CMU Advanced NLP 2024 (4) Sequence Modeling/transcript.vtt

WEBVTT

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started in a moment uh since it's now uh

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12:30 are there any questions before we

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get

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started okay I don't see I don't see any

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so I guess we can uh Jump Right In this

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time I'll be talking about sequence

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modeling and N first I'm going to be

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talking about uh why why we do sequence

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modeling what varieties of sequence

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modeling exist and then after that I'm

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going to talk about kind of three basic

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techniques for sequence modeling namely

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recurrent neural networks convolutional

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networks and

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attention so when we talk about sequence

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modeling in NLP I've kind of already

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made the motivation for doing this but

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basically NLP is full of sequential data

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and this can be everything from words

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and sentences or tokens and sentences to

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uh characters and words to sentences in

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a discourse or a paragraph or a

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document um it can also be multiple

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documents in time multiple social media

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posts whatever else you want there's

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just you know sequences all over

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NLP and I mentioned this uh last time

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also but there's also long-distance

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dependencies in language so uh just to

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give an example there's agreement in

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number uh gender Etc so in order to

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create a fluent language model you'll

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have to handle this agreement so if we

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you say he does not have very much

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confidence in uh it would have to be

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himself but if you say she does not have

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very much confidence in it would have to

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be herself and this is this gender

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agreement is not super frequent in

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English but it's very frequent in other

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languages like French or uh you know

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most languages in the world in some uh

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way or

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another then separately from that you

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also have things like selectional

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preferences um like the Reign has lasted

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as long as the life of the queen and the

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rain has lasted as long as the life of

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the clouds uh in American English the

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only way you could know uh which word

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came beforehand if you were doing speech

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recognition is if you uh like had that

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kind of semantic uh idea of uh that

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these agree with each other in some way

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and there's also factual knowledge

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there's all kinds of other things uh

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that you need to carry over long

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contexts um these can be comp

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complicated so this is a a nice example

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so if we try to figure out what it

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refers to here uh the trophy would not

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fit in the brown suitcase because it was

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too big what is it

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here the trophy yeah and then what about

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uh the trophy would not fit in the brown

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suitcase because it was too

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small suit suitcase right um does anyone

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know what the name of something like

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this is

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has anyone heard of this challenge uh

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before no one okay um this this is

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called the winegrad schema challenge or

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these are called winegrad schemas and

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basically winterr schemas are a type

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of they're type of kind of linguistic

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challenge where you create two paired uh

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examples

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that you vary in very minimal ways where

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the answer differs between the two um

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and so uh there's lots of other examples

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about how you can create these things

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and they're good for testing uh whether

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language models are able to do things

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because they're able to uh kind of

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control for the fact that you know like

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the answer might be

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um the answer might be very uh like

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more frequent or less frequent and so

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the language model could just pick that

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so another example is we uh we came up

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with a benchmark of figurative language

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where we tried to figure out whether

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language models would be able

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to interpret figur figurative language

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and I actually have the multilingual uh

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version on the suggested projects uh on

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the Piaza oh yeah that's one

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announcement I posted a big list of

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suggested projects on pza I think a lot

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of people saw it you don't have to

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follow these but if you're interested in

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them feel free to talk to the contacts

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and we can give you more information

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about them um but anyway uh so in this

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data set what we did is we came up with

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some figurative language like this movie

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had the depth of of a waiting pool and

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this movie had the depth of a diving

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pool and so then after that you would

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have two choices this movie was uh this

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movie was very deep and interesting this

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movie was not very deep and interesting

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and so you have these like like two

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pairs of questions and answers and you

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need to decide between them and

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depending on what the input is the

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output will change and so that's a good

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way to control for um and test whether

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language models really understand

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something so if you're interested in

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benchmarking or other things like that

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it's a good parad time to think about

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anyway that's a little bit of an aside

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um so now I'd like to go on to types of

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sequential prediction problems

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and types of prediction problems in

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general uh binary and multiclass we

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already talked about that's when we're

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doing for example uh classification

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between two classes or classification

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between multiple

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classes but there's also another variety

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of prediction called structured

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prediction and structured prediction is

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when you have a very large number of

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labels it's not you know a finite number

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of labels and uh so that would be

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something like uh if you take in an

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input and you want to predict all of the

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parts of speech of all the words in the

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input and if you had like 50 parts of

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speech the number of labels that you

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would have for each sentence

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is any any

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ideas 50 50 parts of speech and like

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let's say for

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wordss 60 um it it's every combination

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of parts of speech for every words so

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uh close but maybe the opposite it's uh

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50 to the four because you have 50 50

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choices here 50 choices here so it's a c

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cross product of all of the

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choices um and so that becomes very

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quickly un untenable um let's say you're

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talking about translation from English

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to Japanese uh now you don't really even

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have a finite number of choices because

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the length could be even longer uh the

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length of the output could be even

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longer than the

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C

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rules

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together makes it

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fewer yeah so really good question um so

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the question or the the question or

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comment was if there are certain rules

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about one thing not ever being able to

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follow the other you can actually reduce

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the number um you could do that with a

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hard constraint and make things uh kind

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of

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and like actually cut off things that

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you know have zero probability but in

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reality what people do is they just trim

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hypotheses that have low probability and

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so that has kind of the same effect like

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you almost never see a determiner after

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a determiner in English um and so yeah

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we're going to talk about uh algorithms

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to do this in the Generation section so

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we could talk more about that

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that um but anyway the basic idea behind

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structured prediction is that you don't

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like language modeling like I said last

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time you don't predict all of the the

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whole sequence at once you usually

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predict each element at once and then

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somehow calculate the conditional

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probability of the next element given

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the the current element or other things

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like that so that's how we solve

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structured prediction

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problems another thing is unconditioned

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versus conditioned predictions so

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uncondition prediction we don't do this

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very often um but basically uh we

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predict the probability of a a single

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variable or generate a single variable

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and condition pro prediction is

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predicting the probability of an output

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variable given an input like

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this so um for unconditioned prediction

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um the way we can do this is left to

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right autoagressive models and these are

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the ones that I talked about last time

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when I was talking about how we build

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language models um and these could be uh

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specifically this kind though is a kind

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that doesn't have any context limit so

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it's looking all the way back to the

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beginning of the the sequence and this

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could be like an infinite length endr

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model but practically we can't use those

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because they would have too many

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parameters they would be too sparse for

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us to estimate the parameters so um what

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we do instead with engram models which I

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talked about last time is we limit the

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the context length so we have something

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like a trigram model where we don't

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actually reference all of the previous

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outputs uh when we make a prediction oh

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and sorry actually I I should explain

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how how do we uh how do we read this

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graph so this would be we're predicting

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number one here we're predicting word

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number one and we're conditioning we're

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not conditioning on anything after it

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we're predicting word number two we're

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conditioning on Word number one we're

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predicting word number three we're

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conditioning on Word number two so here

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we would be uh predicting word number

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four conditioning on Words number three

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and two but not number one so that would

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be like a trigram

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bottle um so

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the what is this is there a robot

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walking around somewhere um Howard drill

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okay okay' be a lot more fun if it was a

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robot um so

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uh the things we're going to talk about

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today are largely going to be ones that

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have unlimited length context um and so

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we can uh we'll talk about some examples

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here and then um there's also

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independent prediction so this uh would

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be something like a unigram model where

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you would just uh not condition on any

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previous

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context there's also bidirectional

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prediction where basically when you

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predict each element you predict based

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on all of the other elements not the

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element itself uh this could be

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something like a masked language model

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um but note here that I put a slash

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through here uh because this is not a

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well-formed probability because as I

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mentioned last time um in order to have

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a well-formed probability you need to

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predict the elements based on all of the

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elements that you predicted before and

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you can't predict based on future

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elements so this is not actually a

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probabilistic model but sometimes people

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use this to kind of learn

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representations that could be used

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Downstream for some

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reason cool is this clear any questions

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comments

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yeah so these are all um not

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conditioning on any prior context uh so

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when you predict each word it's

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conditioning on context that you

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previously generated or previously

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predicted yeah so and if I go to the

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conditioned ones these are where you

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have like a source x uh where you're

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given this and then you want to

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calculate the conditional probability of

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something else

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so um to give some examples of this um

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this is autor regressive conditioned

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prediction and um this could be like a

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SE a standard sequence to sequence model

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or it could be a language model where

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you're given a prompt and you want to

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predict the following output like we

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often do with chat GPT or something like

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this and so

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um yeah I I don't think you

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can

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yeah I don't know if any way you can do

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a chat GPT without any conditioning

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context um but there were people who

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were sending uh I saw this about a week

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or two ago there were people who were

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sending things to the chat um to the GPD

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3.5 or gp4 API with no input and it

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would randomly output random questions

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or something like that so that's what's

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what happens when you send things to uh

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to chat GPT without any prior

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conditioning conts but normally what you

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do is you put in you know your prompt

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and then it follows up with your prompt

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and that would be in this uh in this

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Paradigm there's also something called

00:13:08.240 --> 00:13:14.199
non-auto regressive condition prediction

00:13:11.279 --> 00:13:16.760
um and this can be used for something

00:13:14.199 --> 00:13:19.160
like sequence labeling or non- autor

00:13:16.760 --> 00:13:20.760
regressive machine translation I'll talk

00:13:19.160 --> 00:13:22.839
about the first one in this class and

00:13:20.760 --> 00:13:25.600
I'll talk about the the second one maybe

00:13:22.839 --> 00:13:27.399
later um it's kind of a minor topic now

00:13:25.600 --> 00:13:30.040
it used to be popular a few years ago so

00:13:27.399 --> 00:13:33.279
I'm not sure whether it'll cover it but

00:13:30.040 --> 00:13:33.279
um uh

00:13:33.399 --> 00:13:39.279
yeah cool so the basic modeling Paradigm

00:13:37.079 --> 00:13:41.199
that we use for things like this is

00:13:39.279 --> 00:13:42.760
extracting features and predicting so

00:13:41.199 --> 00:13:44.839
this is exactly the same as the bag of

00:13:42.760 --> 00:13:46.680
wordss model right I the bag of wordss

00:13:44.839 --> 00:13:48.680
model that I talked about the first time

00:13:46.680 --> 00:13:50.959
we extracted features uh based on those

00:13:48.680 --> 00:13:53.440
features we made predictions so it's no

00:13:50.959 --> 00:13:55.480
different when we do sequence modeling

00:13:53.440 --> 00:13:57.680
um but the methods that we use for

00:13:55.480 --> 00:14:01.120
feature extraction is different so given

00:13:57.680 --> 00:14:03.920
in the input text X we extract features

00:14:01.120 --> 00:14:06.519
H and predict labels

00:14:03.920 --> 00:14:10.320
Y and for something like text

00:14:06.519 --> 00:14:12.600
classification what we do is we uh so

00:14:10.320 --> 00:14:15.440
for example we have text classification

00:14:12.600 --> 00:14:17.920
or or sequence labeling and for text

00:14:15.440 --> 00:14:19.720
classification usually what we would do

00:14:17.920 --> 00:14:21.360
is we would have a feature extractor

00:14:19.720 --> 00:14:23.120
from this feature extractor we take the

00:14:21.360 --> 00:14:25.199
sequence and we convert it into a single

00:14:23.120 --> 00:14:28.040
vector and then based on this Vector we

00:14:25.199 --> 00:14:30.160
make a prediction so that that's what we

00:14:28.040 --> 00:14:33.160
do for

00:14:30.160 --> 00:14:35.480
classification um for sequence labeling

00:14:33.160 --> 00:14:37.160
normally what we do is we extract one

00:14:35.480 --> 00:14:40.240
vector for each thing that we would like

00:14:37.160 --> 00:14:42.079
to predict about so here that might be

00:14:40.240 --> 00:14:45.639
one vector for each

00:14:42.079 --> 00:14:47.720
word um and then based on this uh we

00:14:45.639 --> 00:14:49.120
would predict something for each word so

00:14:47.720 --> 00:14:50.360
this is an example of part of speech

00:14:49.120 --> 00:14:53.079
tagging but there's a lot of other

00:14:50.360 --> 00:14:56.920
sequence labeling tasks

00:14:53.079 --> 00:14:58.839
also and what tasks exist for something

00:14:56.920 --> 00:15:03.040
like sequence labeling so sequence lab

00:14:58.839 --> 00:15:06.240
in is uh a pretty

00:15:03.040 --> 00:15:09.000
big subset of NLP tasks you can express

00:15:06.240 --> 00:15:11.040
a lot of things as sequence labeling and

00:15:09.000 --> 00:15:13.000
basically given an input text X we

00:15:11.040 --> 00:15:16.079
predict an output label sequence y of

00:15:13.000 --> 00:15:17.560
equal length so this can be used for

00:15:16.079 --> 00:15:20.160
things like part of speech tagging to

00:15:17.560 --> 00:15:22.000
get the parts of speech of each word um

00:15:20.160 --> 00:15:24.639
it can also be used for something like

00:15:22.000 --> 00:15:26.959
lemmatization and litiz basically what

00:15:24.639 --> 00:15:29.880
that is is it is predicting the base

00:15:26.959 --> 00:15:31.480
form of each word uh and this can be

00:15:29.880 --> 00:15:34.560
used for normalization if you want to

00:15:31.480 --> 00:15:36.360
find like for example all instances of a

00:15:34.560 --> 00:15:38.480
a particular verb being used or all

00:15:36.360 --> 00:15:40.800
instances of a particular noun being

00:15:38.480 --> 00:15:42.720
used this is a little bit different than

00:15:40.800 --> 00:15:45.000
something like stemming so stemming

00:15:42.720 --> 00:15:48.160
normally what stemming would do is it

00:15:45.000 --> 00:15:50.560
would uh chop off the plural here it

00:15:48.160 --> 00:15:53.240
would chop off S but it wouldn't be able

00:15:50.560 --> 00:15:56.279
to do things like normalized saw into C

00:15:53.240 --> 00:15:57.759
because uh stemming uh just removes

00:15:56.279 --> 00:15:59.240
suffixes it doesn't do any sort of

00:15:57.759 --> 00:16:02.720
normalization so that's the difference

00:15:59.240 --> 00:16:05.199
between lonization and

00:16:02.720 --> 00:16:08.079
stemon there's also something called

00:16:05.199 --> 00:16:09.680
morphological tagging um in

00:16:08.079 --> 00:16:11.639
morphological tagging basically what

00:16:09.680 --> 00:16:14.360
this is doing is this is a

00:16:11.639 --> 00:16:17.040
more advanced version of part of speech

00:16:14.360 --> 00:16:20.360
tagging uh that predicts things like

00:16:17.040 --> 00:16:23.600
okay this is a a past tense verb uh this

00:16:20.360 --> 00:16:25.639
is a plural um this is a particular verb

00:16:23.600 --> 00:16:27.240
form and you have multiple tags here

00:16:25.639 --> 00:16:28.959
this is less interesting in English

00:16:27.240 --> 00:16:30.920
because English is kind of boring

00:16:28.959 --> 00:16:32.319
language morphology morphologically it

00:16:30.920 --> 00:16:33.399
doesn't have a lot of conjugation and

00:16:32.319 --> 00:16:35.839
other stuff but it's a lot more

00:16:33.399 --> 00:16:38.319
interesting in more complex languages

00:16:35.839 --> 00:16:40.040
like Japanese or Hindi or other things

00:16:38.319 --> 00:16:42.480
like

00:16:40.040 --> 00:16:43.920
that Chinese is even more boring than

00:16:42.480 --> 00:16:46.120
English so if you're interested in

00:16:43.920 --> 00:16:47.000
Chinese then you don't need to worry

00:16:46.120 --> 00:16:50.680
about

00:16:47.000 --> 00:16:52.560
that cool um but actually what's maybe

00:16:50.680 --> 00:16:55.000
more widely used from the sequence

00:16:52.560 --> 00:16:57.480
labeling perspective is span labeling

00:16:55.000 --> 00:17:01.040
and here you want to predict spans and

00:16:57.480 --> 00:17:03.560
labels and this could be uh named entity

00:17:01.040 --> 00:17:05.360
recognitions so if you say uh Graham nub

00:17:03.560 --> 00:17:07.199
is teaching at Carnegie melan University

00:17:05.360 --> 00:17:09.520
you would want to identify each entity

00:17:07.199 --> 00:17:11.480
is being like a person organization

00:17:09.520 --> 00:17:16.039
Place governmental entity other stuff

00:17:11.480 --> 00:17:18.760
like that um there's also

00:17:16.039 --> 00:17:20.439
uh things like syntactic chunking where

00:17:18.760 --> 00:17:23.640
you want to find all noun phrases and

00:17:20.439 --> 00:17:26.799
verb phrases um also semantic role

00:17:23.640 --> 00:17:30.360
labeling where semantic role labeling is

00:17:26.799 --> 00:17:32.480
uh demonstrating who did what to whom so

00:17:30.360 --> 00:17:34.440
it's saying uh this is the actor the

00:17:32.480 --> 00:17:36.120
person who did the thing this is the

00:17:34.440 --> 00:17:38.520
thing that is being done and this is the

00:17:36.120 --> 00:17:40.280
place where it's being done so uh this

00:17:38.520 --> 00:17:42.840
can be useful if you want to do any sort

00:17:40.280 --> 00:17:45.559
of analysis about who does what to whom

00:17:42.840 --> 00:17:48.160
uh other things like

00:17:45.559 --> 00:17:50.360
that um there's also a more complicated

00:17:48.160 --> 00:17:52.080
thing called an entity linking which

00:17:50.360 --> 00:17:54.559
isn't really a span linking task but

00:17:52.080 --> 00:17:58.400
it's basically named entity recognition

00:17:54.559 --> 00:18:00.799
and you link it to um and you link it to

00:17:58.400 --> 00:18:04.200
to like a database like Wiki data or

00:18:00.799 --> 00:18:06.600
Wikipedia or something like this and

00:18:04.200 --> 00:18:09.520
this doesn't seem very glamorous perhaps

00:18:06.600 --> 00:18:10.799
you know a lot of people might not you

00:18:09.520 --> 00:18:13.400
might not

00:18:10.799 --> 00:18:15.000
sound like immediately excit be

00:18:13.400 --> 00:18:16.799
immediately excited by entity linking

00:18:15.000 --> 00:18:18.520
but actually it's super super important

00:18:16.799 --> 00:18:20.080
for things like news aggregation and

00:18:18.520 --> 00:18:21.640
other stuff like that find all the news

00:18:20.080 --> 00:18:23.799
articles about the celebrity or

00:18:21.640 --> 00:18:26.919
something like this uh find all of the

00:18:23.799 --> 00:18:29.720
mentions of our product um our company's

00:18:26.919 --> 00:18:33.400
product and uh social media or things so

00:18:29.720 --> 00:18:33.400
it's actually a really widely used

00:18:33.720 --> 00:18:38.000
technology and then finally span

00:18:36.039 --> 00:18:40.240
labeling can also be treated as sequence

00:18:38.000 --> 00:18:43.240
labeling um and the way we normally do

00:18:40.240 --> 00:18:45.600
this is we use something called bio tags

00:18:43.240 --> 00:18:47.760
and uh here you predict the beginning uh

00:18:45.600 --> 00:18:50.200
in and out tags for each word or spans

00:18:47.760 --> 00:18:52.400
so if we have this example of spans uh

00:18:50.200 --> 00:18:56.120
we just convert this into tags uh where

00:18:52.400 --> 00:18:57.760
you say uh begin person in person o

00:18:56.120 --> 00:18:59.640
means it's not an entity begin

00:18:57.760 --> 00:19:02.799
organization in organization and then

00:18:59.640 --> 00:19:05.520
you canvert that back into um into these

00:19:02.799 --> 00:19:09.880
spans so this makes it relatively easy

00:19:05.520 --> 00:19:09.880
to uh kind of do the span

00:19:10.480 --> 00:19:15.120
prediction cool um so now you know uh

00:19:13.640 --> 00:19:16.600
now you know what to do if you want to

00:19:15.120 --> 00:19:18.280
predict entities or other things like

00:19:16.600 --> 00:19:20.240
that there's a lot of models on like

00:19:18.280 --> 00:19:22.400
hugging face for example that uh allow

00:19:20.240 --> 00:19:25.640
you to do these things are there any

00:19:22.400 --> 00:19:25.640
questions uh before I move

00:19:27.080 --> 00:19:32.440
on okay

00:19:28.799 --> 00:19:34.039
cool I'll just go forward then so um now

00:19:32.440 --> 00:19:37.000
I'm going to talk about how we actually

00:19:34.039 --> 00:19:38.559
model these in machine learning models

00:19:37.000 --> 00:19:40.919
and there's three major types of

00:19:38.559 --> 00:19:43.120
sequence models uh there are other types

00:19:40.919 --> 00:19:45.320
of sequence models but I'd say the great

00:19:43.120 --> 00:19:47.840
majority of work uses one of these three

00:19:45.320 --> 00:19:51.720
different types and the first one is

00:19:47.840 --> 00:19:54.840
recurrence um what recurrence does it is

00:19:51.720 --> 00:19:56.240
it conditions on representations on an

00:19:54.840 --> 00:19:58.720
encoding of the

00:19:56.240 --> 00:20:01.360
history and so the way this works works

00:19:58.720 --> 00:20:04.679
is essentially you have your input

00:20:01.360 --> 00:20:06.280
vectors like this uh usually word

00:20:04.679 --> 00:20:08.600
embeddings or embeddings from the

00:20:06.280 --> 00:20:10.880
previous layer of the model and you have

00:20:08.600 --> 00:20:12.840
a recurrent neural network and the

00:20:10.880 --> 00:20:14.600
recurrent neural network um at the very

00:20:12.840 --> 00:20:17.280
beginning might only take the first

00:20:14.600 --> 00:20:19.480
Vector but every subsequent step it

00:20:17.280 --> 00:20:23.760
takes the input vector and it takes the

00:20:19.480 --> 00:20:23.760
hidden Vector from the previous uh

00:20:24.080 --> 00:20:32.280
input and the uh then you keep on going

00:20:29.039 --> 00:20:32.280
uh like this all the way through the

00:20:32.320 --> 00:20:37.600
sequence the convolution is a

00:20:35.799 --> 00:20:40.880
conditioning representations on local

00:20:37.600 --> 00:20:44.200
context so you have the inputs like this

00:20:40.880 --> 00:20:47.200
and here you're conditioning on the word

00:20:44.200 --> 00:20:51.240
itself and the surrounding um words on

00:20:47.200 --> 00:20:52.960
the right or the left so um you would do

00:20:51.240 --> 00:20:55.240
something like this this is a typical

00:20:52.960 --> 00:20:57.480
convolution where you have this this

00:20:55.240 --> 00:20:59.039
certain one here and the left one and

00:20:57.480 --> 00:21:01.080
the right one and this would be a size

00:20:59.039 --> 00:21:03.480
three convolution you could also have a

00:21:01.080 --> 00:21:06.520
size five convolution 7 n you know

00:21:03.480 --> 00:21:08.600
whatever else um that would take in more

00:21:06.520 --> 00:21:11.520
surrounding words like

00:21:08.600 --> 00:21:13.720
this and then finally we have attention

00:21:11.520 --> 00:21:15.640
um and attention is conditioned

00:21:13.720 --> 00:21:19.080
representations at a weighted average of

00:21:15.640 --> 00:21:21.000
all tokens in the sequence and so here

00:21:19.080 --> 00:21:24.600
um we're conditioning on all of the

00:21:21.000 --> 00:21:26.279
other tokens in the sequence but um the

00:21:24.600 --> 00:21:28.919
amount that we condition on each of the

00:21:26.279 --> 00:21:32.039
tokens differs uh between

00:21:28.919 --> 00:21:34.919
so we might get more of this token less

00:21:32.039 --> 00:21:37.600
of this token and other things like that

00:21:34.919 --> 00:21:39.720
and I'll go into the mechanisms of each

00:21:37.600 --> 00:21:43.159
of

00:21:39.720 --> 00:21:45.720
these one important thing to think about

00:21:43.159 --> 00:21:49.279
is uh the computational complexity of

00:21:45.720 --> 00:21:51.960
each of these and um the computational

00:21:49.279 --> 00:21:56.240
complexity can be

00:21:51.960 --> 00:21:58.600
expressed as the sequence length let's

00:21:56.240 --> 00:22:00.840
call the sequence length n and

00:21:58.600 --> 00:22:02.520
convolution has a convolution window

00:22:00.840 --> 00:22:05.080
size so I'll call that

00:22:02.520 --> 00:22:08.039
W so does anyone have an idea of the

00:22:05.080 --> 00:22:10.360
computational complexity of a recurrent

00:22:08.039 --> 00:22:10.360
neural

00:22:11.480 --> 00:22:16.640
network so how um how quickly does the

00:22:15.120 --> 00:22:18.640
computation of a recurrent neural

00:22:16.640 --> 00:22:20.760
network grow and one way you can look at

00:22:18.640 --> 00:22:24.360
this is uh figure out the number of

00:22:20.760 --> 00:22:24.360
arrows uh that you see

00:22:24.480 --> 00:22:29.080
here yeah it's it's linear so it's

00:22:27.440 --> 00:22:32.520
basically

00:22:29.080 --> 00:22:35.520
n um what about

00:22:32.520 --> 00:22:36.760
convolution any other ideas any ideas

00:22:35.520 --> 00:22:42.039
about

00:22:36.760 --> 00:22:45.120
convolution n yeah NW n

00:22:42.039 --> 00:22:47.559
w and what about

00:22:45.120 --> 00:22:52.200
attention n squar

00:22:47.559 --> 00:22:53.559
yeah so what you can see is um for very

00:22:52.200 --> 00:22:58.000
long

00:22:53.559 --> 00:23:00.400
sequences um for very long sequences the

00:22:58.000 --> 00:23:04.480
asymptotic complexity of running a

00:23:00.400 --> 00:23:06.039
recurrent neural network is uh lower so

00:23:04.480 --> 00:23:08.960
you can run a recurrent neural network

00:23:06.039 --> 00:23:10.480
over a sequence of length uh you know 20

00:23:08.960 --> 00:23:12.480
million or something like that and as

00:23:10.480 --> 00:23:15.200
long as you had enough memory it would

00:23:12.480 --> 00:23:16.520
take a linear time but um if you do

00:23:15.200 --> 00:23:18.400
something like attention over a really

00:23:16.520 --> 00:23:20.240
long sequence it would be more difficult

00:23:18.400 --> 00:23:22.080
there's a lot of caveats here because

00:23:20.240 --> 00:23:23.320
attention and convolution are easily

00:23:22.080 --> 00:23:26.200
paral

00:23:23.320 --> 00:23:28.520
parallelized uh whereas uh recurrence is

00:23:26.200 --> 00:23:30.919
not um and I'll talk about that a second

00:23:28.520 --> 00:23:32.679
but any anyway it's a good thing to keep

00:23:30.919 --> 00:23:36.240
in

00:23:32.679 --> 00:23:37.679
mind cool um so the next the first

00:23:36.240 --> 00:23:39.799
sequence model I want to introduce is

00:23:37.679 --> 00:23:42.559
recurrent neural networks oh um sorry

00:23:39.799 --> 00:23:45.799
one other thing I want to mention is all

00:23:42.559 --> 00:23:47.600
of these are still used um it might seem

00:23:45.799 --> 00:23:49.960
that like if you're very plugged into

00:23:47.600 --> 00:23:52.640
NLP it might seem like Well everybody's

00:23:49.960 --> 00:23:55.080
using attention um so why do we need to

00:23:52.640 --> 00:23:56.880
learn about the other ones uh but

00:23:55.080 --> 00:23:59.679
actually all of these are used and

00:23:56.880 --> 00:24:02.600
usually recurrence and convolution are

00:23:59.679 --> 00:24:04.960
used in combination with attention uh in

00:24:02.600 --> 00:24:07.799
some way for particular applications

00:24:04.960 --> 00:24:09.960
where uh like uh recurrence or a

00:24:07.799 --> 00:24:12.640
convolution are are useful so I'll I'll

00:24:09.960 --> 00:24:15.279
go into details of that

00:24:12.640 --> 00:24:18.159
l so let's talk about the first sequence

00:24:15.279 --> 00:24:20.600
model uh recurrent neural networks so

00:24:18.159 --> 00:24:22.919
recurrent neural networks um they're

00:24:20.600 --> 00:24:26.399
basically tools to remember information

00:24:22.919 --> 00:24:28.520
uh they were invented in uh around

00:24:26.399 --> 00:24:30.520
1990 and

00:24:28.520 --> 00:24:34.120
the way they work is a feedforward

00:24:30.520 --> 00:24:35.600
neural network looks a bit like this we

00:24:34.120 --> 00:24:38.000
have some sort of look up over the

00:24:35.600 --> 00:24:40.120
context we calculate embeddings we do a

00:24:38.000 --> 00:24:41.000
transform we get a hidden State and we

00:24:40.120 --> 00:24:43.039
make the

00:24:41.000 --> 00:24:46.159
prediction whereas a recurrent neural

00:24:43.039 --> 00:24:49.360
network uh feeds in the previous hidden

00:24:46.159 --> 00:24:53.360
State and a very simple Elman style

00:24:49.360 --> 00:24:54.840
neural network looks um or I'll contrast

00:24:53.360 --> 00:24:56.559
the feed forward neural network that we

00:24:54.840 --> 00:24:58.279
already know with an Elman style neural

00:24:56.559 --> 00:25:00.399
network um

00:24:58.279 --> 00:25:01.880
uh recurrent neural network so basically

00:25:00.399 --> 00:25:06.120
the feed forward Network that we already

00:25:01.880 --> 00:25:07.840
know does a um linear transform over the

00:25:06.120 --> 00:25:09.279
input and then it runs it through a

00:25:07.840 --> 00:25:11.640
nonlinear function and this could be

00:25:09.279 --> 00:25:14.200
like a tan function or a Ru function or

00:25:11.640 --> 00:25:17.080
anything like that in a recurrent neural

00:25:14.200 --> 00:25:19.559
network we add uh multiplication by the

00:25:17.080 --> 00:25:22.080
hidden the previous hidden state so it

00:25:19.559 --> 00:25:25.120
looks like

00:25:22.080 --> 00:25:27.000
this and so if we look at what

00:25:25.120 --> 00:25:29.080
processing a sequence looks like uh

00:25:27.000 --> 00:25:31.080
basically what we do is we start out

00:25:29.080 --> 00:25:32.720
with an initial State this initial State

00:25:31.080 --> 00:25:34.320
could be like all zeros or it could be

00:25:32.720 --> 00:25:35.200
randomized or it could be learned or

00:25:34.320 --> 00:25:38.480
whatever

00:25:35.200 --> 00:25:42.080
else and then based on based on this uh

00:25:38.480 --> 00:25:44.279
we run it through an RNN function um and

00:25:42.080 --> 00:25:46.600
then you know use calculate the hidden

00:25:44.279 --> 00:25:48.960
State use it to make a prediction uh we

00:25:46.600 --> 00:25:50.760
have the RNN function uh make a

00:25:48.960 --> 00:25:51.760
prediction RNN make a prediction RNN

00:25:50.760 --> 00:25:54.520
make a

00:25:51.760 --> 00:25:56.960
prediction so one important thing here

00:25:54.520 --> 00:25:58.360
is that this RNN is exactly the same

00:25:56.960 --> 00:26:01.880
function

00:25:58.360 --> 00:26:04.960
no matter which position it appears in

00:26:01.880 --> 00:26:06.640
and so because of that we just no matter

00:26:04.960 --> 00:26:08.279
how long the sequence becomes we always

00:26:06.640 --> 00:26:10.200
have the same number of parameters which

00:26:08.279 --> 00:26:12.600
is always like really important for a

00:26:10.200 --> 00:26:15.120
sequence model so uh that's what this

00:26:12.600 --> 00:26:15.120
looks like

00:26:15.799 --> 00:26:20.480
here so how do we train

00:26:18.320 --> 00:26:22.679
rnns um

00:26:20.480 --> 00:26:24.399
basically if you remember we can trade

00:26:22.679 --> 00:26:27.159
neural networks as long as we have a

00:26:24.399 --> 00:26:29.240
directed e cyclic graph that calculates

00:26:27.159 --> 00:26:30.919
our loss function and then for uh

00:26:29.240 --> 00:26:32.640
forward propagation and back propagation

00:26:30.919 --> 00:26:35.720
we'll do all the rest to calculate our

00:26:32.640 --> 00:26:38.760
parameters and we uh we update the

00:26:35.720 --> 00:26:40.480
parameters so the way this works is uh

00:26:38.760 --> 00:26:42.000
let's say we're doing sequence labeling

00:26:40.480 --> 00:26:45.200
in each of these predictions is a part

00:26:42.000 --> 00:26:47.559
of speech uh each of these labels is a

00:26:45.200 --> 00:26:49.000
true part of speech label or sorry each

00:26:47.559 --> 00:26:50.760
of these predictions is like a

00:26:49.000 --> 00:26:52.919
probability over the part parts of

00:26:50.760 --> 00:26:55.720
speech for that sequence each of these

00:26:52.919 --> 00:26:57.640
labels is a true part of speech label so

00:26:55.720 --> 00:26:59.320
basically what we do is from this we

00:26:57.640 --> 00:27:02.200
calculate the negative log likelihood of

00:26:59.320 --> 00:27:05.559
the true part of speech we get a

00:27:02.200 --> 00:27:09.120
loss and so now we have four losses uh

00:27:05.559 --> 00:27:11.559
here this is no longer a nice directed

00:27:09.120 --> 00:27:13.000
acyclic uh graph that ends in a single

00:27:11.559 --> 00:27:15.279
loss function which is kind of what we

00:27:13.000 --> 00:27:17.559
needed for back propagation right so

00:27:15.279 --> 00:27:20.240
what do we do uh very simple we just add

00:27:17.559 --> 00:27:22.440
them together uh we take the sum and now

00:27:20.240 --> 00:27:24.120
we have a single loss function uh which

00:27:22.440 --> 00:27:26.240
is the sum of all of the loss functions

00:27:24.120 --> 00:27:28.679
for each prediction that we

00:27:26.240 --> 00:27:30.799
made and that's our total loss and now

00:27:28.679 --> 00:27:32.600
we do have a directed asli graph where

00:27:30.799 --> 00:27:34.320
this is the terminal node and we can do

00:27:32.600 --> 00:27:36.480
backr like

00:27:34.320 --> 00:27:37.799
this this is true for all sequence

00:27:36.480 --> 00:27:39.320
models I'm going to talk about today I'm

00:27:37.799 --> 00:27:41.559
just illustrating it with recurrent

00:27:39.320 --> 00:27:43.279
networks um any any questions here

00:27:41.559 --> 00:27:45.240
everything

00:27:43.279 --> 00:27:47.919
good

00:27:45.240 --> 00:27:50.279
okay cool um yeah so now we have the

00:27:47.919 --> 00:27:52.960
loss it's a Well form dag uh we can run

00:27:50.279 --> 00:27:55.320
backrop so uh basically what we do is we

00:27:52.960 --> 00:27:58.399
just run back propop and our loss goes

00:27:55.320 --> 00:28:01.120
out uh back into all of the

00:27:58.399 --> 00:28:04.200
places now parameters are tied across

00:28:01.120 --> 00:28:06.080
time so the derivatives into the

00:28:04.200 --> 00:28:07.200
parameters are aggregated over all of

00:28:06.080 --> 00:28:10.760
the time

00:28:07.200 --> 00:28:13.760
steps um and this has been called back

00:28:10.760 --> 00:28:16.320
propagation through time uh since uh

00:28:13.760 --> 00:28:18.679
these were originally invented so

00:28:16.320 --> 00:28:21.720
basically what it looks like is because

00:28:18.679 --> 00:28:25.600
the parameters for this RNN function are

00:28:21.720 --> 00:28:27.120
shared uh they'll essentially be updated

00:28:25.600 --> 00:28:29.480
they'll only be updated once but they're

00:28:27.120 --> 00:28:32.640
updated from like four different

00:28:29.480 --> 00:28:32.640
positions in this network

00:28:34.120 --> 00:28:38.440
essentially yeah and this is the same

00:28:36.120 --> 00:28:40.559
for all sequence uh sequence models that

00:28:38.440 --> 00:28:43.519
I'm going to talk about

00:28:40.559 --> 00:28:45.360
today um another variety of models that

00:28:43.519 --> 00:28:47.559
people use are bidirectional rnns and

00:28:45.360 --> 00:28:49.880
these are uh used when you want to you

00:28:47.559 --> 00:28:52.960
know do something like sequence labeling

00:28:49.880 --> 00:28:54.399
and so you just uh run two rnns you want

00:28:52.960 --> 00:28:56.279
run one from the beginning one from the

00:28:54.399 --> 00:28:59.399
end and concatenate them together like

00:28:56.279 --> 00:28:59.399
this make predictions

00:29:01.200 --> 00:29:08.200
cool uh any questions yeah if you run

00:29:05.559 --> 00:29:09.960
the does that change your

00:29:08.200 --> 00:29:11.679
complexity does this change the

00:29:09.960 --> 00:29:13.000
complexity it doesn't change the ASM

00:29:11.679 --> 00:29:16.519
totic complexity because you're

00:29:13.000 --> 00:29:18.320
multiplying by two uh and like Big O

00:29:16.519 --> 00:29:21.559
notation doesn't care if you multiply by

00:29:18.320 --> 00:29:23.880
a constant but it it does double the Ty

00:29:21.559 --> 00:29:23.880
that it would

00:29:24.080 --> 00:29:28.080
do cool any

00:29:26.320 --> 00:29:32.799
other

00:29:28.080 --> 00:29:35.720
okay let's go forward um another problem

00:29:32.799 --> 00:29:37.240
that is particularly Salient in rnns and

00:29:35.720 --> 00:29:40.440
part of the reason why attention models

00:29:37.240 --> 00:29:42.000
are so useful is Vanishing gradients but

00:29:40.440 --> 00:29:43.880
you should be aware of this regardless

00:29:42.000 --> 00:29:46.799
of whether like no matter which model

00:29:43.880 --> 00:29:48.799
you're using and um thinking about it

00:29:46.799 --> 00:29:50.720
very carefully is actually a really good

00:29:48.799 --> 00:29:52.399
way to design better architectures if

00:29:50.720 --> 00:29:54.000
you're going to be designing uh

00:29:52.399 --> 00:29:56.039
designing

00:29:54.000 --> 00:29:58.000
architectures so basically the problem

00:29:56.039 --> 00:29:59.399
with Vanishing gradients is like let's

00:29:58.000 --> 00:30:01.799
say we have a prediction task where

00:29:59.399 --> 00:30:03.960
we're calculating a regression we're

00:30:01.799 --> 00:30:05.519
inputting a whole bunch of tokens and

00:30:03.960 --> 00:30:08.080
then calculating a regression at the

00:30:05.519 --> 00:30:12.840
very end using a square air loss

00:30:08.080 --> 00:30:16.360
function if we do something like this uh

00:30:12.840 --> 00:30:17.919
the problem is if we have a standard RNN

00:30:16.360 --> 00:30:21.279
when we do back

00:30:17.919 --> 00:30:25.480
propop we'll have a big gradient

00:30:21.279 --> 00:30:27.000
probably for the first RNN unit here but

00:30:25.480 --> 00:30:30.120
every time because we're running this

00:30:27.000 --> 00:30:33.679
through through some sort of

00:30:30.120 --> 00:30:37.080
nonlinearity if we for example if our

00:30:33.679 --> 00:30:39.240
nonlinearity is a t h function uh the

00:30:37.080 --> 00:30:42.000
gradient of the tan H function looks a

00:30:39.240 --> 00:30:42.000
little bit like

00:30:42.120 --> 00:30:50.000
this and um here I if I am not mistaken

00:30:47.200 --> 00:30:53.480
this Peaks at at one and everywhere else

00:30:50.000 --> 00:30:56.919
at zero and so because this is peing at

00:30:53.480 --> 00:30:58.679
one everywhere else at zero let's say um

00:30:56.919 --> 00:31:01.360
we have an input way over here like

00:30:58.679 --> 00:31:03.080
minus minus 3 or something like that if

00:31:01.360 --> 00:31:04.760
we have that that basically destroys our

00:31:03.080 --> 00:31:10.760
gradient our gradient disappears for

00:31:04.760 --> 00:31:13.559
that particular unit um and you know

00:31:10.760 --> 00:31:15.399
maybe one thing that you might say is oh

00:31:13.559 --> 00:31:17.039
well you know if this is getting so

00:31:15.399 --> 00:31:19.320
small because this only goes up to one

00:31:17.039 --> 00:31:22.960
let's do like 100 time t

00:31:19.320 --> 00:31:24.880
h as our uh as our activation function

00:31:22.960 --> 00:31:26.600
we'll do 100 time tan H and so now this

00:31:24.880 --> 00:31:28.279
goes up to 100 and now our gradients are

00:31:26.600 --> 00:31:30.080
not going to disapp here but then you

00:31:28.279 --> 00:31:31.720
have the the opposite problem you have

00:31:30.080 --> 00:31:34.760
exploding gradients where it goes up by

00:31:31.720 --> 00:31:36.360
100 every time uh it gets unmanageable

00:31:34.760 --> 00:31:40.000
and destroys your gradient descent

00:31:36.360 --> 00:31:41.720
itself so basically we have uh we have

00:31:40.000 --> 00:31:43.200
this problem because if you apply a

00:31:41.720 --> 00:31:45.639
function over and over again your

00:31:43.200 --> 00:31:47.240
gradient gets smaller and smaller every

00:31:45.639 --> 00:31:49.080
smaller and smaller bigger and bigger

00:31:47.240 --> 00:31:50.480
every time you do that and uh you have

00:31:49.080 --> 00:31:51.720
the vanishing gradient or exploding

00:31:50.480 --> 00:31:54.799
gradient

00:31:51.720 --> 00:31:56.919
problem um it's not just a problem with

00:31:54.799 --> 00:31:59.039
nonlinearities so it also happens when

00:31:56.919 --> 00:32:00.480
you do do your weight Matrix multiplies

00:31:59.039 --> 00:32:03.840
and other stuff like that basically

00:32:00.480 --> 00:32:05.960
anytime you modify uh the the input into

00:32:03.840 --> 00:32:07.720
a different output it will have a

00:32:05.960 --> 00:32:10.240
gradient and so it will either be bigger

00:32:07.720 --> 00:32:14.000
than one or less than

00:32:10.240 --> 00:32:16.000
one um so I mentioned this is a problem

00:32:14.000 --> 00:32:18.120
for rnns it's particularly a problem for

00:32:16.000 --> 00:32:20.799
rnns over long sequences but it's also a

00:32:18.120 --> 00:32:23.039
problem for any other model you use and

00:32:20.799 --> 00:32:24.960
the reason why this is important to know

00:32:23.039 --> 00:32:26.799
is if there's important information in

00:32:24.960 --> 00:32:29.000
your model finding a way that you can

00:32:26.799 --> 00:32:30.559
get a direct path from that important

00:32:29.000 --> 00:32:32.600
information to wherever you're making a

00:32:30.559 --> 00:32:34.440
prediction often is a way to improve

00:32:32.600 --> 00:32:39.120
your model

00:32:34.440 --> 00:32:41.159
um improve your model performance and on

00:32:39.120 --> 00:32:42.919
the contrary if there's unimportant

00:32:41.159 --> 00:32:45.320
information if there's information that

00:32:42.919 --> 00:32:47.159
you think is likely to be unimportant

00:32:45.320 --> 00:32:49.159
putting it farther away or making it a

00:32:47.159 --> 00:32:51.279
more indirect path so the model has to

00:32:49.159 --> 00:32:53.200
kind of work harder to use it is a good

00:32:51.279 --> 00:32:54.840
way to prevent the model from being

00:32:53.200 --> 00:32:57.679
distracted by like tons and tons of

00:32:54.840 --> 00:33:00.200
information um uh some of it

00:32:57.679 --> 00:33:03.960
which may be irrelevant so it's a good

00:33:00.200 --> 00:33:03.960
thing to know about in general for model

00:33:05.360 --> 00:33:13.080
design so um how did RNN solve this

00:33:09.559 --> 00:33:15.360
problem of uh of the vanishing gradient

00:33:13.080 --> 00:33:16.880
there is a method called long short-term

00:33:15.360 --> 00:33:20.360
memory

00:33:16.880 --> 00:33:22.840
um and the basic idea is to make

00:33:20.360 --> 00:33:24.360
additive connections between time

00:33:22.840 --> 00:33:29.919
steps

00:33:24.360 --> 00:33:32.799
and so addition is the

00:33:29.919 --> 00:33:36.399
only addition or kind of like the

00:33:32.799 --> 00:33:38.159
identity is the only thing that does not

00:33:36.399 --> 00:33:40.880
change the gradient it's guaranteed to

00:33:38.159 --> 00:33:43.279
not change the gradient because um the

00:33:40.880 --> 00:33:46.639
identity function is like f

00:33:43.279 --> 00:33:49.159
ofx equals X and if you take the

00:33:46.639 --> 00:33:51.480
derivative of this it's one so you're

00:33:49.159 --> 00:33:55.440
guaranteed to always have a gradient of

00:33:51.480 --> 00:33:57.360
one according to this function so um

00:33:55.440 --> 00:33:59.559
long shortterm memory makes sure that

00:33:57.360 --> 00:34:01.840
you have this additive uh input between

00:33:59.559 --> 00:34:04.600
time steps and this is what it looks

00:34:01.840 --> 00:34:05.919
like it's not super super important to

00:34:04.600 --> 00:34:09.119
understand everything that's going on

00:34:05.919 --> 00:34:12.200
here but just to explain it very quickly

00:34:09.119 --> 00:34:15.720
this uh C here is something called the

00:34:12.200 --> 00:34:20.520
memory cell it's passed on linearly like

00:34:15.720 --> 00:34:24.679
this and then um you have some gates the

00:34:20.520 --> 00:34:27.320
update gate is determining whether uh

00:34:24.679 --> 00:34:28.919
whether you update this hidden state or

00:34:27.320 --> 00:34:31.440
how much you update given this hidden

00:34:28.919 --> 00:34:34.480
State this input gate is deciding how

00:34:31.440 --> 00:34:36.760
much of the input you take in um and

00:34:34.480 --> 00:34:39.879
then the output gate is deciding how

00:34:36.760 --> 00:34:43.280
much of uh the output from the cell you

00:34:39.879 --> 00:34:45.599
uh you basically push out after using

00:34:43.280 --> 00:34:47.079
the cells so um it has these three gates

00:34:45.599 --> 00:34:48.760
that control the information flow and

00:34:47.079 --> 00:34:51.520
the model can learn to turn them on or

00:34:48.760 --> 00:34:53.720
off uh or something like that so uh

00:34:51.520 --> 00:34:55.679
that's the basic uh basic idea of the

00:34:53.720 --> 00:34:57.240
LSM and there's lots of other like

00:34:55.679 --> 00:34:59.359
variants of this like gated recurrent

00:34:57.240 --> 00:35:01.520
units that are a little bit simpler but

00:34:59.359 --> 00:35:03.920
the basic idea of an additive connection

00:35:01.520 --> 00:35:07.240
plus gating is uh something that appears

00:35:03.920 --> 00:35:07.240
a lot in many different types of

00:35:07.440 --> 00:35:14.240
architectures um any questions

00:35:12.079 --> 00:35:15.760
here another thing I should mention that

00:35:14.240 --> 00:35:19.200
I just realized I don't have on my

00:35:15.760 --> 00:35:24.480
slides but it's a good thing to know is

00:35:19.200 --> 00:35:29.040
that this is also used in uh deep

00:35:24.480 --> 00:35:32.440
networks and uh multi-layer

00:35:29.040 --> 00:35:32.440
networks and so

00:35:34.240 --> 00:35:39.520
basically lstms uh this is

00:35:39.720 --> 00:35:45.359
time lstms have this additive connection

00:35:43.359 --> 00:35:47.599
between the member eel where you're

00:35:45.359 --> 00:35:50.079
always

00:35:47.599 --> 00:35:53.119
adding um adding this into to whatever

00:35:50.079 --> 00:35:53.119
input you

00:35:54.200 --> 00:36:00.720
get and then you you get an input and

00:35:57.000 --> 00:36:00.720
you add this in you get an

00:36:00.839 --> 00:36:07.000
input and so this this makes sure you

00:36:03.440 --> 00:36:09.640
pass your gradients forward in

00:36:07.000 --> 00:36:11.720
time there's also uh something called

00:36:09.640 --> 00:36:13.000
residual connections which I think a lot

00:36:11.720 --> 00:36:14.319
of people have heard of if you've done a

00:36:13.000 --> 00:36:16.000
deep learning class or something like

00:36:14.319 --> 00:36:18.079
that but if you haven't uh they're a

00:36:16.000 --> 00:36:20.599
good thing to know residual connections

00:36:18.079 --> 00:36:22.440
are if you run your input through

00:36:20.599 --> 00:36:25.720
multiple

00:36:22.440 --> 00:36:28.720
layers like let's say you have a block

00:36:25.720 --> 00:36:28.720
here

00:36:36.480 --> 00:36:41.280
let's let's call this an RNN for now

00:36:38.560 --> 00:36:44.280
because we know um we know about RNN

00:36:41.280 --> 00:36:44.280
already so

00:36:45.119 --> 00:36:49.560
RNN so this this connection here is

00:36:48.319 --> 00:36:50.920
called the residual connection and

00:36:49.560 --> 00:36:55.240
basically it's adding an additive

00:36:50.920 --> 00:36:57.280
connection before and after layers so um

00:36:55.240 --> 00:36:58.640
this allows you to pass information from

00:36:57.280 --> 00:37:00.880
the very beginning of a network to the

00:36:58.640 --> 00:37:03.520
very end of a network um through

00:37:00.880 --> 00:37:05.480
multiple layers and it also is there to

00:37:03.520 --> 00:37:08.800
help prevent the gradient finishing

00:37:05.480 --> 00:37:11.520
problem so like in a way you can view uh

00:37:08.800 --> 00:37:14.560
you can view lstms what lstms are doing

00:37:11.520 --> 00:37:15.800
is preventing loss of gradient in time

00:37:14.560 --> 00:37:17.280
and these are preventing loss of

00:37:15.800 --> 00:37:19.480
gradient as you go through like multiple

00:37:17.280 --> 00:37:21.119
layers of the network and this is super

00:37:19.480 --> 00:37:24.079
standard this is used in all like

00:37:21.119 --> 00:37:25.599
Transformer models and llama and GPT and

00:37:24.079 --> 00:37:31.200
whatever

00:37:25.599 --> 00:37:31.200
else cool um any other questions about

00:37:32.760 --> 00:37:39.079
that okay cool um so next I'd like to go

00:37:36.880 --> 00:37:41.760
into convolution um one one thing I

00:37:39.079 --> 00:37:44.760
should mention is rnns or RNN style

00:37:41.760 --> 00:37:46.920
models are used extensively in very long

00:37:44.760 --> 00:37:48.160
sequence modeling and we're going to

00:37:46.920 --> 00:37:50.440
talk more about like actual

00:37:48.160 --> 00:37:52.640
architectures that people use uh to do

00:37:50.440 --> 00:37:55.119
this um usually in combination with

00:37:52.640 --> 00:37:57.720
attention based models uh but they're

00:37:55.119 --> 00:38:01.800
used in very long sequence modeling

00:37:57.720 --> 00:38:05.640
convolutions tend to be used in um a lot

00:38:01.800 --> 00:38:07.160
in speech and image processing uh and

00:38:05.640 --> 00:38:10.880
the reason why they're used a lot in

00:38:07.160 --> 00:38:13.560
speech and image processing is

00:38:10.880 --> 00:38:16.800
because when we're processing

00:38:13.560 --> 00:38:18.599
language uh we have like

00:38:16.800 --> 00:38:22.720
um

00:38:18.599 --> 00:38:22.720
this is

00:38:23.599 --> 00:38:29.400
wonderful like this is wonderful is

00:38:26.599 --> 00:38:33.319
three tokens in language but if we look

00:38:29.400 --> 00:38:36.960
at it in speech it's going to be

00:38:33.319 --> 00:38:36.960
like many many

00:38:37.560 --> 00:38:46.079
frames so kind of

00:38:41.200 --> 00:38:47.680
the semantics of language is already

00:38:46.079 --> 00:38:48.960
kind of like if you look at a single

00:38:47.680 --> 00:38:51.599
token you already get something

00:38:48.960 --> 00:38:52.839
semantically meaningful um but in

00:38:51.599 --> 00:38:54.560
contrast if you're looking at like

00:38:52.839 --> 00:38:56.000
speech or you're looking at pixels and

00:38:54.560 --> 00:38:57.400
images or something like that you're not

00:38:56.000 --> 00:39:00.359
going to get something semantically

00:38:57.400 --> 00:39:01.920
meaningful uh so uh convolution is used

00:39:00.359 --> 00:39:03.359
a lot in that case and also you could

00:39:01.920 --> 00:39:06.079
create a convolutional model over

00:39:03.359 --> 00:39:08.599
characters as well

00:39:06.079 --> 00:39:10.599
um so what is convolution in the first

00:39:08.599 --> 00:39:13.319
place um as I mentioned before basically

00:39:10.599 --> 00:39:16.359
you take the local window uh around an

00:39:13.319 --> 00:39:19.680
input and you run it through um

00:39:16.359 --> 00:39:22.079
basically a model and a a good way to

00:39:19.680 --> 00:39:24.400
think about it is it's essentially a

00:39:22.079 --> 00:39:26.440
feed forward Network where you can

00:39:24.400 --> 00:39:28.240
catenate uh all of the surrounding

00:39:26.440 --> 00:39:30.280
vectors together and run them through a

00:39:28.240 --> 00:39:34.400
linear transform like this so you can

00:39:30.280 --> 00:39:34.400
Cate XT minus XT XT

00:39:35.880 --> 00:39:43.040
plus1 convolution can also be used in

00:39:39.440 --> 00:39:45.400
Auto regressive models and normally like

00:39:43.040 --> 00:39:48.079
we think of it like this so we think

00:39:45.400 --> 00:39:50.640
that we're taking the previous one the

00:39:48.079 --> 00:39:53.839
current one and the next one and making

00:39:50.640 --> 00:39:54.960
a prediction based on this but this

00:39:53.839 --> 00:39:56.440
would be good for something like

00:39:54.960 --> 00:39:57.720
sequence labeling but it's not good for

00:39:56.440 --> 00:39:59.040
for something like language modeling

00:39:57.720 --> 00:40:01.400
because in language modeling we can't

00:39:59.040 --> 00:40:05.200
look at the future right but there's a

00:40:01.400 --> 00:40:07.280
super simple uh solution to this which

00:40:05.200 --> 00:40:11.280
is you have a convolution that just

00:40:07.280 --> 00:40:13.720
looks at the past basically um and

00:40:11.280 --> 00:40:15.319
predicts the next word based on the the

00:40:13.720 --> 00:40:16.760
you know current word in the past so

00:40:15.319 --> 00:40:19.520
here you would be predicting the word

00:40:16.760 --> 00:40:21.040
movie um this is actually essentially

00:40:19.520 --> 00:40:23.839
equivalent to the feed forward language

00:40:21.040 --> 00:40:25.880
model that I talked about last time uh

00:40:23.839 --> 00:40:27.240
so you can also think of that as a

00:40:25.880 --> 00:40:30.599
convolution

00:40:27.240 --> 00:40:32.119
a convolutional language model um so

00:40:30.599 --> 00:40:33.359
when whenever you say feed forward or

00:40:32.119 --> 00:40:36.160
convolutional language model they're

00:40:33.359 --> 00:40:38.880
basically the same uh modulo some uh

00:40:36.160 --> 00:40:42.359
some details about striding and stuff

00:40:38.880 --> 00:40:42.359
which I'm going to talk about the class

00:40:43.000 --> 00:40:49.359
today cool um I covered convolution very

00:40:47.400 --> 00:40:51.440
briefly because it's also the least used

00:40:49.359 --> 00:40:53.400
of the three uh sequence modeling things

00:40:51.440 --> 00:40:55.400
in NLP nowadays but um are there any

00:40:53.400 --> 00:40:58.319
questions there or can I just run into

00:40:55.400 --> 00:40:58.319
attention

00:40:59.119 --> 00:41:04.040
okay cool I'll go into attention next so

00:41:02.400 --> 00:41:06.400
uh the basic idea about

00:41:04.040 --> 00:41:11.119
attention um

00:41:06.400 --> 00:41:12.839
is that we encode uh each token and the

00:41:11.119 --> 00:41:14.440
sequence into a

00:41:12.839 --> 00:41:19.119
vector

00:41:14.440 --> 00:41:21.640
um or so we we have input an input

00:41:19.119 --> 00:41:24.240
sequence that we'd like to encode over

00:41:21.640 --> 00:41:27.800
and we perform a linear combination of

00:41:24.240 --> 00:41:30.640
the vectors weighted by attention weight

00:41:27.800 --> 00:41:33.359
and there's two varieties of attention

00:41:30.640 --> 00:41:35.160
uh that are good to know about the first

00:41:33.359 --> 00:41:37.440
one is cross

00:41:35.160 --> 00:41:40.040
atten where each element in a sequence

00:41:37.440 --> 00:41:41.960
attends to elements of another sequence

00:41:40.040 --> 00:41:44.280
and this is widely used in encoder

00:41:41.960 --> 00:41:47.359
decoder models where you have one

00:41:44.280 --> 00:41:50.319
encoder and you have a separate decoder

00:41:47.359 --> 00:41:51.880
um these models the popular models that

00:41:50.319 --> 00:41:55.119
are like this that people still use a

00:41:51.880 --> 00:41:57.480
lot are T5 uh is a example of an encoder

00:41:55.119 --> 00:42:00.760
decoder model or embar is another

00:41:57.480 --> 00:42:03.160
example of encoder decoder model um but

00:42:00.760 --> 00:42:07.880
basically the uh The Way Cross attention

00:42:03.160 --> 00:42:10.359
works is we have for example an English

00:42:07.880 --> 00:42:14.079
uh sentence here and we want to

00:42:10.359 --> 00:42:17.560
translate it into uh into a Japanese

00:42:14.079 --> 00:42:23.040
sentence and so when we output the first

00:42:17.560 --> 00:42:25.119
word we would mostly uh upweight this or

00:42:23.040 --> 00:42:26.800
sorry we have a we have a Japanese

00:42:25.119 --> 00:42:29.119
sentence and we would like to translated

00:42:26.800 --> 00:42:31.680
into an English sentence for example so

00:42:29.119 --> 00:42:35.160
when we generate the first word in

00:42:31.680 --> 00:42:38.400
Japanese means this so in order to

00:42:35.160 --> 00:42:40.079
Output the first word we would first uh

00:42:38.400 --> 00:42:43.559
do a weighted sum of all of the

00:42:40.079 --> 00:42:46.240
embeddings of the Japanese sentence and

00:42:43.559 --> 00:42:49.359
we would focus probably most on this

00:42:46.240 --> 00:42:51.920
word up here C because it corresponds to

00:42:49.359 --> 00:42:51.920
the word

00:42:53.160 --> 00:42:59.800
this in the next step of generating an

00:42:55.960 --> 00:43:01.319
out output uh we would uh attend to

00:42:59.800 --> 00:43:04.119
different words because different words

00:43:01.319 --> 00:43:07.680
correspond to is so you would attend to

00:43:04.119 --> 00:43:11.040
which corresponds to is um when you

00:43:07.680 --> 00:43:12.599
output n actually there's no word in the

00:43:11.040 --> 00:43:16.839
Japanese sentence that correspon to and

00:43:12.599 --> 00:43:18.720
so you might get a very like blob like

00:43:16.839 --> 00:43:21.319
uh in attention weight that doesn't look

00:43:18.720 --> 00:43:23.319
very uh that looks very smooth not very

00:43:21.319 --> 00:43:25.119
peaky and then when you do example you'd

00:43:23.319 --> 00:43:27.880
have strong attention on uh on the word

00:43:25.119 --> 00:43:29.400
that corresponds to example

00:43:27.880 --> 00:43:31.599
there's also self

00:43:29.400 --> 00:43:33.480
attention and um self attention

00:43:31.599 --> 00:43:36.000
basically what it does is each element

00:43:33.480 --> 00:43:38.640
in a sequence attends to elements of the

00:43:36.000 --> 00:43:40.240
same sequence and so this is a good way

00:43:38.640 --> 00:43:43.359
of doing sequence encoding just like we

00:43:40.240 --> 00:43:46.280
used rnns by rnns uh convolutional

00:43:43.359 --> 00:43:47.559
neural networks and so um the reason why

00:43:46.280 --> 00:43:50.119
you would want to do something like this

00:43:47.559 --> 00:43:52.760
just to give an example let's say we

00:43:50.119 --> 00:43:54.280
wanted to run this we wanted to encode

00:43:52.760 --> 00:43:56.920
the English sentence before doing

00:43:54.280 --> 00:44:00.040
something like translation into Japanese

00:43:56.920 --> 00:44:01.559
and if we did that um this maybe we

00:44:00.040 --> 00:44:02.960
don't need to attend to a whole lot of

00:44:01.559 --> 00:44:06.440
other things because it's kind of clear

00:44:02.960 --> 00:44:08.920
what this means but um

00:44:06.440 --> 00:44:10.880
is the way you would translate it would

00:44:08.920 --> 00:44:12.280
be rather heavily dependent on what the

00:44:10.880 --> 00:44:13.640
other words in the sentence so you might

00:44:12.280 --> 00:44:17.280
want to attend to all the other words in

00:44:13.640 --> 00:44:20.559
the sentence say oh this is is co

00:44:17.280 --> 00:44:22.839
cooccurring with this and example and so

00:44:20.559 --> 00:44:24.440
if that's the case then well we would

00:44:22.839 --> 00:44:26.920
need to translate it in this way or we'

00:44:24.440 --> 00:44:28.960
need to handle it in this way and that's

00:44:26.920 --> 00:44:29.880
exactly the same for you know any other

00:44:28.960 --> 00:44:32.720
sort of

00:44:29.880 --> 00:44:35.880
disambiguation uh style

00:44:32.720 --> 00:44:37.720
task so uh yeah we do something similar

00:44:35.880 --> 00:44:39.040
like this so basically cross attention

00:44:37.720 --> 00:44:42.520
is attending to a different sequence

00:44:39.040 --> 00:44:42.520
self attention is attending to the same

00:44:42.680 --> 00:44:46.559
sequence so how do we do this

00:44:44.960 --> 00:44:48.200
mechanistically in the first place so

00:44:46.559 --> 00:44:51.480
like let's say We're translating from

00:44:48.200 --> 00:44:52.880
Japanese to English um we would have uh

00:44:51.480 --> 00:44:55.960
and we're doing it with an encoder

00:44:52.880 --> 00:44:57.480
decoder model where we have already ENC

00:44:55.960 --> 00:45:00.640
coded the

00:44:57.480 --> 00:45:02.920
input sequence and now we're generating

00:45:00.640 --> 00:45:05.240
the output sequence with a for example a

00:45:02.920 --> 00:45:09.880
recurrent neural network um and so if

00:45:05.240 --> 00:45:12.400
that's the case we have uh I I hate uh

00:45:09.880 --> 00:45:14.440
like this and we want to predict the

00:45:12.400 --> 00:45:17.280
next word so what we would do is we

00:45:14.440 --> 00:45:19.480
would take the current state

00:45:17.280 --> 00:45:21.480
here and uh we use something called a

00:45:19.480 --> 00:45:22.760
query vector and the query Vector is

00:45:21.480 --> 00:45:24.880
essentially the vector that we want to

00:45:22.760 --> 00:45:28.720
use to decide what to attend

00:45:24.880 --> 00:45:31.800
to we then have key vectors and the key

00:45:28.720 --> 00:45:35.319
vectors are the vectors that we would

00:45:31.800 --> 00:45:37.480
like to use to decide which ones we

00:45:35.319 --> 00:45:40.720
should be attending

00:45:37.480 --> 00:45:42.040
to and then for each query key pair we

00:45:40.720 --> 00:45:45.319
calculate a

00:45:42.040 --> 00:45:48.319
weight and we do it like this um this

00:45:45.319 --> 00:45:50.680
gear here is some function that takes in

00:45:48.319 --> 00:45:53.200
the uh query vector and the key vector

00:45:50.680 --> 00:45:55.599
and outputs a weight and notably we use

00:45:53.200 --> 00:45:57.559
the same function every single time this

00:45:55.599 --> 00:46:00.960
is really important again because like

00:45:57.559 --> 00:46:03.760
RNN that allows us to extrapolate

00:46:00.960 --> 00:46:05.960
unlimited length sequences because uh we

00:46:03.760 --> 00:46:08.280
only have one set of you know we only

00:46:05.960 --> 00:46:10.359
have one function no matter how long the

00:46:08.280 --> 00:46:13.200
sequence gets so we can just apply it

00:46:10.359 --> 00:46:15.839
over and over and over

00:46:13.200 --> 00:46:17.920
again uh once we calculate these values

00:46:15.839 --> 00:46:20.839
we normalize so that they add up to one

00:46:17.920 --> 00:46:22.559
using the softmax function and um

00:46:20.839 --> 00:46:27.800
basically in this case that would be

00:46:22.559 --> 00:46:27.800
like 0.76 uh etc etc oops

00:46:28.800 --> 00:46:33.559
so step number two is once we have this

00:46:32.280 --> 00:46:37.839
uh these

00:46:33.559 --> 00:46:40.160
attention uh values here notably these

00:46:37.839 --> 00:46:41.359
values aren't really probabilities uh

00:46:40.160 --> 00:46:42.800
despite the fact that they're between

00:46:41.359 --> 00:46:44.240
zero and one and they add up to one

00:46:42.800 --> 00:46:47.440
because all we're doing is we're using

00:46:44.240 --> 00:46:50.480
them to uh to combine together uh

00:46:47.440 --> 00:46:51.800
multiple vectors so I we don't really

00:46:50.480 --> 00:46:53.319
normally call them attention

00:46:51.800 --> 00:46:54.680
probabilities or anything like that I

00:46:53.319 --> 00:46:56.319
just call them attention values or

00:46:54.680 --> 00:46:59.680
normalized attention values

00:46:56.319 --> 00:47:03.760
is um but once we have these uh

00:46:59.680 --> 00:47:05.760
attention uh attention weights we have

00:47:03.760 --> 00:47:07.200
value vectors and these value vectors

00:47:05.760 --> 00:47:10.000
are the vectors that we would actually

00:47:07.200 --> 00:47:12.319
like to combine together to get the uh

00:47:10.000 --> 00:47:14.000
encoding here and so we take these

00:47:12.319 --> 00:47:17.559
vectors we do a weighted some of the

00:47:14.000 --> 00:47:21.200
vectors and get a final final sum

00:47:17.559 --> 00:47:22.920
here and we can take this uh some and

00:47:21.200 --> 00:47:26.920
use it in any part of the model that we

00:47:22.920 --> 00:47:29.079
would like um and so is very broad it

00:47:26.920 --> 00:47:31.200
can be used in any way now the most

00:47:29.079 --> 00:47:33.240
common way to use it is just have lots

00:47:31.200 --> 00:47:35.000
of self attention layers like in

00:47:33.240 --> 00:47:37.440
something in a Transformer but um you

00:47:35.000 --> 00:47:40.160
can also use it in decoder or other

00:47:37.440 --> 00:47:42.920
things like that as

00:47:40.160 --> 00:47:45.480
well this is an actual graphical example

00:47:42.920 --> 00:47:47.319
from the original attention paper um I'm

00:47:45.480 --> 00:47:50.000
going to give some other examples from

00:47:47.319 --> 00:47:52.480
Transformers in the next class but

00:47:50.000 --> 00:47:55.400
basically you can see that the attention

00:47:52.480 --> 00:47:57.559
weights uh for this English to French I

00:47:55.400 --> 00:48:00.520
think it's English French translation

00:47:57.559 --> 00:48:02.920
task basically um overlap with what you

00:48:00.520 --> 00:48:04.440
would expect uh if you can read English

00:48:02.920 --> 00:48:06.599
and French it's kind of the words that

00:48:04.440 --> 00:48:09.319
are semantically similar to each other

00:48:06.599 --> 00:48:12.920
um it even learns to do this reordering

00:48:09.319 --> 00:48:14.880
uh in an appropriate way here and all of

00:48:12.920 --> 00:48:16.720
this is completely unsupervised so you

00:48:14.880 --> 00:48:18.079
never actually give the model

00:48:16.720 --> 00:48:19.440
information about what it should be

00:48:18.079 --> 00:48:21.559
attending to it's all learned through

00:48:19.440 --> 00:48:23.520
gradient descent and the model learns to

00:48:21.559 --> 00:48:27.640
do this by making the embeddings of the

00:48:23.520 --> 00:48:27.640
key and query vectors closer together

00:48:28.440 --> 00:48:33.240
cool

00:48:30.000 --> 00:48:33.240
um any

00:48:33.800 --> 00:48:40.040
questions okay so um next I'd like to go

00:48:38.440 --> 00:48:41.680
a little bit into how we actually

00:48:40.040 --> 00:48:43.599
calculate the attention score function

00:48:41.680 --> 00:48:44.839
so that's the little gear that I had on

00:48:43.599 --> 00:48:50.280
my

00:48:44.839 --> 00:48:53.559
uh my slide before so here Q is a query

00:48:50.280 --> 00:48:56.440
and K is the key um the original

00:48:53.559 --> 00:48:58.400
attention paper used a multi-layer layer

00:48:56.440 --> 00:49:00.119
uh a multi-layer neural network to

00:48:58.400 --> 00:49:02.440
calculate this so basically what it did

00:49:00.119 --> 00:49:05.319
is it concatenated the query and key

00:49:02.440 --> 00:49:08.000
Vector together multiplied it by a

00:49:05.319 --> 00:49:12.240
weight Matrix calculated a tan H and

00:49:08.000 --> 00:49:15.040
then ran it through uh a weight

00:49:12.240 --> 00:49:19.799
Vector so this

00:49:15.040 --> 00:49:22.480
is essentially very expressive

00:49:19.799 --> 00:49:24.799
um uh it's flexible it's often good with

00:49:22.480 --> 00:49:27.960
large data but it adds extra parameters

00:49:24.799 --> 00:49:30.359
and uh computation time uh to your

00:49:27.960 --> 00:49:31.559
calculations here so it's not as widely

00:49:30.359 --> 00:49:34.359
used

00:49:31.559 --> 00:49:37.799
anymore the uh other thing which was

00:49:34.359 --> 00:49:41.599
proposed by long ad all is a bilinear

00:49:37.799 --> 00:49:43.200
function um and a bilinear function

00:49:41.599 --> 00:49:45.920
basically what it does is it has your

00:49:43.200 --> 00:49:48.319
key Vector it has your query vector and

00:49:45.920 --> 00:49:51.440
it has a matrix in between them like

00:49:48.319 --> 00:49:53.000
this and uh then you calculate uh you

00:49:51.440 --> 00:49:54.520
calculate the

00:49:53.000 --> 00:49:56.680
alut

00:49:54.520 --> 00:49:59.880
so

00:49:56.680 --> 00:50:03.200
this is uh nice because it basically um

00:49:59.880 --> 00:50:05.760
Can Transform uh the key and

00:50:03.200 --> 00:50:08.760
query uh together

00:50:05.760 --> 00:50:08.760
here

00:50:09.119 --> 00:50:13.559
um people have also experimented with

00:50:11.760 --> 00:50:16.079
DOT product and the dot product is

00:50:13.559 --> 00:50:19.839
basically query times

00:50:16.079 --> 00:50:23.480
key uh query transpose times key or

00:50:19.839 --> 00:50:25.760
query. key this is okay but the problem

00:50:23.480 --> 00:50:27.280
with this is then the query vector and

00:50:25.760 --> 00:50:30.160
the key vectors have to be in exactly

00:50:27.280 --> 00:50:31.920
the same space and that's kind of too

00:50:30.160 --> 00:50:34.799
hard of a constraint so it doesn't scale

00:50:31.920 --> 00:50:38.000
very well if you're um if you're working

00:50:34.799 --> 00:50:40.839
hard uh if you're uh like training on

00:50:38.000 --> 00:50:45.400
lots of data um then the scaled dot

00:50:40.839 --> 00:50:47.880
product um the scale dot product here uh

00:50:45.400 --> 00:50:50.079
one problem is that the scale of the dot

00:50:47.880 --> 00:50:53.680
product increases as the dimensions get

00:50:50.079 --> 00:50:55.880
larger and so there's a fix to scale by

00:50:53.680 --> 00:50:58.839
the square root of the length of one of

00:50:55.880 --> 00:51:00.680
the vectors um and so basically you're

00:50:58.839 --> 00:51:04.559
multiplying uh you're taking the dot

00:51:00.680 --> 00:51:06.559
product but you're dividing by the uh

00:51:04.559 --> 00:51:09.359
the square root of the length of one of

00:51:06.559 --> 00:51:11.839
the vectors uh does anyone have an idea

00:51:09.359 --> 00:51:13.599
why you might take the square root here

00:51:11.839 --> 00:51:16.920
if you've taken a machine

00:51:13.599 --> 00:51:20.000
learning uh or maybe statistics class

00:51:16.920 --> 00:51:20.000
you might have a an

00:51:20.599 --> 00:51:26.599
idea any any ideas yeah it normalization

00:51:24.720 --> 00:51:29.079
to make sure

00:51:26.599 --> 00:51:32.760
because otherwise it will impact the

00:51:29.079 --> 00:51:35.640
result because we want normalize one yes

00:51:32.760 --> 00:51:37.920
so we do we do want to normalize it um

00:51:35.640 --> 00:51:40.000
and so that's the reason why we divide

00:51:37.920 --> 00:51:41.920
by the length um and that prevents it

00:51:40.000 --> 00:51:43.839
from getting too large

00:51:41.920 --> 00:51:45.920
specifically does anyone have an idea

00:51:43.839 --> 00:51:49.440
why you take the square root here as

00:51:45.920 --> 00:51:49.440
opposed to dividing just by the length

00:51:52.400 --> 00:51:59.480
overall so um this is this is pretty

00:51:55.400 --> 00:52:01.720
tough and actually uh we I didn't know

00:51:59.480 --> 00:52:04.359
one of the last times I did this class

00:52:01.720 --> 00:52:06.640
uh and had to actually go look for it

00:52:04.359 --> 00:52:09.000
but basically the reason why is because

00:52:06.640 --> 00:52:11.400
if you um if you have a whole bunch of

00:52:09.000 --> 00:52:12.720
random variables so let's say you have a

00:52:11.400 --> 00:52:14.040
whole bunch of random variables no

00:52:12.720 --> 00:52:15.240
matter what kind they are as long as

00:52:14.040 --> 00:52:19.680
they're from the same distribution

00:52:15.240 --> 00:52:19.680
they're IID and you add them all

00:52:20.160 --> 00:52:25.720
together um then the variance I believe

00:52:23.200 --> 00:52:27.760
yeah the variance of this variant

00:52:25.720 --> 00:52:31.119
standard deviation maybe standard

00:52:27.760 --> 00:52:33.319
deviation of this goes uh goes up uh

00:52:31.119 --> 00:52:35.640
square root uh yeah I think standard

00:52:33.319 --> 00:52:38.880
deviation goes

00:52:35.640 --> 00:52:41.040
up dividing by something that would

00:52:38.880 --> 00:52:44.040
divide by this the standard deviation

00:52:41.040 --> 00:52:48.240
here so it's made like normalizing by

00:52:44.040 --> 00:52:51.040
that so um it's a it's that's actually I

00:52:48.240 --> 00:52:53.359
don't think explicitly explained and the

00:52:51.040 --> 00:52:54.720
uh attention is all you need paper uh

00:52:53.359 --> 00:52:57.920
the vasani paper where they introduce

00:52:54.720 --> 00:53:01.079
this but that's basic idea um in terms

00:52:57.920 --> 00:53:03.839
of what people use most widely nowadays

00:53:01.079 --> 00:53:07.680
um they

00:53:03.839 --> 00:53:07.680
are basically doing

00:53:24.160 --> 00:53:27.160
this

00:53:30.280 --> 00:53:34.880
so they're taking the the hidden state

00:53:33.000 --> 00:53:36.599
from the keys and multiplying it by a

00:53:34.880 --> 00:53:39.440
matrix the hidden state by the queries

00:53:36.599 --> 00:53:41.680
and multiplying it by a matrix um this

00:53:39.440 --> 00:53:46.559
is what is done in uh in

00:53:41.680 --> 00:53:50.280
Transformers and the uh and then they're

00:53:46.559 --> 00:53:54.160
using this to um they're normalizing it

00:53:50.280 --> 00:53:57.160
by this uh square root here

00:53:54.160 --> 00:53:57.160
and

00:53:59.440 --> 00:54:05.040
so this is essentially a bilinear

00:54:02.240 --> 00:54:07.680
model um it's a bilinear model that is

00:54:05.040 --> 00:54:09.119
normalized uh they call it uh scale do

00:54:07.680 --> 00:54:11.119
product detention but actually because

00:54:09.119 --> 00:54:15.520
they have these weight matrices uh it's

00:54:11.119 --> 00:54:18.839
a bilinear model so um that's the the

00:54:15.520 --> 00:54:18.839
most standard thing to be used

00:54:20.200 --> 00:54:24.079
nowadays cool any any questions about

00:54:22.520 --> 00:54:27.079
this

00:54:24.079 --> 00:54:27.079
part

00:54:28.240 --> 00:54:36.559
okay so um finally when you actually

00:54:32.280 --> 00:54:36.559
train the model um as I mentioned

00:54:41.960 --> 00:54:45.680
before right at the very

00:54:48.040 --> 00:54:52.400
beginning

00:54:49.839 --> 00:54:55.760
we when we're training an autor

00:54:52.400 --> 00:54:57.400
regressive model we don't want to be

00:54:55.760 --> 00:54:59.799
referring to the Future to things in the

00:54:57.400 --> 00:55:01.240
future um because then you know

00:54:59.799 --> 00:55:03.079
basically we'd be cheating and we'd have

00:55:01.240 --> 00:55:04.599
a nonprobabilistic model it wouldn't be

00:55:03.079 --> 00:55:08.960
good when we actually have to generate

00:55:04.599 --> 00:55:12.119
left to right um and

00:55:08.960 --> 00:55:15.720
so we essentially want to prevent

00:55:12.119 --> 00:55:17.480
ourselves from using information from

00:55:15.720 --> 00:55:20.319
the

00:55:17.480 --> 00:55:22.839
future

00:55:20.319 --> 00:55:24.240
and in an unconditioned model we want to

00:55:22.839 --> 00:55:27.400
prevent ourselves from using any

00:55:24.240 --> 00:55:29.680
information in the feature here um in a

00:55:27.400 --> 00:55:31.520
conditioned model we're okay with doing

00:55:29.680 --> 00:55:33.480
kind of bir

00:55:31.520 --> 00:55:35.880
directional conditioning here to

00:55:33.480 --> 00:55:37.359
calculate the representations but we're

00:55:35.880 --> 00:55:40.440
not okay with doing it on the target

00:55:37.359 --> 00:55:40.440
side so basically what we

00:55:44.240 --> 00:55:50.960
do basically what we do is we create a

00:55:47.920 --> 00:55:52.400
mask that prevents us from attending to

00:55:50.960 --> 00:55:54.559
any of the information in the future

00:55:52.400 --> 00:55:56.440
when we're uh predicting when we're

00:55:54.559 --> 00:56:00.799
calculating the representations of the

00:55:56.440 --> 00:56:04.880
the current thing uh word and

00:56:00.799 --> 00:56:08.280
technically how we do this is we have

00:56:04.880 --> 00:56:08.280
the attention

00:56:09.079 --> 00:56:13.799
values uh like

00:56:11.680 --> 00:56:15.480
2.1

00:56:13.799 --> 00:56:17.880
attention

00:56:15.480 --> 00:56:19.920
0.3 and

00:56:17.880 --> 00:56:22.480
attention uh

00:56:19.920 --> 00:56:24.960
0.5 or something like

00:56:22.480 --> 00:56:27.480
that these are eventually going to be

00:56:24.960 --> 00:56:29.799
fed through the soft Max to calculate

00:56:27.480 --> 00:56:32.119
the attention values that we use to do

00:56:29.799 --> 00:56:33.680
the waiting so what we do is any ones we

00:56:32.119 --> 00:56:36.160
don't want to attend to we just add

00:56:33.680 --> 00:56:39.799
negative infinity or add a very large

00:56:36.160 --> 00:56:42.119
negative number so we uh cross that out

00:56:39.799 --> 00:56:44.000
and set this the negative infinity and

00:56:42.119 --> 00:56:45.440
so then when we take the softb basically

00:56:44.000 --> 00:56:47.839
the value goes to zero and we don't

00:56:45.440 --> 00:56:49.359
attend to it so um this is called the

00:56:47.839 --> 00:56:53.240
attention mask and you'll see it when

00:56:49.359 --> 00:56:53.240
you have to implement

00:56:53.440 --> 00:56:56.880
attention cool

00:56:57.039 --> 00:57:00.200
any any questions about

00:57:02.079 --> 00:57:08.599
this okay great um so next I'd like to

00:57:05.839 --> 00:57:11.039
go to Applications of sequence models um

00:57:08.599 --> 00:57:13.200
there's a bunch of ways that you can use

00:57:11.039 --> 00:57:16.160
sequence models of any variety I wrote

00:57:13.200 --> 00:57:18.400
RNN here arbitrarily but it could be

00:57:16.160 --> 00:57:21.720
convolution or Transformer or anything

00:57:18.400 --> 00:57:23.559
else so the first one is encoding

00:57:21.720 --> 00:57:26.839
sequences

00:57:23.559 --> 00:57:29.240
um and essentially if you do it with an

00:57:26.839 --> 00:57:31.559
RNN this is one way you can encode a

00:57:29.240 --> 00:57:35.799
sequence basically you take the

00:57:31.559 --> 00:57:36.960
last uh value here and you use it to uh

00:57:35.799 --> 00:57:40.559
encode the

00:57:36.960 --> 00:57:42.720
output this can be used for any sort of

00:57:40.559 --> 00:57:45.839
uh like binary or multiclass prediction

00:57:42.720 --> 00:57:48.280
problem it's also right now used very

00:57:45.839 --> 00:57:50.920
widely in sentence representations for

00:57:48.280 --> 00:57:54.200
retrieval uh so for example you build a

00:57:50.920 --> 00:57:55.520
big retrieval index uh with these

00:57:54.200 --> 00:57:57.920
vectors

00:57:55.520 --> 00:57:59.480
and then you do a vector near you also

00:57:57.920 --> 00:58:02.119
in quote a query and you do a vector

00:57:59.480 --> 00:58:04.760
nearest neighbor search to look up uh

00:58:02.119 --> 00:58:06.760
the most similar sentence here so this

00:58:04.760 --> 00:58:10.160
is uh these are two applications where

00:58:06.760 --> 00:58:13.440
you use something like this right on

00:58:10.160 --> 00:58:15.520
this slide I wrote that you use the last

00:58:13.440 --> 00:58:17.359
Vector here but actually a lot of the

00:58:15.520 --> 00:58:20.039
time it's also a good idea to just take

00:58:17.359 --> 00:58:22.599
the mean of the vectors or take the max

00:58:20.039 --> 00:58:26.640
of all of the vectors

00:58:22.599 --> 00:58:29.119
uh in fact I would almost I would almost

00:58:26.640 --> 00:58:30.520
say that that's usually a better choice

00:58:29.119 --> 00:58:32.760
if you're doing any sort of thing where

00:58:30.520 --> 00:58:35.359
you need a single Vector unless your

00:58:32.760 --> 00:58:38.200
model has been specifically trained to

00:58:35.359 --> 00:58:41.480
have good like output vectors uh from

00:58:38.200 --> 00:58:44.359
the final Vector here so um you could

00:58:41.480 --> 00:58:46.880
also just take the the mean of all of

00:58:44.359 --> 00:58:46.880
the purple

00:58:48.240 --> 00:58:52.960
ones um another thing you can do is

00:58:50.280 --> 00:58:54.359
encode tokens for sequence labeling Um

00:58:52.960 --> 00:58:56.200
this can also be used for language

00:58:54.359 --> 00:58:58.280
modeling and what do I mean it can be

00:58:56.200 --> 00:59:00.039
used for language

00:58:58.280 --> 00:59:03.319
modeling

00:59:00.039 --> 00:59:06.599
basically you can view this as first

00:59:03.319 --> 00:59:09.200
running along sequence encoding and then

00:59:06.599 --> 00:59:12.319
after that making all of the predictions

00:59:09.200 --> 00:59:15.240
um it's also a good thing to know

00:59:12.319 --> 00:59:18.440
computationally because um often you can

00:59:15.240 --> 00:59:20.720
do sequence encoding uh kind of all in

00:59:18.440 --> 00:59:22.440
parallel and yeah actually I said I was

00:59:20.720 --> 00:59:23.359
going to mention I said I was going to

00:59:22.440 --> 00:59:25.079
mention that but I don't think I

00:59:23.359 --> 00:59:27.319
actually have a slide about it but um

00:59:25.079 --> 00:59:29.720
one important thing about rnn's compared

00:59:27.319 --> 00:59:33.079
to convolution or Transformers uh sorry

00:59:29.720 --> 00:59:34.839
convolution or attention is rnns in

00:59:33.079 --> 00:59:37.440
order to calculate this RNN you need to

00:59:34.839 --> 00:59:39.599
wait for this RNN to finish so it's

00:59:37.440 --> 00:59:41.200
sequential and you need to go like here

00:59:39.599 --> 00:59:43.480
and then here and then here and then

00:59:41.200 --> 00:59:45.720
here and then here and that's a pretty

00:59:43.480 --> 00:59:48.200
big bottleneck because uh things like

00:59:45.720 --> 00:59:50.760
gpus or tpus they're actually really

00:59:48.200 --> 00:59:52.839
good at doing a bunch of things at once

00:59:50.760 --> 00:59:56.440
and so attention even though its ASM

00:59:52.839 --> 00:59:57.400
totic complexity is worse o of n squ uh

00:59:56.440 --> 00:59:59.319
just because you don't have that

00:59:57.400 --> 01:00:01.680
bottleneck of doing things sequentially

00:59:59.319 --> 01:00:03.640
it can be way way faster on a GPU

01:00:01.680 --> 01:00:04.960
because you're not wasting your time

01:00:03.640 --> 01:00:07.640
waiting for the previous thing to be

01:00:04.960 --> 01:00:11.039
calculated so that's actually why uh

01:00:07.640 --> 01:00:13.520
Transformers are so fast

01:00:11.039 --> 01:00:14.599
um uh Transformers and attention models

01:00:13.520 --> 01:00:17.160
are so

01:00:14.599 --> 01:00:21.119
fast

01:00:17.160 --> 01:00:23.079
um another thing to note so that's one

01:00:21.119 --> 01:00:25.039
of the big reasons why attention models

01:00:23.079 --> 01:00:27.359
are so popular nowadays because fast to

01:00:25.039 --> 01:00:30.200
calculate on Modern Hardware another

01:00:27.359 --> 01:00:33.520
reason why attention models are popular

01:00:30.200 --> 01:00:34.799
nowadays does anyone have a um does

01:00:33.520 --> 01:00:37.280
anyone have an

01:00:34.799 --> 01:00:38.839
idea uh about another reason it's based

01:00:37.280 --> 01:00:41.200
on how easy they are to learn and

01:00:38.839 --> 01:00:43.680
there's a reason why and that reason why

01:00:41.200 --> 01:00:46.240
has to do with

01:00:43.680 --> 01:00:48.520
um that reason why has to do with uh

01:00:46.240 --> 01:00:49.400
something I introduced in this lecture

01:00:48.520 --> 01:00:52.039
uh

01:00:49.400 --> 01:00:54.720
earlier I'll give a

01:00:52.039 --> 01:00:58.079
hint gradients yeah more more

01:00:54.720 --> 01:01:00.480
specifically what what's nice about

01:00:58.079 --> 01:01:02.920
attention with respect to gradients or

01:01:00.480 --> 01:01:02.920
Vanishing

01:01:04.119 --> 01:01:07.319
gradients any

01:01:07.680 --> 01:01:15.160
ideas let's say we have a really long

01:01:10.160 --> 01:01:17.839
sentence it's like X1 X2 X3

01:01:15.160 --> 01:01:21.799
X4 um

01:01:17.839 --> 01:01:26.440
X200 over here and in order to predict

01:01:21.799 --> 01:01:26.440
X200 you need to pay attention to X3

01:01:27.359 --> 01:01:29.640
any

01:01:33.079 --> 01:01:37.359
ideas another another hint how many

01:01:35.599 --> 01:01:38.960
nonlinearities do you have to pass

01:01:37.359 --> 01:01:41.440
through in order to pass that

01:01:38.960 --> 01:01:44.839
information from X3 to

01:01:41.440 --> 01:01:48.839
X200 in a recurrent Network um in a

01:01:44.839 --> 01:01:48.839
recurrent Network or

01:01:51.920 --> 01:01:57.160
attention netw should be

01:01:54.960 --> 01:02:00.680
197 yeah in a recurrent Network it's

01:01:57.160 --> 01:02:03.480
basically 197 or may maybe 196 I haven't

01:02:00.680 --> 01:02:06.319
paid attention but every time every time

01:02:03.480 --> 01:02:08.319
you pass it to the hidden

01:02:06.319 --> 01:02:10.200
state it has to go through a

01:02:08.319 --> 01:02:13.240
nonlinearity so it goes through like

01:02:10.200 --> 01:02:17.119
1907 nonlinearities and even if you're

01:02:13.240 --> 01:02:19.680
using an lstm um it's still the lstm

01:02:17.119 --> 01:02:21.559
hidden cell is getting information added

01:02:19.680 --> 01:02:23.400
to it and subtracted to it and other

01:02:21.559 --> 01:02:24.960
things like that so it's still a bit

01:02:23.400 --> 01:02:27.880
tricky

01:02:24.960 --> 01:02:27.880
um what about

01:02:28.119 --> 01:02:35.160
attention yeah basically one time so

01:02:31.520 --> 01:02:39.319
attention um in the next layer here

01:02:35.160 --> 01:02:41.119
you're passing it all the way you're

01:02:39.319 --> 01:02:45.000
passing all of the information directly

01:02:41.119 --> 01:02:46.480
in and the only qualifying thing is that

01:02:45.000 --> 01:02:47.760
your weight has to be good it has to

01:02:46.480 --> 01:02:49.079
find a good attention weight so that

01:02:47.760 --> 01:02:50.920
it's actually paying attention to that

01:02:49.079 --> 01:02:53.039
information so this is actually

01:02:50.920 --> 01:02:54.400
discussed in the vaswani at all

01:02:53.039 --> 01:02:57.359
attention is all you need paper that

01:02:54.400 --> 01:02:59.920
introduced Transformers um convolutions

01:02:57.359 --> 01:03:03.640
are kind of in the middle so like let's

01:02:59.920 --> 01:03:06.400
say you have a convolution of length 10

01:03:03.640 --> 01:03:09.880
um and then you have two layers of it um

01:03:06.400 --> 01:03:09.880
if you have a convolution of length

01:03:10.200 --> 01:03:15.880
10 or yeah let's say you have a

01:03:12.559 --> 01:03:18.520
convolution of length 10 you would need

01:03:15.880 --> 01:03:19.520
basically you would pass from 10

01:03:18.520 --> 01:03:21.720
previous

01:03:19.520 --> 01:03:23.319
ones and then you would pass again from

01:03:21.720 --> 01:03:27.359
10 previous ones and then you would have

01:03:23.319 --> 01:03:29.160
to go through like 16 or like I guess

01:03:27.359 --> 01:03:31.279
almost 20 layers of convolution in order

01:03:29.160 --> 01:03:34.720
to pass that information along so it's

01:03:31.279 --> 01:03:39.200
kind of in the middle of RNs in uh in

01:03:34.720 --> 01:03:43.480
lsms uh sorry RNN in attention

01:03:39.200 --> 01:03:47.359
Ms Yeah question so regarding how you

01:03:43.480 --> 01:03:51.319
have to wait for one r& the next one can

01:03:47.359 --> 01:03:53.000
you inflence on one RNN once it's done

01:03:51.319 --> 01:03:54.839
even though the next one's competing off

01:03:53.000 --> 01:03:58.400
that one

01:03:54.839 --> 01:04:01.160
yes yeah you can you can do

01:03:58.400 --> 01:04:03.880
inference you could is well so as long

01:04:01.160 --> 01:04:03.880
as

01:04:05.599 --> 01:04:10.640
the as long as the output doesn't affect

01:04:08.079 --> 01:04:14.000
the next input so in this

01:04:10.640 --> 01:04:17.119
case in this case because of language

01:04:14.000 --> 01:04:19.400
modeling or generation is because the

01:04:17.119 --> 01:04:21.000
output doesn't affect the ne uh because

01:04:19.400 --> 01:04:22.440
the output affects the next input if

01:04:21.000 --> 01:04:26.680
you're predicting the output you have to

01:04:22.440 --> 01:04:28.920
weigh if you know the output already um

01:04:26.680 --> 01:04:30.599
if you know the output already you could

01:04:28.920 --> 01:04:33.599
make the prediction at the same time

01:04:30.599 --> 01:04:34.799
miscalculating this next hidden State um

01:04:33.599 --> 01:04:36.200
so if you're just calculating the

01:04:34.799 --> 01:04:38.559
probability you could do that and that's

01:04:36.200 --> 01:04:40.880
actually where Transformers or attention

01:04:38.559 --> 01:04:44.839
models shine attention models actually

01:04:40.880 --> 01:04:46.000
aren't great for Generation Um and the

01:04:44.839 --> 01:04:49.279
reason why they're not great for

01:04:46.000 --> 01:04:52.279
generation is because they're

01:04:49.279 --> 01:04:52.279
um

01:04:52.799 --> 01:04:57.680
like when you're you're generating the

01:04:55.039 --> 01:04:59.200
next token you still need to wait you

01:04:57.680 --> 01:05:00.559
can't calculate in parallel because you

01:04:59.200 --> 01:05:03.039
need to generate the next token before

01:05:00.559 --> 01:05:04.839
you can encode the next uh the previous

01:05:03.039 --> 01:05:07.119
sorry need to generate the next token

01:05:04.839 --> 01:05:08.680
before you can encode it so you can't do

01:05:07.119 --> 01:05:10.359
everything in parallel so Transformers

01:05:08.680 --> 01:05:15.039
for generation are actually

01:05:10.359 --> 01:05:16.559
slow and um there are models uh I don't

01:05:15.039 --> 01:05:18.520
know if people are using them super

01:05:16.559 --> 01:05:22.200
widely now but there were actually

01:05:18.520 --> 01:05:23.640
transform uh language model sorry

01:05:22.200 --> 01:05:26.319
machine translation model set we in

01:05:23.640 --> 01:05:28.279
production they had a really big strong

01:05:26.319 --> 01:05:34.359
Transformer encoder and then they had a

01:05:28.279 --> 01:05:34.359
tiny fast RNN decoder um

01:05:35.440 --> 01:05:40.960
and and if you want a actual

01:05:52.000 --> 01:05:59.440
reference there's there's

01:05:55.079 --> 01:05:59.440
this deep encoder shellow

01:05:59.559 --> 01:06:05.520
decoder um and then there's also the the

01:06:03.079 --> 01:06:07.599
Maran machine translation toolkit that

01:06:05.520 --> 01:06:11.119
supports uh supports those types of

01:06:07.599 --> 01:06:13.839
things as well so um it's also the

01:06:11.119 --> 01:06:16.200
reason why uh if you're using if you're

01:06:13.839 --> 01:06:18.839
using uh like the GPT models through the

01:06:16.200 --> 01:06:21.680
API that decoding is more expensive

01:06:18.839 --> 01:06:21.680
right like

01:06:22.119 --> 01:06:27.960
encoding I forget exactly is it 0.03

01:06:26.279 --> 01:06:30.839
cents for 1,000 tokens for encoding and

01:06:27.960 --> 01:06:33.039
0.06 cents for 1,000 tokens for decoding

01:06:30.839 --> 01:06:34.799
in like gp4 or something like this the

01:06:33.039 --> 01:06:36.839
reason why is precisely that just

01:06:34.799 --> 01:06:37.760
because it's so much more expensive to

01:06:36.839 --> 01:06:41.599
to run the

01:06:37.760 --> 01:06:45.160
decoder um cool I have a few final

01:06:41.599 --> 01:06:47.039
things also about efficiency so um these

01:06:45.160 --> 01:06:50.720
go back to the efficiency things that I

01:06:47.039 --> 01:06:52.279
talked about last time um handling mini

01:06:50.720 --> 01:06:54.440
batching so what do we have to do when

01:06:52.279 --> 01:06:56.359
we're handling mini batching if we were

01:06:54.440 --> 01:06:59.440
handling mini batching in feed forward

01:06:56.359 --> 01:07:02.880
networks it's actually relatively easy

01:06:59.440 --> 01:07:04.880
um because we all of our computations

01:07:02.880 --> 01:07:06.400
are the same shape so we just

01:07:04.880 --> 01:07:09.359
concatenate them all together into a big

01:07:06.400 --> 01:07:11.000
tensor and run uh run over it uh we saw

01:07:09.359 --> 01:07:12.599
mini batching makes things much faster

01:07:11.000 --> 01:07:15.160
but mini batching and sequence modeling

01:07:12.599 --> 01:07:17.240
is harder than in feed forward networks

01:07:15.160 --> 01:07:20.240
um one reason is in rnns each word

01:07:17.240 --> 01:07:22.680
depends on the previous word um also

01:07:20.240 --> 01:07:26.359
because sequences are of various

01:07:22.680 --> 01:07:30.279
lengths so so what we do to handle this

01:07:26.359 --> 01:07:33.480
is uh we do padding and masking uh

01:07:30.279 --> 01:07:35.680
so we can do padding like this uh so we

01:07:33.480 --> 01:07:37.279
just add an extra token at the end to

01:07:35.680 --> 01:07:40.440
make all of the sequences at the same

01:07:37.279 --> 01:07:44.480
length um if we are doing an encoder

01:07:40.440 --> 01:07:47.160
decoder style model uh where we have an

01:07:44.480 --> 01:07:48.440
input and then we want to generate all

01:07:47.160 --> 01:07:50.640
the outputs based on the input one of

01:07:48.440 --> 01:07:54.920
the easy things is to add pads to the

01:07:50.640 --> 01:07:56.520
beginning um and then so yeah it doesn't

01:07:54.920 --> 01:07:58.000
really matter but you can add pads to

01:07:56.520 --> 01:07:59.440
the beginning so they're all starting at

01:07:58.000 --> 01:08:03.079
the same place especially if you're

01:07:59.440 --> 01:08:05.799
using RNN style models um then we

01:08:03.079 --> 01:08:08.920
calculate the loss over the output for

01:08:05.799 --> 01:08:11.000
example we multiply the loss by a mask

01:08:08.920 --> 01:08:13.480
to remove the loss over the tokens that

01:08:11.000 --> 01:08:16.880
we don't care about and we take the sum

01:08:13.480 --> 01:08:19.120
of these and so luckily most of this is

01:08:16.880 --> 01:08:20.719
implemented in for example ptch or

01:08:19.120 --> 01:08:22.279
huging face Transformers already so you

01:08:20.719 --> 01:08:23.560
don't need to worry about it but it is a

01:08:22.279 --> 01:08:24.799
good idea to know what's going on under

01:08:23.560 --> 01:08:28.560
the hood if you want to implement

01:08:24.799 --> 01:08:32.440
anything unusual and also um it's good

01:08:28.560 --> 01:08:35.600
to know for the following reason also

01:08:32.440 --> 01:08:38.799
which is bucketing and

01:08:35.600 --> 01:08:40.319
sorting so if we use sentences of vastly

01:08:38.799 --> 01:08:43.359
different lengths and we put them in the

01:08:40.319 --> 01:08:46.640
same mini batch this can uh waste a

01:08:43.359 --> 01:08:48.000
really large amount of computation so

01:08:46.640 --> 01:08:50.759
like let's say we're processing

01:08:48.000 --> 01:08:52.480
documents or movie reviews or something

01:08:50.759 --> 01:08:54.799
like that and you have a most movie

01:08:52.480 --> 01:08:57.719
reviews are like

01:08:54.799 --> 01:09:00.080
10 words long but you have one movie

01:08:57.719 --> 01:09:02.319
review in your mini batch of uh a

01:09:00.080 --> 01:09:04.359
thousand words so basically what that

01:09:02.319 --> 01:09:08.279
means is you're padding most of your

01:09:04.359 --> 01:09:11.120
sequences 990 times to process 10

01:09:08.279 --> 01:09:12.120
sequences which is like a lot of waste

01:09:11.120 --> 01:09:14.000
right because you're running them all

01:09:12.120 --> 01:09:16.799
through your GPU and other things like

01:09:14.000 --> 01:09:19.080
that so one way to remedy this is to

01:09:16.799 --> 01:09:22.719
sort sentences so similarly length

01:09:19.080 --> 01:09:27.480
sentences are in the same batch so you

01:09:22.719 --> 01:09:29.920
uh you first sort before building all of

01:09:27.480 --> 01:09:31.640
your batches and then uh that makes it

01:09:29.920 --> 01:09:32.960
so that similarly sized ones are the

01:09:31.640 --> 01:09:35.239
same

01:09:32.960 --> 01:09:37.040
batch this goes into the problem that I

01:09:35.239 --> 01:09:39.359
mentioned before but only in passing

01:09:37.040 --> 01:09:42.440
which is uh let's say you're calculating

01:09:39.359 --> 01:09:44.199
your batch based on the number of

01:09:42.440 --> 01:09:47.679
sequences that you're

01:09:44.199 --> 01:09:51.400
processing if you say Okay I want 64

01:09:47.679 --> 01:09:53.359
sequences in my mini batch um if most of

01:09:51.400 --> 01:09:55.159
the time those 64 sequences are are 10

01:09:53.359 --> 01:09:57.480
tokens that's fine but then when you get

01:09:55.159 --> 01:10:01.440
the One Mini batch that has a thousand

01:09:57.480 --> 01:10:02.760
tokens in each sentence or each sequence

01:10:01.440 --> 01:10:04.920
um suddenly you're going to run out of

01:10:02.760 --> 01:10:07.800
GPU memory and you're like training is

01:10:04.920 --> 01:10:08.920
going to crash right which is you really

01:10:07.800 --> 01:10:10.440
don't want that to happen when you

01:10:08.920 --> 01:10:12.440
started running your homework assignment

01:10:10.440 --> 01:10:15.560
and then went to bed and then wake up

01:10:12.440 --> 01:10:18.440
and it crashed you know uh 15 minutes

01:10:15.560 --> 01:10:21.040
into Computing or something so uh this

01:10:18.440 --> 01:10:23.440
is an important thing to be aware of

01:10:21.040 --> 01:10:26.760
practically uh again this can be solved

01:10:23.440 --> 01:10:29.239
by a lot of toolkits like I know fer uh

01:10:26.760 --> 01:10:30.840
does it and hugging face does it if you

01:10:29.239 --> 01:10:33.159
set the appropriate settings but it's

01:10:30.840 --> 01:10:36.239
something you should be aware of um

01:10:33.159 --> 01:10:37.880
another note is that if you do this it's

01:10:36.239 --> 01:10:41.280
reducing the randomness in your

01:10:37.880 --> 01:10:42.880
distribution of data so um stochastic

01:10:41.280 --> 01:10:44.520
gradient descent is really heavily

01:10:42.880 --> 01:10:47.480
reliant on the fact that your ordering

01:10:44.520 --> 01:10:49.440
of data is randomized or at least it's a

01:10:47.480 --> 01:10:52.159
distributed appropriately so it's

01:10:49.440 --> 01:10:56.840
something to definitely be aware of um

01:10:52.159 --> 01:10:59.560
so uh this is a good thing to to think

01:10:56.840 --> 01:11:01.400
about another really useful thing to

01:10:59.560 --> 01:11:03.800
think about is strided

01:11:01.400 --> 01:11:05.440
architectures um strided architectures

01:11:03.800 --> 01:11:07.520
appear in rnns they appear in

01:11:05.440 --> 01:11:10.080
convolution they appear in trans

01:11:07.520 --> 01:11:12.320
Transformers or attention based models

01:11:10.080 --> 01:11:15.199
um they're called different things in

01:11:12.320 --> 01:11:18.159
each of them so in rnns they're called

01:11:15.199 --> 01:11:21.280
pyramidal rnns in convolution they're

01:11:18.159 --> 01:11:22.400
called strided architectures and in

01:11:21.280 --> 01:11:25.080
attention they're called sparse

01:11:22.400 --> 01:11:27.440
attention usually they all actually kind

01:11:25.080 --> 01:11:30.800
of mean the same thing um and basically

01:11:27.440 --> 01:11:33.440
what they mean is you don't you have a

01:11:30.800 --> 01:11:37.040
multi-layer model and when you have a

01:11:33.440 --> 01:11:40.920
multi-layer model you don't process

01:11:37.040 --> 01:11:43.920
every input uh from the uh from the

01:11:40.920 --> 01:11:45.560
previous layer so here's an example um

01:11:43.920 --> 01:11:47.840
like let's say you have a whole bunch of

01:11:45.560 --> 01:11:50.199
inputs um each of the inputs is

01:11:47.840 --> 01:11:53.159
processed in the first layer in some way

01:11:50.199 --> 01:11:56.639
but in the second layer you actually

01:11:53.159 --> 01:12:01.520
input for example uh two inputs to the

01:11:56.639 --> 01:12:03.560
RNN but you you skip so you have one

01:12:01.520 --> 01:12:05.440
state that corresponds to state number

01:12:03.560 --> 01:12:06.840
one and two another state that

01:12:05.440 --> 01:12:08.440
corresponds to state number two and

01:12:06.840 --> 01:12:10.920
three another state that corresponds to

01:12:08.440 --> 01:12:13.280
state number three and four so what that

01:12:10.920 --> 01:12:15.199
means is you can gradually decrease the

01:12:13.280 --> 01:12:18.199
number like the length of the sequence

01:12:15.199 --> 01:12:20.719
every time you process so uh this is a

01:12:18.199 --> 01:12:22.360
really useful thing that to do if you're

01:12:20.719 --> 01:12:25.480
processing very long sequences so you

01:12:22.360 --> 01:12:25.480
should be aware of it

01:12:27.440 --> 01:12:34.120
cool um everything

01:12:30.639 --> 01:12:36.920
okay okay the final thing is truncated

01:12:34.120 --> 01:12:39.239
back propagation through time and uh

01:12:36.920 --> 01:12:41.000
truncated back propagation Through Time

01:12:39.239 --> 01:12:43.560
what this is doing is basically you do

01:12:41.000 --> 01:12:46.120
back propop over shorter segments but

01:12:43.560 --> 01:12:47.840
you initialize with the state from the

01:12:46.120 --> 01:12:51.040
previous

01:12:47.840 --> 01:12:52.440
segment and the way this works is uh

01:12:51.040 --> 01:12:56.080
like for example if you're running an

01:12:52.440 --> 01:12:57.600
RNN uh you would run the RNN over the

01:12:56.080 --> 01:12:59.400
previous segment maybe it's length four

01:12:57.600 --> 01:13:02.120
maybe it's length 400 it doesn't really

01:12:59.400 --> 01:13:04.520
matter but it's uh coherently length

01:13:02.120 --> 01:13:06.360
segment and then when you do the next

01:13:04.520 --> 01:13:08.840
segment what you do is you only pass the

01:13:06.360 --> 01:13:12.960
hidden state but you throw away the rest

01:13:08.840 --> 01:13:16.360
of the previous computation graph and

01:13:12.960 --> 01:13:18.040
then walk through uh like this uh so you

01:13:16.360 --> 01:13:22.159
won't actually be updating the

01:13:18.040 --> 01:13:24.080
parameters of this based on the result

01:13:22.159 --> 01:13:25.800
the lost from this but you're still

01:13:24.080 --> 01:13:28.159
passing the information so this can use

01:13:25.800 --> 01:13:30.400
the information for the previous state

01:13:28.159 --> 01:13:32.239
so this is an example from RNN this is

01:13:30.400 --> 01:13:35.159
used pretty widely in RNN but there's

01:13:32.239 --> 01:13:38.000
also a lot of Transformer architectures

01:13:35.159 --> 01:13:39.400
that do things like this um the original

01:13:38.000 --> 01:13:41.000
one is something called Transformer

01:13:39.400 --> 01:13:44.560
Excel that was actually created here at

01:13:41.000 --> 01:13:46.560
CMU but this is also um used in the new

01:13:44.560 --> 01:13:48.719
mistol models and other things like this

01:13:46.560 --> 01:13:51.719
as well so um it's something that's

01:13:48.719 --> 01:13:54.719
still very much alive and well nowadays

01:13:51.719 --> 01:13:56.320
as well

01:13:54.719 --> 01:13:57.840
cool um that's all I have for today are

01:13:56.320 --> 01:13:59.760
there any questions people want to ask

01:13:57.840 --> 01:14:02.760
before we wrap

01:13:59.760 --> 01:14:02.760
up

01:14:12.840 --> 01:14:20.000
yeah doesent yeah so for condition

01:14:16.960 --> 01:14:25.040
prediction what is Source X and Target y

01:14:20.000 --> 01:14:26.520
um I think I kind of maybe carried over

01:14:25.040 --> 01:14:28.679
uh some terminology from machine

01:14:26.520 --> 01:14:31.400
translation uh by accident maybe it

01:14:28.679 --> 01:14:34.080
should be input X and output y uh that

01:14:31.400 --> 01:14:36.600
would be a better way to put it and so

01:14:34.080 --> 01:14:38.080
uh it could be anything for translation

01:14:36.600 --> 01:14:39.560
it's like something in the source

01:14:38.080 --> 01:14:42.600
language and something in the target

01:14:39.560 --> 01:14:44.520
language so like English and Japanese um

01:14:42.600 --> 01:14:47.280
if it's just a regular language model it

01:14:44.520 --> 01:14:50.560
could be something like a prompt and the

01:14:47.280 --> 01:14:55.280
output so for

01:14:50.560 --> 01:14:55.280
UNC y example that

01:14:57.400 --> 01:15:01.400
yeah so for unconditioned prediction

01:14:59.760 --> 01:15:03.840
that could just be straight up language

01:15:01.400 --> 01:15:07.040
modeling for example so um language

01:15:03.840 --> 01:15:11.840
modeling with no not necessarily any

01:15:07.040 --> 01:15:11.840
problems okay thanks and anything

01:15:12.440 --> 01:15:17.880
else okay great thanks a lot I'm happy

01:15:14.639 --> 01:15:17.880
to take questions

01:15:18.639 --> 01:15:21.639
to