the max of the

753
00:35:19,760 --> 00:35:26,119
label times the score that is output by

754
00:35:22,760 --> 00:35:29,200
the model and zero and what this looks

755
00:35:26,119 --> 00:35:33,480
like is we have a hinged loss uh where

756
00:35:29,200 --> 00:35:36,880
if Y is equal to one the loss if Y is

757
00:35:33,480 --> 00:35:39,520
greater than zero is zero so as long as

758
00:35:36,880 --> 00:35:42,680
we get basically as long as we get the

759
00:35:39,520 --> 00:35:45,079
answer right there's no loss um as the

760
00:35:42,680 --> 00:35:47,400
answer gets more wrong the loss gets

761
00:35:45,079 --> 00:35:49,880
worse like this and then similarly if

762
00:35:47,400 --> 00:35:53,160
the label is negative if we get a

763
00:35:49,880 --> 00:35:54,839
negative score uh then we get zero loss

764
00:35:53,160 --> 00:35:55,800
and the loss increases if we have a

765
00:35:54,839 --> 00:35:58,800
positive

766
00:35:55,800 --> 00:36:00,800
score so the sigmoid plus negative log

767
00:35:58,800 --> 00:36:05,440
likelihood the way this works is you

768
00:36:00,800 --> 00:36:07,400
multiply y * the score here and um then

769
00:36:05,440 --> 00:36:09,960
we have the sigmoid function which is

770
00:36:07,400 --> 00:36:14,079
just kind of a nice function that looks

771
00:36:09,960 --> 00:36:15,440
like this with zero and one centered

772
00:36:14,079 --> 00:36:19,480
around

773
00:36:15,440 --> 00:36:21,240
zero and then we take the negative log

774
00:36:19,480 --> 00:36:22,319
of this sigmoid function or the negative

775
00:36:21,240 --> 00:36:27,160
log

776
00:36:22,319 --> 00:36:28,520
likelihood and that gives us a uh L that

777
00:36:27,160 --> 00:36:30,440
looks a little bit like this so

778
00:36:28,520 --> 00:36:32,640
basically you can see that these look

779
00:36:30,440 --> 00:36:36,040
very similar right the difference being

780
00:36:32,640 --> 00:36:37,760
that the hinge loss is uh sharp and we

781
00:36:36,040 --> 00:36:41,119
get exactly a zero loss if we get the

782
00:36:37,760 --> 00:36:44,319
answer right and the sigmoid is smooth

783
00:36:41,119 --> 00:36:48,440
uh and we never get a zero

784
00:36:44,319 --> 00:36:50,680
loss um so does anyone have an idea of

785
00:36:48,440 --> 00:36:53,119
the benefits and disadvantages of

786
00:36:50,680 --> 00:36:55,680
these I kind of flashed one on the

787
00:36:53,119 --> 00:36:57,599
screen already

788
00:36:55,680 --> 00:36:59,400
but

789
00:36:57,599 --> 00:37:01,359
so I flash that on the screen so I'll

790
00:36:59,400 --> 00:37:03,680
give this one and then I can have a quiz

791
00:37:01,359 --> 00:37:06,319
about the sign but the the hinge glass

792
00:37:03,680 --> 00:37:07,720
is more closely linked to accuracy and

793
00:37:06,319 --> 00:37:10,400
the reason why it's more closely linked

794
00:37:07,720 --> 00:37:13,640
to accuracy is because basically we will

795
00:37:10,400 --> 00:37:16,079
get a zero loss if the model gets the

796
00:37:13,640 --> 00:37:18,319
answer right so when the model gets all

797
00:37:16,079 --> 00:37:20,240
of the answers right we will just stop

798
00:37:18,319 --> 00:37:22,760
updating our model whatsoever because we

799
00:37:20,240 --> 00:37:25,440
never we don't have any loss whatsoever

800
00:37:22,760 --> 00:37:27,720
and the gradient of the loss is zero um

801
00:37:25,440 --> 00:37:29,960
what about the sigmoid uh a negative log

802
00:37:27,720 --> 00:37:33,160
likelihood uh there there's kind of two

803
00:37:29,960 --> 00:37:36,160
major advantages of this anyone want to

804
00:37:33,160 --> 00:37:36,160
review their machine learning

805
00:37:38,240 --> 00:37:41,800
test sorry what was

806
00:37:43,800 --> 00:37:49,960
that for for R uh yeah maybe there's a

807
00:37:48,200 --> 00:37:51,319
more direct I think I know what you're

808
00:37:49,960 --> 00:37:54,560
saying but maybe there's a more direct

809
00:37:51,319 --> 00:37:54,560
way to say that um

810
00:37:54,839 --> 00:38:00,760
yeah yeah so the gradient is nonzero

811
00:37:57,560 --> 00:38:04,240
everywhere and uh the gradient also kind

812
00:38:00,760 --> 00:38:05,839
of increases as your score gets worse so

813
00:38:04,240 --> 00:38:08,440
those are that's one advantage it makes

814
00:38:05,839 --> 00:38:11,240
it easier to optimize models um another

815
00:38:08,440 --> 00:38:13,839
one linked to the ROC score but maybe we

816
00:38:11,240 --> 00:38:13,839
could say it more

817
00:38:16,119 --> 00:38:19,400
directly any

818
00:38:20,040 --> 00:38:26,920
ideas okay um basically the sigmoid can

819
00:38:23,240 --> 00:38:30,160
be interpreted as a probability so um if

820
00:38:26,920 --> 00:38:32,839
the the sigmoid is between Zer and one

821
00:38:30,160 --> 00:38:34,640
uh and because it's between zero and one

822
00:38:32,839 --> 00:38:36,720
we can say the sigmoid is a

823
00:38:34,640 --> 00:38:38,640
probability um and that can be useful

824
00:38:36,720 --> 00:38:40,119
for various things like if we want a

825
00:38:38,640 --> 00:38:41,960
downstream model or if we want a

826
00:38:40,119 --> 00:38:45,480
confidence prediction out of the model

827
00:38:41,960 --> 00:38:48,200
so those are two uh advantages of using

828
00:38:45,480 --> 00:38:49,920
a s plus negative log likelihood there's

829
00:38:48,200 --> 00:38:53,160
no probabilistic interpretation to

830
00:38:49,920 --> 00:38:56,560
something transing theas

831
00:38:53,160 --> 00:38:59,200
basically cool um so the next thing that

832
00:38:56,560 --> 00:39:01,240
that we do is we calculate derivatives

833
00:38:59,200 --> 00:39:04,040
and we calculate the derivative of the

834
00:39:01,240 --> 00:39:05,920
parameter given the loss function um to

835
00:39:04,040 --> 00:39:09,839
give an example of the bag of words

836
00:39:05,920 --> 00:39:13,480
model and the hinge loss um the hinge

837
00:39:09,839 --> 00:39:16,480
loss as I said is the max of the score

838
00:39:13,480 --> 00:39:19,359
and times y in the bag of words model

839
00:39:16,480 --> 00:39:22,640
the score was the frequency of that

840
00:39:19,359 --> 00:39:25,880
vocabulary item in the input multiplied

841
00:39:22,640 --> 00:39:27,680
by the weight here and so if we this is

842
00:39:25,880 --> 00:39:29,520
a simple a function that I can just do

843
00:39:27,680 --> 00:39:34,440
the derivative by hand and if I do the

844
00:39:29,520 --> 00:39:36,920
deriva by hand what comes out is if y *

845
00:39:34,440 --> 00:39:39,319
this value is greater than zero so in

846
00:39:36,920 --> 00:39:44,640
other words if this Max uh picks this

847
00:39:39,319 --> 00:39:48,319
instead of this then the derivative is y

848
00:39:44,640 --> 00:39:52,359
* stre and otherwise uh it

849
00:39:48,319 --> 00:39:52,359
is in the opposite

850
00:39:55,400 --> 00:40:00,160
direction

851
00:39:56,920 --> 00:40:02,839
then uh optimizing gradients uh we do

852
00:40:00,160 --> 00:40:06,200
standard uh in standard stochastic

853
00:40:02,839 --> 00:40:07,839
gradient descent uh which is the most

854
00:40:06,200 --> 00:40:10,920
standard optimization algorithm for

855
00:40:07,839 --> 00:40:14,440
these models uh we basically have a

856
00:40:10,920 --> 00:40:17,440
gradient over uh you take the gradient

857
00:40:14,440 --> 00:40:20,040
over the parameter of the loss function

858
00:40:17,440 --> 00:40:22,480
and we call it GT so here um sorry I

859
00:40:20,040 --> 00:40:25,599
switched my terminology between W and

860
00:40:22,480 --> 00:40:28,280
Theta so this could be W uh the previous

861
00:40:25,599 --> 00:40:31,000
value of w

862
00:40:28,280 --> 00:40:35,440
um and this is the gradient of the loss

863
00:40:31,000 --> 00:40:37,040
and then uh we take the previous value

864
00:40:35,440 --> 00:40:39,680
and then we subtract out the learning

865
00:40:37,040 --> 00:40:39,680
rate times the

866
00:40:40,680 --> 00:40:45,720
gradient and uh there are many many

867
00:40:43,200 --> 00:40:47,280
other optimization options uh I'll cover

868
00:40:45,720 --> 00:40:50,960
the more frequent one called Adam at the

869
00:40:47,280 --> 00:40:54,319
end of this uh this lecture but um this

870
00:40:50,960 --> 00:40:57,160
is the basic way of optimizing the

871
00:40:54,319 --> 00:41:00,599
model so

872
00:40:57,160 --> 00:41:03,359
then my question now is what is this

873
00:41:00,599 --> 00:41:07,000
algorithm with respect

874
00:41:03,359 --> 00:41:10,119
to this is an algorithm that is

875
00:41:07,000 --> 00:41:12,280
taking that has a loss function it's

876
00:41:10,119 --> 00:41:14,079
calculating derivatives and it's

877
00:41:12,280 --> 00:41:17,240
optimizing gradients using stochastic

878
00:41:14,079 --> 00:41:18,839
gradient descent so does anyone have a

879
00:41:17,240 --> 00:41:20,960
guess about what the loss function is

880
00:41:18,839 --> 00:41:23,520
here and maybe what is the learning rate

881
00:41:20,960 --> 00:41:23,520
of stas

882
00:41:24,319 --> 00:41:29,480
gradient I kind of gave you a hint about

883
00:41:26,599 --> 00:41:29,480
the L one

884
00:41:31,640 --> 00:41:37,839
actually and just to recap what this is

885
00:41:34,440 --> 00:41:41,440
doing here it's um if predicted Y is

886
00:41:37,839 --> 00:41:44,560
equal to Y then it is moving the uh the

887
00:41:41,440 --> 00:41:48,240
future weights in the direction of Y

888
00:41:44,560 --> 00:41:48,240
times the frequency

889
00:41:52,599 --> 00:41:56,960
Vector

890
00:41:55,240 --> 00:41:59,079
yeah

891
00:41:56,960 --> 00:42:01,640
yeah exactly so the loss function is

892
00:41:59,079 --> 00:42:05,800
hinge loss and the learning rate is one

893
00:42:01,640 --> 00:42:07,880
um and just to show how that you know

894
00:42:05,800 --> 00:42:12,359
corresponds we have this if statement

895
00:42:07,880 --> 00:42:12,359
here and we have the increment of the

896
00:42:12,960 --> 00:42:20,240
features and this is what the um what

897
00:42:16,920 --> 00:42:21,599
the L sorry the derivative looked like

898
00:42:20,240 --> 00:42:24,240
so we have

899
00:42:21,599 --> 00:42:26,920
if this is moving in the right direction

900
00:42:24,240 --> 00:42:29,520
for the label uh then we increment

901
00:42:26,920 --> 00:42:31,599
otherwise we do nothing so

902
00:42:29,520 --> 00:42:33,559
basically you can see that even this

903
00:42:31,599 --> 00:42:35,200
really simple algorithm that I you know

904
00:42:33,559 --> 00:42:37,480
implemented with a few lines of python

905
00:42:35,200 --> 00:42:38,839
is essentially equivalent to this uh

906
00:42:37,480 --> 00:42:40,760
stochastic gradient descent that we

907
00:42:38,839 --> 00:42:44,559
doing

908
00:42:40,760 --> 00:42:46,359
models so the good news about this is

909
00:42:44,559 --> 00:42:48,359
you know this this is really simple but

910
00:42:46,359 --> 00:42:50,599
it only really works forit like a bag of

911
00:42:48,359 --> 00:42:55,400
words model or a simple feature based

912
00:42:50,599 --> 00:42:57,200
model uh but it opens up a lot of uh new

913
00:42:55,400 --> 00:43:00,440
possibilities for how we can optimize

914
00:42:57,200 --> 00:43:01,599
models and in particular I mentioned uh

915
00:43:00,440 --> 00:43:04,839
that there was a problem with

916
00:43:01,599 --> 00:43:08,200
combination features last class like

917
00:43:04,839 --> 00:43:11,200
don't hate and don't love are not just

918
00:43:08,200 --> 00:43:12,760
you know hate plus don't and love plus

919
00:43:11,200 --> 00:43:14,119
don't it's actually the combination of

920
00:43:12,760 --> 00:43:17,680
the two is really

921
00:43:14,119 --> 00:43:20,160
important and so um yeah just to give an

922
00:43:17,680 --> 00:43:23,440
example we have don't love is maybe bad

923
00:43:20,160 --> 00:43:26,960
uh nothing I don't love is very

924
00:43:23,440 --> 00:43:30,960
good and so in order

925
00:43:26,960 --> 00:43:34,040
to solve this problem we turn to neural

926
00:43:30,960 --> 00:43:37,160
networks and the way we do this is we

927
00:43:34,040 --> 00:43:39,119
have a lookup of dense embeddings sorry

928
00:43:37,160 --> 00:43:41,839
I actually I just realized my coloring

929
00:43:39,119 --> 00:43:44,119
is off I was using red to indicate dense

930
00:43:41,839 --> 00:43:46,480
embeddings so this should be maybe red

931
00:43:44,119 --> 00:43:49,319
instead of blue but um we take these

932
00:43:46,480 --> 00:43:51,200
stents embeddings and then we create

933
00:43:49,319 --> 00:43:53,720
some complicated function to extract

934
00:43:51,200 --> 00:43:55,079
combination features um and then use

935
00:43:53,720 --> 00:43:57,359
those to calculate

936
00:43:55,079 --> 00:44:02,200
scores

937
00:43:57,359 --> 00:44:04,480
um and so we calculate these combination

938
00:44:02,200 --> 00:44:08,240
features and what we want to do is we

939
00:44:04,480 --> 00:44:12,880
want to extract vectors from the input

940
00:44:08,240 --> 00:44:12,880
where each Vector has features

941
00:44:15,839 --> 00:44:21,040
um sorry this is in the wrong order so

942
00:44:18,240 --> 00:44:22,559
I'll I'll get back to this um so this

943
00:44:21,040 --> 00:44:25,319
this was talking about the The

944
00:44:22,559 --> 00:44:27,200
Continuous bag of words features so the

945
00:44:25,319 --> 00:44:30,960
problem with the continuous bag of words

946
00:44:27,200 --> 00:44:30,960
features was we were extracting

947
00:44:31,359 --> 00:44:36,359
features

948
00:44:33,079 --> 00:44:36,359
um like

949
00:44:36,839 --> 00:44:41,400
this but then we were directly using the

950
00:44:39,760 --> 00:44:43,359
the feature the dense features that we

951
00:44:41,400 --> 00:44:45,559
extracted to make predictions without

952
00:44:43,359 --> 00:44:48,839
actually allowing for any interactions

953
00:44:45,559 --> 00:44:51,839
between the features um and

954
00:44:48,839 --> 00:44:55,160
so uh neural networks the way we fix

955
00:44:51,839 --> 00:44:57,079
this is we first extract these features

956
00:44:55,160 --> 00:44:59,440
uh we take these these features of each

957
00:44:57,079 --> 00:45:04,000
word embedding and then we run them

958
00:44:59,440 --> 00:45:07,240
through uh kind of linear transforms in

959
00:45:04,000 --> 00:45:09,880
nonlinear uh like linear multiplications

960
00:45:07,240 --> 00:45:10,880
and then nonlinear transforms to extract

961
00:45:09,880 --> 00:45:13,920
additional

962
00:45:10,880 --> 00:45:15,839
features and uh finally run this through

963
00:45:13,920 --> 00:45:18,640
several layers and then use the

964
00:45:15,839 --> 00:45:21,119
resulting features to make our

965
00:45:18,640 --> 00:45:23,200
predictions and when we do this this

966
00:45:21,119 --> 00:45:25,319
allows us to do more uh interesting

967
00:45:23,200 --> 00:45:28,319
things so like for example we could

968
00:45:25,319 --> 00:45:30,000
learn feature combination a node in the

969
00:45:28,319 --> 00:45:32,599
second layer might be feature one and

970
00:45:30,000 --> 00:45:35,240
feature five are active so that could be

971
00:45:32,599 --> 00:45:38,680
like feature one corresponds to negative

972
00:45:35,240 --> 00:45:43,640
sentiment words like hate

973
00:45:38,680 --> 00:45:45,839
despise um and other things like that so

974
00:45:43,640 --> 00:45:50,079
for hate and despise feature one would

975
00:45:45,839 --> 00:45:53,119
have a high value like 8.0 and then

976
00:45:50,079 --> 00:45:55,480
7.2 and then we also have negation words

977
00:45:53,119 --> 00:45:57,040
like don't or not or something like that

978
00:45:55,480 --> 00:46:00,040
and those would

979
00:45:57,040 --> 00:46:00,040
have

980
00:46:03,720 --> 00:46:08,640
don't would have a high value for like 2

981
00:46:11,880 --> 00:46:15,839
five and so these would be the word

982
00:46:14,200 --> 00:46:18,040
embeddings where each word embedding

983
00:46:15,839 --> 00:46:20,599
corresponded to you know features of the

984
00:46:18,040 --> 00:46:23,480
words and

985
00:46:20,599 --> 00:46:25,480
then um after that we would extract

986
00:46:23,480 --> 00:46:29,319
feature combinations in this second

987
00:46:25,480 --> 00:46:32,079
layer that say oh we see at least one

988
00:46:29,319 --> 00:46:33,760
word where the first feature is active

989
00:46:32,079 --> 00:46:36,359
and we see at least one word where the

990
00:46:33,760 --> 00:46:37,920
fifth feature is active so now that

991
00:46:36,359 --> 00:46:40,640
allows us to capture the fact that we

992
00:46:37,920 --> 00:46:42,319
saw like don't hate or don't despise or

993
00:46:40,640 --> 00:46:44,559
not hate or not despise or something

994
00:46:42,319 --> 00:46:44,559
like

995
00:46:45,079 --> 00:46:51,760
that so this is the way uh kind of this

996
00:46:49,680 --> 00:46:54,839
is a deep uh continuous bag of words

997
00:46:51,760 --> 00:46:56,839
model um this actually was proposed in

998
00:46:54,839 --> 00:46:58,119
205 15 I don't think I have the

999
00:46:56,839 --> 00:47:02,599
reference on the slide but I think it's

1000
00:46:58,119 --> 00:47:05,040
in the notes um on the website and

1001
00:47:02,599 --> 00:47:07,200
actually at that point in time they

1002
00:47:05,040 --> 00:47:09,200
demon there were several interesting

1003
00:47:07,200 --> 00:47:11,960
results that showed that even this like

1004
00:47:09,200 --> 00:47:13,960
really simple model did really well uh

1005
00:47:11,960 --> 00:47:16,319
at text classification and other simple

1006
00:47:13,960 --> 00:47:18,640
tasks like that because it was able to

1007
00:47:16,319 --> 00:47:21,720
you know share features of the words and

1008
00:47:18,640 --> 00:47:23,800
then extract combinations to the

1009
00:47:21,720 --> 00:47:28,200
features

1010
00:47:23,800 --> 00:47:29,760
so um in order order to learn these we

1011
00:47:28,200 --> 00:47:30,920
need to start turning to neural networks

1012
00:47:29,760 --> 00:47:34,400
and the reason why we need to start

1013
00:47:30,920 --> 00:47:38,040
turning to neural networks is

1014
00:47:34,400 --> 00:47:41,920
because while I can calculate the loss

1015
00:47:38,040 --> 00:47:43,280
function of the while I can calculate

1016
00:47:41,920 --> 00:47:44,839
the loss function of the hinged loss for

1017
00:47:43,280 --> 00:47:47,720
a bag of words model by hand I

1018
00:47:44,839 --> 00:47:49,359
definitely don't I probably could but

1019
00:47:47,720 --> 00:47:51,240
don't want to do it for a model that

1020
00:47:49,359 --> 00:47:53,200
starts become as complicated as this

1021
00:47:51,240 --> 00:47:57,440
with multiple Matrix multiplications

1022
00:47:53,200 --> 00:48:00,520
Andes and stuff like that so the way we

1023
00:47:57,440 --> 00:48:05,000
do this just a very brief uh coverage of

1024
00:48:00,520 --> 00:48:06,200
this uh for because um I think probably

1025
00:48:05,000 --> 00:48:08,400
a lot of people have dealt with neural

1026
00:48:06,200 --> 00:48:10,200
networks before um the original

1027
00:48:08,400 --> 00:48:12,880
motivation was that we had neurons in

1028
00:48:10,200 --> 00:48:16,160
the brain uh where

1029
00:48:12,880 --> 00:48:18,839
the each of the neuron synapses took in

1030
00:48:16,160 --> 00:48:21,480
an electrical signal and once they got

1031
00:48:18,839 --> 00:48:24,079
enough electrical signal they would fire

1032
00:48:21,480 --> 00:48:25,960
um but now the current conception of

1033
00:48:24,079 --> 00:48:28,160
neural networks or deep learning models

1034
00:48:25,960 --> 00:48:30,440
is basically computation

1035
00:48:28,160 --> 00:48:32,400
graphs and the way a computation graph

1036
00:48:30,440 --> 00:48:34,760
Works um and I'm especially going to

1037
00:48:32,400 --> 00:48:36,240
talk about the way it works in natural

1038
00:48:34,760 --> 00:48:38,119
language processing which might be a

1039
00:48:36,240 --> 00:48:42,319
contrast to the way it works in computer

1040
00:48:38,119 --> 00:48:43,960
vision is um we have an expression uh

1041
00:48:42,319 --> 00:48:46,480
that looks like this and maybe maybe

1042
00:48:43,960 --> 00:48:47,640
it's the expression X corresponding to

1043
00:48:46,480 --> 00:48:51,880
uh a

1044
00:48:47,640 --> 00:48:53,400
scal um and each node corresponds to

1045
00:48:51,880 --> 00:48:55,599
something like a tensor a matrix a

1046
00:48:53,400 --> 00:48:57,599
vector a scalar so scaler is uh kind

1047
00:48:55,599 --> 00:49:00,480
kind of Zero Dimensional it's a single

1048
00:48:57,599 --> 00:49:01,720
value one dimensional two dimensional or

1049
00:49:00,480 --> 00:49:04,200
arbitrary

1050
00:49:01,720 --> 00:49:06,040
dimensional um and then we also have

1051
00:49:04,200 --> 00:49:08,000
nodes that correspond to the result of

1052
00:49:06,040 --> 00:49:11,480
function applications so if we have X be

1053
00:49:08,000 --> 00:49:14,079
a vector uh we take the vector transpose

1054
00:49:11,480 --> 00:49:18,160
and so each Edge represents a function

1055
00:49:14,079 --> 00:49:20,559
argument and also a data

1056
00:49:18,160 --> 00:49:23,960
dependency and a node with an incoming

1057
00:49:20,559 --> 00:49:27,000
Edge is a function of that Edge's tail

1058
00:49:23,960 --> 00:49:29,040
node and importantly each node knows how

1059
00:49:27,000 --> 00:49:30,640
to compute its value and the value of

1060
00:49:29,040 --> 00:49:32,640
its derivative with respect to each

1061
00:49:30,640 --> 00:49:34,440
argument times the derivative of an

1062
00:49:32,640 --> 00:49:37,920
arbitrary

1063
00:49:34,440 --> 00:49:41,000
input and functions could be basically

1064
00:49:37,920 --> 00:49:45,400
arbitrary functions it can be unary Nary

1065
00:49:41,000 --> 00:49:49,440
unary binary Nary often unary or binary

1066
00:49:45,400 --> 00:49:52,400
and computation graphs are directed in

1067
00:49:49,440 --> 00:49:57,040
cyclic and um one important thing to

1068
00:49:52,400 --> 00:50:00,640
note is that you can um have multiple

1069
00:49:57,040 --> 00:50:02,559
ways of expressing the same function so

1070
00:50:00,640 --> 00:50:04,839
this is actually really important as you

1071
00:50:02,559 --> 00:50:06,920
start implementing things and the reason

1072
00:50:04,839 --> 00:50:09,359
why is the left graph and the right

1073
00:50:06,920 --> 00:50:12,960
graph both express the same thing the

1074
00:50:09,359 --> 00:50:18,640
left graph expresses X

1075
00:50:12,960 --> 00:50:22,559
transpose time A Time X where is whereas

1076
00:50:18,640 --> 00:50:27,160
this one has x a and then it puts it

1077
00:50:22,559 --> 00:50:28,760
into a node that is X transpose a x

1078
00:50:27,160 --> 00:50:30,319
and so these Express exactly the same

1079
00:50:28,760 --> 00:50:32,319
thing but the graph on the left is

1080
00:50:30,319 --> 00:50:33,760
larger and the reason why this is

1081
00:50:32,319 --> 00:50:38,920
important is for practical

1082
00:50:33,760 --> 00:50:40,359
implementation of neural networks um you

1083
00:50:38,920 --> 00:50:43,200
the larger graphs are going to take more

1084
00:50:40,359 --> 00:50:46,799
memory and going to be slower usually

1085
00:50:43,200 --> 00:50:48,200
and so often um in a neural network we

1086
00:50:46,799 --> 00:50:49,559
look at like pipe part which we're going

1087
00:50:48,200 --> 00:50:52,160
to look at in a

1088
00:50:49,559 --> 00:50:55,520
second

1089
00:50:52,160 --> 00:50:57,920
um you will have something you will be

1090
00:50:55,520 --> 00:50:57,920
able to

1091
00:50:58,680 --> 00:51:01,680
do

1092
00:51:03,079 --> 00:51:07,880
this or you'll be able to do

1093
00:51:18,760 --> 00:51:22,880
like

1094
00:51:20,359 --> 00:51:24,839
this so these are two different options

1095
00:51:22,880 --> 00:51:26,920
this one is using more operations and

1096
00:51:24,839 --> 00:51:29,559
this one is using using less operations

1097
00:51:26,920 --> 00:51:31,000
and this is going to be faster because

1098
00:51:29,559 --> 00:51:33,119
basically the implementation within

1099
00:51:31,000 --> 00:51:34,799
Pythor will have been optimized for you

1100
00:51:33,119 --> 00:51:36,799
it will only require one graph node

1101
00:51:34,799 --> 00:51:37,880
instead of multiple graph nodes and

1102
00:51:36,799 --> 00:51:39,799
that's even more important when you

1103
00:51:37,880 --> 00:51:41,040
start talking about like attention or

1104
00:51:39,799 --> 00:51:43,920
something like that which we're going to

1105
00:51:41,040 --> 00:51:46,079
be covering very soon um attention is a

1106
00:51:43,920 --> 00:51:47,359
very multi-head attention or something

1107
00:51:46,079 --> 00:51:49,839
like that is a very complicated

1108
00:51:47,359 --> 00:51:52,079
operation so you want to make sure that

1109
00:51:49,839 --> 00:51:54,359
you're using the operators that are

1110
00:51:52,079 --> 00:51:57,359
available to you to make this more

1111
00:51:54,359 --> 00:51:57,359
efficient

1112
00:51:57,440 --> 00:52:00,760
um and then finally we could like add

1113
00:51:59,280 --> 00:52:01,920
all of these together at the end we

1114
00:52:00,760 --> 00:52:04,000
could add a

1115
00:52:01,920 --> 00:52:05,880
constant um and then we get this

1116
00:52:04,000 --> 00:52:09,520
expression here which gives us kind of a

1117
00:52:05,880 --> 00:52:09,520
polinomial polom

1118
00:52:09,680 --> 00:52:15,760
expression um also another thing to note

1119
00:52:13,480 --> 00:52:17,599
is within a neural network computation

1120
00:52:15,760 --> 00:52:21,920
graph variable names are just labelings

1121
00:52:17,599 --> 00:52:25,359
of nodes and so if you're using a a

1122
00:52:21,920 --> 00:52:27,680
computation graph like this you might

1123
00:52:25,359 --> 00:52:29,240
only be declaring one variable here but

1124
00:52:27,680 --> 00:52:30,839
actually there's a whole bunch of stuff

1125
00:52:29,240 --> 00:52:32,359
going on behind the scenes and all of

1126
00:52:30,839 --> 00:52:34,240
that will take memory and computation

1127
00:52:32,359 --> 00:52:35,440
time and stuff like that so it's

1128
00:52:34,240 --> 00:52:37,119
important to be aware of that if you

1129
00:52:35,440 --> 00:52:40,400
want to make your implementations more

1130
00:52:37,119 --> 00:52:40,400
efficient than other other

1131
00:52:41,119 --> 00:52:46,680
things so we have several algorithms

1132
00:52:44,480 --> 00:52:49,079
that go into implementing neural nuts um

1133
00:52:46,680 --> 00:52:50,760
the first one is graph construction uh

1134
00:52:49,079 --> 00:52:53,480
the second one is forward

1135
00:52:50,760 --> 00:52:54,839
propagation uh and graph construction is

1136
00:52:53,480 --> 00:52:56,359
basically constructing the graph

1137
00:52:54,839 --> 00:52:58,680
declaring ing all the variables stuff

1138
00:52:56,359 --> 00:53:01,520
like this the second one is forward

1139
00:52:58,680 --> 00:53:03,880
propagation and um the way you do this

1140
00:53:01,520 --> 00:53:06,480
is in topological order uh you compute

1141
00:53:03,880 --> 00:53:08,280
the value of a node given its inputs and

1142
00:53:06,480 --> 00:53:11,000
so basically you start out with all of

1143
00:53:08,280 --> 00:53:12,680
the nodes that you give is input and

1144
00:53:11,000 --> 00:53:16,040
then you find any node in the graph

1145
00:53:12,680 --> 00:53:17,799
where all of its uh all of its tail

1146
00:53:16,040 --> 00:53:20,280
nodes or all of its children have been

1147
00:53:17,799 --> 00:53:22,119
calculated so in this case that would be

1148
00:53:20,280 --> 00:53:24,640
these two nodes and then in arbitrary

1149
00:53:22,119 --> 00:53:27,000
order or even in parallel you calculate

1150
00:53:24,640 --> 00:53:28,280
the value of all of the satisfied nodes

1151
00:53:27,000 --> 00:53:31,799
until you get to the

1152
00:53:28,280 --> 00:53:34,280
end and then uh the remaining algorithms

1153
00:53:31,799 --> 00:53:36,200
are back propagation and parameter

1154
00:53:34,280 --> 00:53:38,240
update I already talked about parameter

1155
00:53:36,200 --> 00:53:40,799
update uh using stochastic gradient

1156
00:53:38,240 --> 00:53:42,760
descent but for back propagation we then

1157
00:53:40,799 --> 00:53:45,400
process examples in Reverse topological

1158
00:53:42,760 --> 00:53:47,640
order uh calculate derivatives of

1159
00:53:45,400 --> 00:53:50,400
parameters with respect to final

1160
00:53:47,640 --> 00:53:52,319
value and so we start out with the very

1161
00:53:50,400 --> 00:53:54,200
final value usually this is your loss

1162
00:53:52,319 --> 00:53:56,200
function and then you just step

1163
00:53:54,200 --> 00:54:00,440
backwards in top ological order to

1164
00:53:56,200 --> 00:54:04,160
calculate the derivatives of all these

1165
00:54:00,440 --> 00:54:05,920
so um this is pretty simple I think a

1166
00:54:04,160 --> 00:54:08,040
lot of people may have seen this already

1167
00:54:05,920 --> 00:54:09,920
but keeping this in mind as you're

1168
00:54:08,040 --> 00:54:12,480
implementing NLP models especially

1169
00:54:09,920 --> 00:54:14,240
models that are really memory intensive

1170
00:54:12,480 --> 00:54:16,559
or things like that is pretty important

1171
00:54:14,240 --> 00:54:19,040
because if you accidentally like for

1172
00:54:16,559 --> 00:54:21,799
example calculate the same thing twice

1173
00:54:19,040 --> 00:54:23,559
or accidentally create a graph that is

1174
00:54:21,799 --> 00:54:25,720
manipulating very large tensors and

1175
00:54:23,559 --> 00:54:27,319
creating very large intermediate States

1176
00:54:25,720 --> 00:54:29,720
that can kill your memory and and cause

1177
00:54:27,319 --> 00:54:31,839
big problems so it's an important thing

1178
00:54:29,720 --> 00:54:31,839
to

1179
00:54:34,359 --> 00:54:38,880
be um cool any any questions about

1180
00:54:39,040 --> 00:54:44,440
this okay if not I will go on to the

1181
00:54:41,680 --> 00:54:45,680
next one so neural network Frameworks

1182
00:54:44,440 --> 00:54:48,920
there's several neural network

1183
00:54:45,680 --> 00:54:52,880
Frameworks but in NLP nowadays I really

1184
00:54:48,920 --> 00:54:55,079
only see two and mostly only see one um

1185
00:54:52,880 --> 00:54:57,960
so that one that almost everybody us

1186
00:54:55,079 --> 00:55:01,240
uses is pie torch um and I would

1187
00:54:57,960 --> 00:55:04,559
recommend using it unless you uh you

1188
00:55:01,240 --> 00:55:07,480
know if you're a fan of like rust or you

1189
00:55:04,559 --> 00:55:09,200
know esoteric uh not esoteric but like

1190
00:55:07,480 --> 00:55:11,960
unusual programming languages and you

1191
00:55:09,200 --> 00:55:14,720
like Beauty and things like this another

1192
00:55:11,960 --> 00:55:15,799
option might be Jacks uh so I'll explain

1193
00:55:14,720 --> 00:55:18,440
a little bit about the difference

1194
00:55:15,799 --> 00:55:19,960
between them uh and you can pick

1195
00:55:18,440 --> 00:55:23,559
accordingly

1196
00:55:19,960 --> 00:55:25,359
um first uh both of these Frameworks uh

1197
00:55:23,559 --> 00:55:26,839
are developed by big companies and they

1198
00:55:25,359 --> 00:55:28,520
have a lot of engineering support behind

1199
00:55:26,839 --> 00:55:29,720
them that's kind of an important thing

1200
00:55:28,520 --> 00:55:31,280
to think about when you're deciding

1201
00:55:29,720 --> 00:55:32,599
which framework to use because you know

1202
00:55:31,280 --> 00:55:36,000
it'll be well

1203
00:55:32,599 --> 00:55:38,039
supported um pytorch is definitely most

1204
00:55:36,000 --> 00:55:40,400
widely used in NLP especially NLP

1205
00:55:38,039 --> 00:55:44,240
research um and it's used in some NLP

1206
00:55:40,400 --> 00:55:47,359
project J is used in some NLP

1207
00:55:44,240 --> 00:55:49,960
projects um pytorch favors Dynamic

1208
00:55:47,359 --> 00:55:53,760
execution so what dynamic execution

1209
00:55:49,960 --> 00:55:55,880
means is um you basically create a

1210
00:55:53,760 --> 00:55:59,760
computation graph and and then execute

1211
00:55:55,880 --> 00:56:02,760
it uh every time you process an input uh

1212
00:55:59,760 --> 00:56:04,680
in contrast there's also you define the

1213
00:56:02,760 --> 00:56:07,200
computation graph first and then execute

1214
00:56:04,680 --> 00:56:09,280
it over and over again so in other words

1215
00:56:07,200 --> 00:56:10,680
the graph construction step only happens

1216
00:56:09,280 --> 00:56:13,119
once kind of at the beginning of

1217
00:56:10,680 --> 00:56:16,799
computation and then you compile it

1218
00:56:13,119 --> 00:56:20,039
afterwards and it's actually pytorch

1219
00:56:16,799 --> 00:56:23,359
supports kind of defining and compiling

1220
00:56:20,039 --> 00:56:27,480
and Jax supports more Dynamic things but

1221
00:56:23,359 --> 00:56:30,160
the way they were designed is uh is kind

1222
00:56:27,480 --> 00:56:32,960
of favoring Dynamic execution or

1223
00:56:30,160 --> 00:56:37,079
favoring definition in population

1224
00:56:32,960 --> 00:56:39,200
and the difference between these two is

1225
00:56:37,079 --> 00:56:41,760
this one gives you more flexibility this

1226
00:56:39,200 --> 00:56:45,440
one gives you better optimization in wor

1227
00:56:41,760 --> 00:56:49,760
speed if you want to if you want to do

1228
00:56:45,440 --> 00:56:52,400
that um another thing about Jax is um

1229
00:56:49,760 --> 00:56:55,200
it's kind of very close to numpy in a

1230
00:56:52,400 --> 00:56:57,440
way like it uses a very num something

1231
00:56:55,200 --> 00:56:59,960
that's kind of close to numpy it's very

1232
00:56:57,440 --> 00:57:02,359
heavily based on tensors and so because

1233
00:56:59,960 --> 00:57:04,640
of this you can kind of easily do some

1234
00:57:02,359 --> 00:57:06,640
interesting things like okay I want to

1235
00:57:04,640 --> 00:57:11,319
take this tensor and I want to split it

1236
00:57:06,640 --> 00:57:14,000
over two gpus um and this is good if

1237
00:57:11,319 --> 00:57:17,119
you're training like a very large model

1238
00:57:14,000 --> 00:57:20,920
and you want to put kind

1239
00:57:17,119 --> 00:57:20,920
of this part of the

1240
00:57:22,119 --> 00:57:26,520
model uh you want to put this part of

1241
00:57:24,119 --> 00:57:30,079
the model on GP 1 this on gpu2 this on

1242
00:57:26,520 --> 00:57:31,599
GPU 3 this on GPU it's slightly simpler

1243
00:57:30,079 --> 00:57:34,400
conceptually to do in Jacks but it's

1244
00:57:31,599 --> 00:57:37,160
also possible to do in

1245
00:57:34,400 --> 00:57:39,119
p and pytorch by far has the most

1246
00:57:37,160 --> 00:57:41,640
vibrant ecosystem so like as I said

1247
00:57:39,119 --> 00:57:44,200
pytorch is a good default choice but you

1248
00:57:41,640 --> 00:57:47,480
can consider using Jack if you uh if you

1249
00:57:44,200 --> 00:57:47,480
like new

1250
00:57:48,079 --> 00:57:55,480
things cool um yeah actually I already

1251
00:57:51,599 --> 00:57:58,079
talked about that so in the interest of

1252
00:57:55,480 --> 00:58:02,119
time I may not go into these very deeply

1253
00:57:58,079 --> 00:58:05,799
but it's important to note that we have

1254
00:58:02,119 --> 00:58:05,799
examples of all of

1255
00:58:06,920 --> 00:58:12,520
the models that I talked about in the

1256
00:58:09,359 --> 00:58:16,720
class today these are created for

1257
00:58:12,520 --> 00:58:17,520
Simplicity not for Speed or efficiency

1258
00:58:16,720 --> 00:58:20,480
of

1259
00:58:17,520 --> 00:58:24,920
implementation um so these are kind of

1260
00:58:20,480 --> 00:58:27,760
torch P torch based uh examples uh where

1261
00:58:24,920 --> 00:58:31,599
you can create the bag of words

1262
00:58:27,760 --> 00:58:36,440
Model A continuous bag of words

1263
00:58:31,599 --> 00:58:39,640
model um and

1264
00:58:36,440 --> 00:58:41,640
a deep continuous bag of wordss

1265
00:58:39,640 --> 00:58:44,359
model

1266
00:58:41,640 --> 00:58:46,039
and all of these I believe are

1267
00:58:44,359 --> 00:58:48,760
implemented in

1268
00:58:46,039 --> 00:58:51,960
model.py and the most important thing is

1269
00:58:48,760 --> 00:58:54,960
where you define the forward pass and

1270
00:58:51,960 --> 00:58:57,319
maybe I can just give a a simple example

1271
00:58:54,960 --> 00:58:58,200
this but here this is where you do the

1272
00:58:57,319 --> 00:59:01,839
word

1273
00:58:58,200 --> 00:59:04,400
embedding this is where you sum up all

1274
00:59:01,839 --> 00:59:08,119
of the embeddings and add a

1275
00:59:04,400 --> 00:59:10,200
bias um and then this is uh where you

1276
00:59:08,119 --> 00:59:13,960
return the the

1277
00:59:10,200 --> 00:59:13,960
score and then oh

1278
00:59:14,799 --> 00:59:19,119
sorry the continuous bag of words model

1279
00:59:17,520 --> 00:59:22,160
sums up some

1280
00:59:19,119 --> 00:59:23,640
embeddings uh or gets the embeddings

1281
00:59:22,160 --> 00:59:25,799
sums up some

1282
00:59:23,640 --> 00:59:28,079
embeddings

1283
00:59:25,799 --> 00:59:30,599
uh gets the score here and then runs it

1284
00:59:28,079 --> 00:59:33,200
through a linear or changes the view

1285
00:59:30,599 --> 00:59:35,119
runs it through a linear layer and then

1286
00:59:33,200 --> 00:59:38,319
the Deep continuous bag of words model

1287
00:59:35,119 --> 00:59:41,160
also adds a few layers of uh like linear

1288
00:59:38,319 --> 00:59:43,119
transformations in Dage so you should be

1289
00:59:41,160 --> 00:59:44,640
able to see that these correspond pretty

1290
00:59:43,119 --> 00:59:47,440
closely to the things that I had on the

1291
00:59:44,640 --> 00:59:49,280
slides so um hopefully that's a good

1292
00:59:47,440 --> 00:59:51,839
start if you're not very familiar with

1293
00:59:49,280 --> 00:59:51,839
implementing

1294
00:59:53,119 --> 00:59:58,440
model oh and yes the recitation uh will

1295
00:59:56,599 --> 00:59:59,799
be about playing around with sentence

1296
00:59:58,440 --> 01:00:01,200
piece and playing around with these so

1297
00:59:59,799 --> 01:00:02,839
if you have any look at them have any

1298
01:00:01,200 --> 01:00:05,000
questions you're welcome to show up

1299
01:00:02,839 --> 01:00:09,880
where I walk

1300
01:00:05,000 --> 01:00:09,880
through cool um any any questions about

1301
01:00:12,839 --> 01:00:19,720
these okay so a few more final important

1302
01:00:16,720 --> 01:00:21,720
Concepts um another concept that you

1303
01:00:19,720 --> 01:00:25,440
should definitely be aware of is the

1304
01:00:21,720 --> 01:00:27,280
atom Optimizer uh so there's lots of uh

1305
01:00:25,440 --> 01:00:30,559
optimizers that you could be using but

1306
01:00:27,280 --> 01:00:32,200
almost all research in NLP uses some uh

1307
01:00:30,559 --> 01:00:38,440
variety of the atom

1308
01:00:32,200 --> 01:00:40,839
Optimizer and the U the way this works

1309
01:00:38,440 --> 01:00:42,559
is it

1310
01:00:40,839 --> 01:00:45,640
optimizes

1311
01:00:42,559 --> 01:00:48,480
the um it optimizes model considering

1312
01:00:45,640 --> 01:00:49,359
the rolling average of the gradient and

1313
01:00:48,480 --> 01:00:53,160
uh

1314
01:00:49,359 --> 01:00:55,920
momentum and the way it works is here we

1315
01:00:53,160 --> 01:00:58,839
have a gradient here we have

1316
01:00:55,920 --> 01:01:04,000
momentum and what you can see is

1317
01:00:58,839 --> 01:01:06,680
happening here is we add a little bit of

1318
01:01:04,000 --> 01:01:09,200
the gradient in uh how much you add in

1319
01:01:06,680 --> 01:01:12,720
is with respect to the size of this beta

1320
01:01:09,200 --> 01:01:16,000
1 parameter and you add it into uh the

1321
01:01:12,720 --> 01:01:18,640
momentum term so this momentum term like

1322
01:01:16,000 --> 01:01:20,440
gradually increases and decreases so in

1323
01:01:18,640 --> 01:01:23,440
contrast to standard gradient percent

1324
01:01:20,440 --> 01:01:25,839
which could be

1325
01:01:23,440 --> 01:01:28,440
updating

1326
01:01:25,839 --> 01:01:31,440
uh each parameter kind of like very

1327
01:01:28,440 --> 01:01:33,359
differently on each time step this will

1328
01:01:31,440 --> 01:01:35,680
make the momentum kind of transition

1329
01:01:33,359 --> 01:01:37,240
more smoothly by taking the rolling

1330
01:01:35,680 --> 01:01:39,880
average of the

1331
01:01:37,240 --> 01:01:43,400
gradient and then the the second thing

1332
01:01:39,880 --> 01:01:47,640
is um by taking the momentum this is the

1333
01:01:43,400 --> 01:01:51,000
rolling average of the I guess gradient

1334
01:01:47,640 --> 01:01:54,440
uh variance sorry I this should be

1335
01:01:51,000 --> 01:01:58,079
variance and the reason why you need

1336
01:01:54,440 --> 01:02:01,319
need to keep track of the variance is

1337
01:01:58,079 --> 01:02:03,319
some uh some parameters will have very

1338
01:02:01,319 --> 01:02:06,559
large variance in their gradients and

1339
01:02:03,319 --> 01:02:11,480
might fluctuate very uh strongly and

1340
01:02:06,559 --> 01:02:13,039
others might have a smaller uh chain

1341
01:02:11,480 --> 01:02:15,240
variant in their gradients and not

1342
01:02:13,039 --> 01:02:18,240
fluctuate very much but we want to make

1343
01:02:15,240 --> 01:02:20,200
sure that we update the ones we still

1344
01:02:18,240 --> 01:02:22,240
update the ones that have a very small

1345
01:02:20,200 --> 01:02:25,760
uh change of their variance and the

1346
01:02:22,240 --> 01:02:27,440
reason why is kind of let's say you have

1347
01:02:25,760 --> 01:02:30,440
a

1348
01:02:27,440 --> 01:02:30,440
multi-layer

1349
01:02:32,480 --> 01:02:38,720
network

1350
01:02:34,480 --> 01:02:41,240
um or actually sorry a better

1351
01:02:38,720 --> 01:02:44,319
um a better example is like let's say we

1352
01:02:41,240 --> 01:02:47,559
have a big word embedding Matrix and

1353
01:02:44,319 --> 01:02:53,359
over here we have like really frequent

1354
01:02:47,559 --> 01:02:56,279
words and then over here we have uh

1355
01:02:53,359 --> 01:02:59,319
gradi

1356
01:02:56,279 --> 01:03:00,880
no we have like less frequent words we

1357
01:02:59,319 --> 01:03:02,799
want to make sure that all of these get

1358
01:03:00,880 --> 01:03:06,160
updated appropriately all of these get

1359
01:03:02,799 --> 01:03:08,640
like enough updates and so over here

1360
01:03:06,160 --> 01:03:10,760
this one will have lots of updates and

1361
01:03:08,640 --> 01:03:13,680
so uh kind of

1362
01:03:10,760 --> 01:03:16,599
the amount that we

1363
01:03:13,680 --> 01:03:20,039
update or the the amount that we update

1364
01:03:16,599 --> 01:03:21,799
the uh this will be relatively large

1365
01:03:20,039 --> 01:03:23,119
whereas over here this will not have

1366
01:03:21,799 --> 01:03:24,880
very many updates we'll have lots of

1367
01:03:23,119 --> 01:03:26,480
zero updates also

1368
01:03:24,880 --> 01:03:29,160
and so the amount that we update this

1369
01:03:26,480 --> 01:03:32,520
will be relatively small and so this

1370
01:03:29,160 --> 01:03:36,119
kind of squared to gradient here will uh

1371
01:03:32,520 --> 01:03:38,400
be smaller for the values over here and

1372
01:03:36,119 --> 01:03:41,359
what that allows us to do is it allows

1373
01:03:38,400 --> 01:03:44,200
us to maybe I can just go to the bottom

1374
01:03:41,359 --> 01:03:46,039
we end up uh dividing by the square root

1375
01:03:44,200 --> 01:03:47,599
of this and because we divide by the

1376
01:03:46,039 --> 01:03:51,000
square root of this if this is really

1377
01:03:47,599 --> 01:03:55,680
large like 50 and 70 and then this over

1378
01:03:51,000 --> 01:03:59,480
here is like one 0.5

1379
01:03:55,680 --> 01:04:01,920
uh or something we will be upgrading the

1380
01:03:59,480 --> 01:04:03,920
ones that have like less Square

1381
01:04:01,920 --> 01:04:06,880
gradients so it will it allows you to

1382
01:04:03,920 --> 01:04:08,760
upweight the less common gradients more

1383
01:04:06,880 --> 01:04:10,440
frequently and then there's also some

1384
01:04:08,760 --> 01:04:13,400
terms for correcting bias early in

1385
01:04:10,440 --> 01:04:16,440
training because these momentum in uh in

1386
01:04:13,400 --> 01:04:19,559
variance or momentum in squared gradient

1387
01:04:16,440 --> 01:04:23,119
terms are not going to be like well

1388
01:04:19,559 --> 01:04:24,839
calibrated yet so it prevents them from

1389
01:04:23,119 --> 01:04:28,880
going very three wire beginning of

1390
01:04:24,839 --> 01:04:30,839
training so this is uh the details of

1391
01:04:28,880 --> 01:04:33,640
this again are not like super super

1392
01:04:30,839 --> 01:04:37,359
important um another thing that I didn't

1393
01:04:33,640 --> 01:04:40,200
write on the slides is uh now in

1394
01:04:37,359 --> 01:04:43,920
Transformers it's also super common to

1395
01:04:40,200 --> 01:04:47,400
have an overall learning rate schle so

1396
01:04:43,920 --> 01:04:50,520
even um Even Adam has this uh Ada

1397
01:04:47,400 --> 01:04:53,440
learning rate parameter here and we what

1398
01:04:50,520 --> 01:04:55,240
we often do is we adjust this so we

1399
01:04:53,440 --> 01:04:57,839
start at low

1400
01:04:55,240 --> 01:04:59,640
we raise it up and then we have a Decay

1401
01:04:57,839 --> 01:05:03,039
uh at the end and exactly how much you

1402
01:04:59,640 --> 01:05:04,440
do this kind of depends on um you know

1403
01:05:03,039 --> 01:05:06,160
how big your model is how much data

1404
01:05:04,440 --> 01:05:09,160
you're tring on eventually and the

1405
01:05:06,160 --> 01:05:12,440
reason why we do this is transformers

1406
01:05:09,160 --> 01:05:13,839
are unfortunately super sensitive to

1407
01:05:12,440 --> 01:05:15,359
having a high learning rate right at the

1408
01:05:13,839 --> 01:05:16,559
very beginning so if you update them

1409
01:05:15,359 --> 01:05:17,920
with a high learning rate right at the

1410
01:05:16,559 --> 01:05:22,920
very beginning they go haywire and you

1411
01:05:17,920 --> 01:05:24,400
get a really weird model um and but you

1412
01:05:22,920 --> 01:05:26,760
want to raise it eventually so your

1413
01:05:24,400 --> 01:05:28,920
model is learning appropriately and then

1414
01:05:26,760 --> 01:05:30,400
in all stochastic gradient descent no

1415
01:05:28,920 --> 01:05:31,680
matter whether you're using atom or

1416
01:05:30,400 --> 01:05:33,400
anything else it's a good idea to

1417
01:05:31,680 --> 01:05:36,200
gradually decrease the learning rate at

1418
01:05:33,400 --> 01:05:38,119
the end to prevent the model from

1419
01:05:36,200 --> 01:05:40,480
continuing to fluctuate and getting it

1420
01:05:38,119 --> 01:05:42,760
to a stable point that gives you good

1421
01:05:40,480 --> 01:05:45,559
accuracy over a large part of data so

1422
01:05:42,760 --> 01:05:47,480
this is often included like if you look

1423
01:05:45,559 --> 01:05:51,000
at any standard Transformer training

1424
01:05:47,480 --> 01:05:53,079
recipe it will have that this so that's

1425
01:05:51,000 --> 01:05:54,799
kind of the the go-to

1426
01:05:53,079 --> 01:05:58,960
optimizer

1427
01:05:54,799 --> 01:06:01,039
um are there any questions or

1428
01:05:58,960 --> 01:06:02,599
discussion there's also tricky things

1429
01:06:01,039 --> 01:06:04,000
like cyclic learning rates where you

1430
01:06:02,599 --> 01:06:06,599
decrease the learning rate increase it

1431
01:06:04,000 --> 01:06:08,559
and stuff like that but I won't go into

1432
01:06:06,599 --> 01:06:11,000
that and don't actually use it that

1433
01:06:08,559 --> 01:06:12,760
much second thing is visualization of

1434
01:06:11,000 --> 01:06:15,400
embeddings so normally when we have word

1435
01:06:12,760 --> 01:06:19,760
embeddings usually they're kind of large

1436
01:06:15,400 --> 01:06:21,559
um and they can be like 512 or 1024

1437
01:06:19,760 --> 01:06:25,079
dimensions

1438
01:06:21,559 --> 01:06:28,720
and so one thing that we can do is we

1439
01:06:25,079 --> 01:06:31,079
can down weight them or sorry down uh

1440
01:06:28,720 --> 01:06:34,400
like reduce the dimensions or perform

1441
01:06:31,079 --> 01:06:35,880
dimensionality reduction and put them in

1442
01:06:34,400 --> 01:06:37,680
like two or three dimensions which are

1443
01:06:35,880 --> 01:06:40,200
easy for humans to

1444
01:06:37,680 --> 01:06:42,000
visualize this is an example using

1445
01:06:40,200 --> 01:06:44,839
principal component analysis which is a

1446
01:06:42,000 --> 01:06:48,279
linear Dimension reduction technique and

1447
01:06:44,839 --> 01:06:50,680
this is uh an example from 10 years ago

1448
01:06:48,279 --> 01:06:52,359
now uh one of the first major word

1449
01:06:50,680 --> 01:06:55,240
embedding papers where they demonstrated

1450
01:06:52,359 --> 01:06:57,720
that if you do this sort of linear

1451
01:06:55,240 --> 01:06:59,440
Dimension reduction uh you get actually

1452
01:06:57,720 --> 01:07:01,279
some interesting things where you can

1453
01:06:59,440 --> 01:07:03,240
draw a vector that's almost the same

1454
01:07:01,279 --> 01:07:06,400
direction between like countries and

1455
01:07:03,240 --> 01:07:09,319
their uh countries and their capitals

1456
01:07:06,400 --> 01:07:13,720
for example so this is a good thing to

1457
01:07:09,319 --> 01:07:16,559
do but actually PCA uh doesn't give

1458
01:07:13,720 --> 01:07:20,760
you in some cases PCA doesn't give you

1459
01:07:16,559 --> 01:07:22,920
super great uh visualizations sorry yeah

1460
01:07:20,760 --> 01:07:25,920
well for like if it's

1461
01:07:22,920 --> 01:07:25,920
like

1462
01:07:29,880 --> 01:07:35,039
um for things like this I think you

1463
01:07:33,119 --> 01:07:37,359
probably would still see vectors in the

1464
01:07:35,039 --> 01:07:38,760
same direction but I don't think it like

1465
01:07:37,359 --> 01:07:40,920
there's a reason why I'm introducing

1466
01:07:38,760 --> 01:07:44,279
nonlinear projections next because the

1467
01:07:40,920 --> 01:07:46,799
more standard way to do this is uh

1468
01:07:44,279 --> 01:07:50,640
nonlinear projections in in particular a

1469
01:07:46,799 --> 01:07:54,880
method called tisne and the way um they

1470
01:07:50,640 --> 01:07:56,880
do this is they try to group

1471
01:07:54,880 --> 01:07:59,000
things that are close together in high

1472
01:07:56,880 --> 01:08:01,240
dimensional space so that they're also

1473
01:07:59,000 --> 01:08:04,440
close together in low dimensional space

1474
01:08:01,240 --> 01:08:08,520
but they remove the Restriction that

1475
01:08:04,440 --> 01:08:10,799
this is uh that this is linear so this

1476
01:08:08,520 --> 01:08:15,480
is an example of just grouping together

1477
01:08:10,799 --> 01:08:18,040
some digits uh from the memus data

1478
01:08:15,480 --> 01:08:20,279
set or sorry reducing the dimension of

1479
01:08:18,040 --> 01:08:23,640
digits from the mest data

1480
01:08:20,279 --> 01:08:25,640
set according to PCA and you can see it

1481
01:08:23,640 --> 01:08:28,000
gives these kind of blobs that overlap

1482
01:08:25,640 --> 01:08:29,799
with each other and stuff like this but

1483
01:08:28,000 --> 01:08:31,679
if you do it with tney this is

1484
01:08:29,799 --> 01:08:34,799
completely unsupervised actually it's

1485
01:08:31,679 --> 01:08:37,080
not training any model for labeling the

1486
01:08:34,799 --> 01:08:39,239
labels are just used to draw the colors

1487
01:08:37,080 --> 01:08:42,520
and you can see that it gets pretty

1488
01:08:39,239 --> 01:08:44,520
coherent um clusters that correspond to

1489
01:08:42,520 --> 01:08:48,120
like what the actual digits

1490
01:08:44,520 --> 01:08:50,120
are um however uh one problem with

1491
01:08:48,120 --> 01:08:53,159
titney I I still think it's better than

1492
01:08:50,120 --> 01:08:55,000
PCA for a large number of uh

1493
01:08:53,159 --> 01:08:59,199
applications

1494
01:08:55,000 --> 01:09:01,040
but settings of tisy matter and tisy has

1495
01:08:59,199 --> 01:09:02,920
a few settings kind of the most

1496
01:09:01,040 --> 01:09:04,120
important ones are the overall

1497
01:09:02,920 --> 01:09:06,560
perplexity

1498
01:09:04,120 --> 01:09:09,040
hyperparameter and uh the number of

1499
01:09:06,560 --> 01:09:12,319
steps that you perform and there's a

1500
01:09:09,040 --> 01:09:14,920
nice example uh of a paper or kind of

1501
01:09:12,319 --> 01:09:16,359
like online post uh that demonstrates

1502
01:09:14,920 --> 01:09:18,560
how if you change these parameters you

1503
01:09:16,359 --> 01:09:22,279
can get very different things so if this

1504
01:09:18,560 --> 01:09:24,080
is the original data you run tisy and it

1505
01:09:22,279 --> 01:09:26,640
gives you very different things based on

1506
01:09:24,080 --> 01:09:29,279
the hyper parameters that you change um

1507
01:09:26,640 --> 01:09:32,880
and here's another example uh you have

1508
01:09:29,279 --> 01:09:36,960
two linear uh things like this and so

1509
01:09:32,880 --> 01:09:40,839
PCA no matter how you ran PCA you would

1510
01:09:36,960 --> 01:09:44,080
still get a linear output from this so

1511
01:09:40,839 --> 01:09:45,960
normally uh you know it might change the

1512
01:09:44,080 --> 01:09:49,239
order it might squash it a little bit or

1513
01:09:45,960 --> 01:09:51,239
something like this but um if you run

1514
01:09:49,239 --> 01:09:53,400
tisy it gives you crazy things it even

1515
01:09:51,239 --> 01:09:56,040
gives you like DNA and other stuff like

1516
01:09:53,400 --> 01:09:58,040
that so so um you do need to be a little

1517
01:09:56,040 --> 01:10:00,600
bit careful that uh this is not

1518
01:09:58,040 --> 01:10:02,320
necessarily going to tell you nice

1519
01:10:00,600 --> 01:10:04,400
linear correlations like this so like

1520
01:10:02,320 --> 01:10:06,159
let's say this correlation existed if

1521
01:10:04,400 --> 01:10:09,199
you use tisy it might not necessarily

1522
01:10:06,159 --> 01:10:09,199
come out to

1523
01:10:09,320 --> 01:10:14,880
TIY

1524
01:10:11,800 --> 01:10:16,920
cool yep uh that that's my final thing

1525
01:10:14,880 --> 01:10:18,520
actually I talked said sequence models

1526
01:10:16,920 --> 01:10:19,679
in the next class but it's in the class

1527
01:10:18,520 --> 01:10:21,440
after this I'm going to be talking about

1528
01:10:19,679 --> 01:10:24,199
language

1529
01:10:21,440 --> 01:10:27,159
modeling uh cool any any questions

1530
01:10:24,199 --> 01:10:27,159
or