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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

282
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something else

283
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so um to give some examples of this um

284
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this is autor regressive conditioned

285
00:12:06,839 --> 00:12:12,920
prediction and um this could be like a

286
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SE a standard sequence to sequence model

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or it could be a language model where

288
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you're given a prompt and you want to

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predict the following output like we

290
00:12:18,600 --> 00:12:24,160
often do with chat GPT or something like

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this and so

292
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um yeah I I don't think you

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can

294
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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

296
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context um but there were people who

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were sending uh I saw this about a week

298
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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

300
00:12:44,079 --> 00:12:50,480
3.5 or gp4 API with no input and it

301
00:12:47,839 --> 00:12:52,279
would randomly output random questions

302
00:12:50,480 --> 00:12:54,800
or something like that so that's what's

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what happens when you send things to uh

304
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to chat GPT without any prior

305
00:12:56,720 --> 00:13:00,120
conditioning conts but normally what you

306
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do is you put in you know your prompt

307
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and then it follows up with your prompt

308
00:13:01,440 --> 00:13:05,320
and that would be in this uh in this

309
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Paradigm there's also something called

310
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non-auto regressive condition prediction

311
00:13:11,279 --> 00:13:16,760
um and this can be used for something

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like sequence labeling or non- autor

313
00:13:16,760 --> 00:13:20,760
regressive machine translation I'll talk

314
00:13:19,160 --> 00:13:22,839
about the first one in this class and

315
00:13:20,760 --> 00:13:25,600
I'll talk about the the second one maybe

316
00:13:22,839 --> 00:13:27,399
later um it's kind of a minor topic now

317
00:13:25,600 --> 00:13:30,040
it used to be popular a few years ago so

318
00:13:27,399 --> 00:13:33,279
I'm not sure whether it'll cover it but

319
00:13:30,040 --> 00:13:33,279
um uh

320
00:13:33,399 --> 00:13:39,279
yeah cool so the basic modeling Paradigm

321
00:13:37,079 --> 00:13:41,199
that we use for things like this is

322
00:13:39,279 --> 00:13:42,760
extracting features and predicting so

323
00:13:41,199 --> 00:13:44,839
this is exactly the same as the bag of

324
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wordss model right I the bag of wordss

325
00:13:44,839 --> 00:13:48,680
model that I talked about the first time

326
00:13:46,680 --> 00:13:50,959
we extracted features uh based on those

327
00:13:48,680 --> 00:13:53,440
features we made predictions so it's no

328
00:13:50,959 --> 00:13:55,480
different when we do sequence modeling

329
00:13:53,440 --> 00:13:57,680
um but the methods that we use for

330
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feature extraction is different so given

331
00:13:57,680 --> 00:14:03,920
in the input text X we extract features

332
00:14:01,120 --> 00:14:06,519
H and predict labels

333
00:14:03,920 --> 00:14:10,320
Y and for something like text

334
00:14:06,519 --> 00:14:12,600
classification what we do is we uh so

335
00:14:10,320 --> 00:14:15,440
for example we have text classification

336
00:14:12,600 --> 00:14:17,920
or or sequence labeling and for text

337
00:14:15,440 --> 00:14:19,720
classification usually what we would do

338
00:14:17,920 --> 00:14:21,360
is we would have a feature extractor

339
00:14:19,720 --> 00:14:23,120
from this feature extractor we take the

340
00:14:21,360 --> 00:14:25,199
sequence and we convert it into a single

341
00:14:23,120 --> 00:14:28,040
vector and then based on this Vector we

342
00:14:25,199 --> 00:14:30,160
make a prediction so that that's what we

343
00:14:28,040 --> 00:14:33,160
do for

344
00:14:30,160 --> 00:14:35,480
classification um for sequence labeling

345
00:14:33,160 --> 00:14:37,160
normally what we do is we extract one

346
00:14:35,480 --> 00:14:40,240
vector for each thing that we would like

347
00:14:37,160 --> 00:14:42,079
to predict about so here that might be

348
00:14:40,240 --> 00:14:45,639
one vector for each

349
00:14:42,079 --> 00:14:47,720
word um and then based on this uh we

350
00:14:45,639 --> 00:14:49,120
would predict something for each word so

351
00:14:47,720 --> 00:14:50,360
this is an example of part of speech

352
00:14:49,120 --> 00:14:53,079
tagging but there's a lot of other

353
00:14:50,360 --> 00:14:56,920
sequence labeling tasks

354
00:14:53,079 --> 00:14:58,839
also and what tasks exist for something

355
00:14:56,920 --> 00:15:03,040
like sequence labeling so sequence lab

356
00:14:58,839 --> 00:15:06,240
in is uh a pretty

357
00:15:03,040 --> 00:15:09,000
big subset of NLP tasks you can express

358
00:15:06,240 --> 00:15:11,040
a lot of things as sequence labeling and

359
00:15:09,000 --> 00:15:13,000
basically given an input text X we

360
00:15:11,040 --> 00:15:16,079
predict an output label sequence y of

361
00:15:13,000 --> 00:15:17,560
equal length so this can be used for

362
00:15:16,079 --> 00:15:20,160
things like part of speech tagging to

363
00:15:17,560 --> 00:15:22,000
get the parts of speech of each word um

364
00:15:20,160 --> 00:15:24,639
it can also be used for something like

365
00:15:22,000 --> 00:15:26,959
lemmatization and litiz basically what

366
00:15:24,639 --> 00:15:29,880
that is is it is predicting the base

367
00:15:26,959 --> 00:15:31,480
form of each word uh and this can be

368
00:15:29,880 --> 00:15:34,560
used for normalization if you want to

369
00:15:31,480 --> 00:15:36,360
find like for example all instances of a

370
00:15:34,560 --> 00:15:38,480
a particular verb being used or all

371
00:15:36,360 --> 00:15:40,800
instances of a particular noun being

372
00:15:38,480 --> 00:15:42,720
used this is a little bit different than

373
00:15:40,800 --> 00:15:45,000
something like stemming so stemming

374
00:15:42,720 --> 00:15:48,160
normally what stemming would do is it

375
00:15:45,000 --> 00:15:50,560
would uh chop off the plural here it

376
00:15:48,160 --> 00:15:53,240
would chop off S but it wouldn't be able

377
00:15:50,560 --> 00:15:56,279
to do things like normalized saw into C

378
00:15:53,240 --> 00:15:57,759
because uh stemming uh just removes

379
00:15:56,279 --> 00:15:59,240
suffixes it doesn't do any sort of

380
00:15:57,759 --> 00:16:02,720
normalization so that's the difference

381
00:15:59,240 --> 00:16:05,199
between lonization and

382
00:16:02,720 --> 00:16:08,079
stemon there's also something called

383
00:16:05,199 --> 00:16:09,680
morphological tagging um in

384
00:16:08,079 --> 00:16:11,639
morphological tagging basically what

385
00:16:09,680 --> 00:16:14,360
this is doing is this is a

386
00:16:11,639 --> 00:16:17,040
more advanced version of part of speech

387
00:16:14,360 --> 00:16:20,360
tagging uh that predicts things like

388
00:16:17,040 --> 00:16:23,600
okay this is a a past tense verb uh this

389
00:16:20,360 --> 00:16:25,639
is a plural um this is a particular verb

390
00:16:23,600 --> 00:16:27,240
form and you have multiple tags here

391
00:16:25,639 --> 00:16:28,959
this is less interesting in English

392
00:16:27,240 --> 00:16:30,920
because English is kind of boring

393
00:16:28,959 --> 00:16:32,319
language morphology morphologically it

394
00:16:30,920 --> 00:16:33,399
doesn't have a lot of conjugation and

395
00:16:32,319 --> 00:16:35,839
other stuff but it's a lot more

396
00:16:33,399 --> 00:16:38,319
interesting in more complex languages

397
00:16:35,839 --> 00:16:40,040
like Japanese or Hindi or other things

398
00:16:38,319 --> 00:16:42,480
like

399
00:16:40,040 --> 00:16:43,920
that Chinese is even more boring than

400
00:16:42,480 --> 00:16:46,120
English so if you're interested in

401
00:16:43,920 --> 00:16:47,000
Chinese then you don't need to worry

402
00:16:46,120 --> 00:16:50,680
about

403
00:16:47,000 --> 00:16:52,560
that cool um but actually what's maybe

404
00:16:50,680 --> 00:16:55,000
more widely used from the sequence

405
00:16:52,560 --> 00:16:57,480
labeling perspective is span labeling

406
00:16:55,000 --> 00:17:01,040
and here you want to predict spans and

407
00:16:57,480 --> 00:17:03,560
labels and this could be uh named entity

408
00:17:01,040 --> 00:17:05,360
recognitions so if you say uh Graham nub

409
00:17:03,560 --> 00:17:07,199
is teaching at Carnegie melan University

410
00:17:05,360 --> 00:17:09,520
you would want to identify each entity

411
00:17:07,199 --> 00:17:11,480
is being like a person organization

412
00:17:09,520 --> 00:17:16,039
Place governmental entity other stuff

413
00:17:11,480 --> 00:17:18,760
like that um there's also

414
00:17:16,039 --> 00:17:20,439
uh things like syntactic chunking where

415
00:17:18,760 --> 00:17:23,640
you want to find all noun phrases and

416
00:17:20,439 --> 00:17:26,799
verb phrases um also semantic role

417
00:17:23,640 --> 00:17:30,360
labeling where semantic role labeling is

418
00:17:26,799 --> 00:17:32,480
uh demonstrating who did what to whom so

419
00:17:30,360 --> 00:17:34,440
it's saying uh this is the actor the

420
00:17:32,480 --> 00:17:36,120
person who did the thing this is the

421
00:17:34,440 --> 00:17:38,520
thing that is being done and this is the

422
00:17:36,120 --> 00:17:40,280
place where it's being done so uh this

423
00:17:38,520 --> 00:17:42,840
can be useful if you want to do any sort

424
00:17:40,280 --> 00:17:45,559
of analysis about who does what to whom

425
00:17:42,840 --> 00:17:48,160
uh other things like

426
00:17:45,559 --> 00:17:50,360
that um there's also a more complicated

427
00:17:48,160 --> 00:17:52,080
thing called an entity linking which

428
00:17:50,360 --> 00:17:54,559
isn't really a span linking task but

429
00:17:52,080 --> 00:17:58,400
it's basically named entity recognition

430
00:17:54,559 --> 00:18:00,799
and you link it to um and you link it to

431
00:17:58,400 --> 00:18:04,200
to like a database like Wiki data or

432
00:18:00,799 --> 00:18:06,600
Wikipedia or something like this and

433
00:18:04,200 --> 00:18:09,520
this doesn't seem very glamorous perhaps

434
00:18:06,600 --> 00:18:10,799
you know a lot of people might not you

435
00:18:09,520 --> 00:18:13,400
might not

436
00:18:10,799 --> 00:18:15,000
sound like immediately excit be

437
00:18:13,400 --> 00:18:16,799
immediately excited by entity linking

438
00:18:15,000 --> 00:18:18,520
but actually it's super super important

439
00:18:16,799 --> 00:18:20,080
for things like news aggregation and

440
00:18:18,520 --> 00:18:21,640
other stuff like that find all the news

441
00:18:20,080 --> 00:18:23,799
articles about the celebrity or

442
00:18:21,640 --> 00:18:26,919
something like this uh find all of the

443
00:18:23,799 --> 00:18:29,720
mentions of our product um our company's

444
00:18:26,919 --> 00:18:33,400
product and uh social media or things so

445
00:18:29,720 --> 00:18:33,400
it's actually a really widely used

446
00:18:33,720 --> 00:18:38,000
technology and then finally span

447
00:18:36,039 --> 00:18:40,240
labeling can also be treated as sequence

448
00:18:38,000 --> 00:18:43,240
labeling um and the way we normally do

449
00:18:40,240 --> 00:18:45,600
this is we use something called bio tags

450
00:18:43,240 --> 00:18:47,760
and uh here you predict the beginning uh

451
00:18:45,600 --> 00:18:50,200
in and out tags for each word or spans

452
00:18:47,760 --> 00:18:52,400
so if we have this example of spans uh

453
00:18:50,200 --> 00:18:56,120
we just convert this into tags uh where

454
00:18:52,400 --> 00:18:57,760
you say uh begin person in person o

455
00:18:56,120 --> 00:18:59,640
means it's not an entity begin

456
00:18:57,760 --> 00:19:02,799
organization in organization and then

457
00:18:59,640 --> 00:19:05,520
you canvert that back into um into these

458
00:19:02,799 --> 00:19:09,880
spans so this makes it relatively easy

459
00:19:05,520 --> 00:19:09,880
to uh kind of do the span

460
00:19:10,480 --> 00:19:15,120
prediction cool um so now you know uh

461
00:19:13,640 --> 00:19:16,600
now you know what to do if you want to

462
00:19:15,120 --> 00:19:18,280
predict entities or other things like

463
00:19:16,600 --> 00:19:20,240
that there's a lot of models on like

464
00:19:18,280 --> 00:19:22,400
hugging face for example that uh allow

465
00:19:20,240 --> 00:19:25,640
you to do these things are there any

466
00:19:22,400 --> 00:19:25,640
questions uh before I move

467
00:19:27,080 --> 00:19:32,440
on okay

468
00:19:28,799 --> 00:19:34,039
cool I'll just go forward then so um now

469
00:19:32,440 --> 00:19:37,000
I'm going to talk about how we actually

470
00:19:34,039 --> 00:19:38,559
model these in machine learning models

471
00:19:37,000 --> 00:19:40,919
and there's three major types of

472
00:19:38,559 --> 00:19:43,120
sequence models uh there are other types

473
00:19:40,919 --> 00:19:45,320
of sequence models but I'd say the great

474
00:19:43,120 --> 00:19:47,840
majority of work uses one of these three

475
00:19:45,320 --> 00:19:51,720
different types and the first one is

476
00:19:47,840 --> 00:19:54,840
recurrence um what recurrence does it is

477
00:19:51,720 --> 00:19:56,240
it conditions on representations on an

478
00:19:54,840 --> 00:19:58,720
encoding of the

479
00:19:56,240 --> 00:20:01,360
history and so the way this works works

480
00:19:58,720 --> 00:20:04,679
is essentially you have your input

481
00:20:01,360 --> 00:20:06,280
vectors like this uh usually word

482
00:20:04,679 --> 00:20:08,600
embeddings or embeddings from the

483
00:20:06,280 --> 00:20:10,880
previous layer of the model and you have

484
00:20:08,600 --> 00:20:12,840
a recurrent neural network and the

485
00:20:10,880 --> 00:20:14,600
recurrent neural network um at the very

486
00:20:12,840 --> 00:20:17,280
beginning might only take the first

487
00:20:14,600 --> 00:20:19,480
Vector but every subsequent step it

488
00:20:17,280 --> 00:20:23,760
takes the input vector and it takes the

489
00:20:19,480 --> 00:20:23,760
hidden Vector from the previous uh

490
00:20:24,080 --> 00:20:32,280
input and the uh then you keep on going

491
00:20:29,039 --> 00:20:32,280
uh like this all the way through the

492
00:20:32,320 --> 00:20:37,600
sequence the convolution is a

493
00:20:35,799 --> 00:20:40,880
conditioning representations on local

494
00:20:37,600 --> 00:20:44,200
context so you have the inputs like this

495
00:20:40,880 --> 00:20:47,200
and here you're conditioning on the word

496
00:20:44,200 --> 00:20:51,240
itself and the surrounding um words on

497
00:20:47,200 --> 00:20:52,960
the right or the left so um you would do

498
00:20:51,240 --> 00:20:55,240
something like this this is a typical

499
00:20:52,960 --> 00:20:57,480
convolution where you have this this

500
00:20:55,240 --> 00:20:59,039
certain one here and the left one and

501
00:20:57,480 --> 00:21:01,080
the right one and this would be a size

502
00:20:59,039 --> 00:21:03,480
three convolution you could also have a

503
00:21:01,080 --> 00:21:06,520
size five convolution 7 n you know

504
00:21:03,480 --> 00:21:08,600
whatever else um that would take in more

505
00:21:06,520 --> 00:21:11,520
surrounding words like

506
00:21:08,600 --> 00:21:13,720
this and then finally we have attention

507
00:21:11,520 --> 00:21:15,640
um and attention is conditioned

508
00:21:13,720 --> 00:21:19,080
representations at a weighted average of

509
00:21:15,640 --> 00:21:21,000
all tokens in the sequence and so here

510
00:21:19,080 --> 00:21:24,600
um we're conditioning on all of the

511
00:21:21,000 --> 00:21:26,279
other tokens in the sequence but um the

512
00:21:24,600 --> 00:21:28,919
amount that we condition on each of the

513
00:21:26,279 --> 00:21:32,039
tokens differs uh between

514
00:21:28,919 --> 00:21:34,919
so we might get more of this token less

515
00:21:32,039 --> 00:21:37,600
of this token and other things like that

516
00:21:34,919 --> 00:21:39,720
and I'll go into the mechanisms of each

517
00:21:37,600 --> 00:21:43,159
of

518
00:21:39,720 --> 00:21:45,720
these one important thing to think about

519
00:21:43,159 --> 00:21:49,279
is uh the computational complexity of

520
00:21:45,720 --> 00:21:51,960
each of these and um the computational

521
00:21:49,279 --> 00:21:56,240
complexity can be

522
00:21:51,960 --> 00:21:58,600
expressed as the sequence length let's

523
00:21:56,240 --> 00:22:00,840
call the sequence length n and

524
00:21:58,600 --> 00:22:02,520
convolution has a convolution window

525
00:22:00,840 --> 00:22:05,080
size so I'll call that

526
00:22:02,520 --> 00:22:08,039
W so does anyone have an idea of the

527
00:22:05,080 --> 00:22:10,360
computational complexity of a recurrent

528
00:22:08,039 --> 00:22:10,360
neural

529
00:22:11,480 --> 00:22:16,640
network so how um how quickly does the

530
00:22:15,120 --> 00:22:18,640
computation of a recurrent neural

531
00:22:16,640 --> 00:22:20,760
network grow and one way you can look at

532
00:22:18,640 --> 00:22:24,360
this is uh figure out the number of

533
00:22:20,760 --> 00:22:24,360
arrows uh that you see

534
00:22:24,480 --> 00:22:29,080
here yeah it's it's linear so it's

535
00:22:27,440 --> 00:22:32,520
basically

536
00:22:29,080 --> 00:22:35,520
n um what about

537
00:22:32,520 --> 00:22:36,760
convolution any other ideas any ideas

538
00:22:35,520 --> 00:22:42,039
about

539
00:22:36,760 --> 00:22:45,120
convolution n yeah NW n

540
00:22:42,039 --> 00:22:47,559
w and what about

541
00:22:45,120 --> 00:22:52,200
attention n squar

542
00:22:47,559 --> 00:22:53,559
yeah so what you can see is um for very

543
00:22:52,200 --> 00:22:58,000
long

544
00:22:53,559 --> 00:23:00,400
sequences um for very long sequences the

545
00:22:58,000 --> 00:23:04,480
asymptotic complexity of running a

546
00:23:00,400 --> 00:23:06,039
recurrent neural network is uh lower so

547
00:23:04,480 --> 00:23:08,960
you can run a recurrent neural network

548
00:23:06,039 --> 00:23:10,480
over a sequence of length uh you know 20

549
00:23:08,960 --> 00:23:12,480
million or something like that and as

550
00:23:10,480 --> 00:23:15,200
long as you had enough memory it would

551
00:23:12,480 --> 00:23:16,520
take a linear time but um if you do

552
00:23:15,200 --> 00:23:18,400
something like attention over a really

553
00:23:16,520 --> 00:23:20,240
long sequence it would be more difficult

554
00:23:18,400 --> 00:23:22,080
there's a lot of caveats here because

555
00:23:20,240 --> 00:23:23,320
attention and convolution are easily

556
00:23:22,080 --> 00:23:26,200
paral

557
00:23:23,320 --> 00:23:28,520
parallelized uh whereas uh recurrence is

558
00:23:26,200 --> 00:23:30,919
not um and I'll talk about that a second

559
00:23:28,520 --> 00:23:32,679
but any anyway it's a good thing to keep

560
00:23:30,919 --> 00:23:36,240
in

561
00:23:32,679 --> 00:23:37,679
mind cool um so the next the first

562
00:23:36,240 --> 00:23:39,799
sequence model I want to introduce is

563
00:23:37,679 --> 00:23:42,559
recurrent neural networks oh um sorry

564
00:23:39,799 --> 00:23:45,799
one other thing I want to mention is all

565
00:23:42,559 --> 00:23:47,600
of these are still used um it might seem

566
00:23:45,799 --> 00:23:49,960
that like if you're very plugged into

567
00:23:47,600 --> 00:23:52,640
NLP it might seem like Well everybody's

568
00:23:49,960 --> 00:23:55,080
using attention um so why do we need to

569
00:23:52,640 --> 00:23:56,880
learn about the other ones uh but

570
00:23:55,080 --> 00:23:59,679
actually all of these are used and

571
00:23:56,880 --> 00:24:02,600
usually recurrence and convolution are

572
00:23:59,679 --> 00:24:04,960
used in combination with attention uh in

573
00:24:02,600 --> 00:24:07,799
some way for particular applications

574
00:24:04,960 --> 00:24:09,960
where uh like uh recurrence or a

575
00:24:07,799 --> 00:24:12,640
convolution are are useful so I'll I'll

576
00:24:09,960 --> 00:24:15,279
go into details of that

577
00:24:12,640 --> 00:24:18,159
l so let's talk about the first sequence

578
00:24:15,279 --> 00:24:20,600
model uh recurrent neural networks so

579
00:24:18,159 --> 00:24:22,919
recurrent neural networks um they're

580
00:24:20,600 --> 00:24:26,399
basically tools to remember information

581
00:24:22,919 --> 00:24:28,520
uh they were invented in uh around

582
00:24:26,399 --> 00:24:30,520
1990 and

583
00:24:28,520 --> 00:24:34,120
the way they work is a feedforward

584
00:24:30,520 --> 00:24:35,600
neural network looks a bit like this we

585
00:24:34,120 --> 00:24:38,000
have some sort of look up over the

586
00:24:35,600 --> 00:24:40,120
context we calculate embeddings we do a

587
00:24:38,000 --> 00:24:41,000
transform we get a hidden State and we

588
00:24:40,120 --> 00:24:43,039
make the

589
00:24:41,000 --> 00:24:46,159
prediction whereas a recurrent neural

590
00:24:43,039 --> 00:24:49,360
network uh feeds in the previous hidden

591
00:24:46,159 --> 00:24:53,360
State and a very simple Elman style

592
00:24:49,360 --> 00:24:54,840
neural network looks um or I'll contrast

593
00:24:53,360 --> 00:24:56,559
the feed forward neural network that we

594
00:24:54,840 --> 00:24:58,279
already know with an Elman style neural

595
00:24:56,559 --> 00:25:00,399
network um

596
00:24:58,279 --> 00:25:01,880
uh recurrent neural network so basically

597
00:25:00,399 --> 00:25:06,120
the feed forward Network that we already

598
00:25:01,880 --> 00:25:07,840
know does a um linear transform over the

599
00:25:06,120 --> 00:25:09,279
input and then it runs it through a

600
00:25:07,840 --> 00:25:11,640
nonlinear function and this could be

601
00:25:09,279 --> 00:25:14,200
like a tan function or a Ru function or

602
00:25:11,640 --> 00:25:17,080
anything like that in a recurrent neural

603
00:25:14,200 --> 00:25:19,559
network we add uh multiplication by the

604
00:25:17,080 --> 00:25:22,080
hidden the previous hidden state so it

605
00:25:19,559 --> 00:25:25,120
looks like

606
00:25:22,080 --> 00:25:27,000
this and so if we look at what

607
00:25:25,120 --> 00:25:29,080
processing a sequence looks like uh

608
00:25:27,000 --> 00:25:31,080
basically what we do is we start out

609
00:25:29,080 --> 00:25:32,720
with an initial State this initial State

610
00:25:31,080 --> 00:25:34,320
could be like all zeros or it could be

611
00:25:32,720 --> 00:25:35,200
randomized or it could be learned or

612
00:25:34,320 --> 00:25:38,480
whatever

613
00:25:35,200 --> 00:25:42,080
else and then based on based on this uh

614
00:25:38,480 --> 00:25:44,279
we run it through an RNN function um and

615
00:25:42,080 --> 00:25:46,600
then you know use calculate the hidden

616
00:25:44,279 --> 00:25:48,960
State use it to make a prediction uh we

617
00:25:46,600 --> 00:25:50,760
have the RNN function uh make a

618
00:25:48,960 --> 00:25:51,760
prediction RNN make a prediction RNN

619
00:25:50,760 --> 00:25:54,520
make a

620
00:25:51,760 --> 00:25:56,960
prediction so one important thing here

621
00:25:54,520 --> 00:25:58,360
is that this RNN is exactly the same

622
00:25:56,960 --> 00:26:01,880
function

623
00:25:58,360 --> 00:26:04,960
no matter which position it appears in

624
00:26:01,880 --> 00:26:06,640
and so because of that we just no matter

625
00:26:04,960 --> 00:26:08,279
how long the sequence becomes we always

626
00:26:06,640 --> 00:26:10,200
have the same number of parameters which

627
00:26:08,279 --> 00:26:12,600
is always like really important for a

628
00:26:10,200 --> 00:26:15,120
sequence model so uh that's what this

629
00:26:12,600 --> 00:26:15,120
looks like

630
00:26:15,799 --> 00:26:20,480
here so how do we train

631
00:26:18,320 --> 00:26:22,679
rnns um

632
00:26:20,480 --> 00:26:24,399
basically if you remember we can trade

633
00:26:22,679 --> 00:26:27,159
neural networks as long as we have a

634
00:26:24,399 --> 00:26:29,240
directed e cyclic graph that calculates

635
00:26:27,159 --> 00:26:30,919
our loss function and then for uh

636
00:26:29,240 --> 00:26:32,640
forward propagation and back propagation

637
00:26:30,919 --> 00:26:35,720
we'll do all the rest to calculate our

638
00:26:32,640 --> 00:26:38,760
parameters and we uh we update the

639
00:26:35,720 --> 00:26:40,480
parameters so the way this works is uh

640
00:26:38,760 --> 00:26:42,000
let's say we're doing sequence labeling

641
00:26:40,480 --> 00:26:45,200
in each of these predictions is a part

642
00:26:42,000 --> 00:26:47,559
of speech uh each of these labels is a

643
00:26:45,200 --> 00:26:49,000
true part of speech label or sorry each

644
00:26:47,559 --> 00:26:50,760
of these predictions is like a

645
00:26:49,000 --> 00:26:52,919
probability over the part parts of

646
00:26:50,760 --> 00:26:55,720
speech for that sequence each of these

647
00:26:52,919 --> 00:26:57,640
labels is a true part of speech label so

648
00:26:55,720 --> 00:26:59,320
basically what we do is from this we

649
00:26:57,640 --> 00:27:02,200
calculate the negative log likelihood of

650
00:26:59,320 --> 00:27:05,559
the true part of speech we get a

651
00:27:02,200 --> 00:27:09,120
loss and so now we have four losses uh

652
00:27:05,559 --> 00:27:11,559
here this is no longer a nice directed

653
00:27:09,120 --> 00:27:13,000
acyclic uh graph that ends in a single

654
00:27:11,559 --> 00:27:15,279
loss function which is kind of what we

655
00:27:13,000 --> 00:27:17,559
needed for back propagation right so

656
00:27:15,279 --> 00:27:20,240
what do we do uh very simple we just add

657
00:27:17,559 --> 00:27:22,440
them together uh we take the sum and now

658
00:27:20,240 --> 00:27:24,120
we have a single loss function uh which

659
00:27:22,440 --> 00:27:26,240
is the sum of all of the loss functions

660
00:27:24,120 --> 00:27:28,679
for each prediction that we

661
00:27:26,240 --> 00:27:30,799
made and that's our total loss and now

662
00:27:28,679 --> 00:27:32,600
we do have a directed asli graph where

663
00:27:30,799 --> 00:27:34,320
this is the terminal node and we can do

664
00:27:32,600 --> 00:27:36,480
backr like

665
00:27:34,320 --> 00:27:37,799
this this is true for all sequence

666
00:27:36,480 --> 00:27:39,320
models I'm going to talk about today I'm

667
00:27:37,799 --> 00:27:41,559
just illustrating it with recurrent

668
00:27:39,320 --> 00:27:43,279
networks um any any questions here

669
00:27:41,559 --> 00:27:45,240
everything

670
00:27:43,279 --> 00:27:47,919
good

671
00:27:45,240 --> 00:27:50,279
okay cool um yeah so now we have the

672
00:27:47,919 --> 00:27:52,960
loss it's a Well form dag uh we can run

673
00:27:50,279 --> 00:27:55,320
backrop so uh basically what we do is we

674
00:27:52,960 --> 00:27:58,399
just run back propop and our loss goes

675
00:27:55,320 --> 00:28:01,120
out uh back into all of the

676
00:27:58,399 --> 00:28:04,200
places now parameters are tied across

677
00:28:01,120 --> 00:28:06,080
time so the derivatives into the

678
00:28:04,200 --> 00:28:07,200
parameters are aggregated over all of

679
00:28:06,080 --> 00:28:10,760
the time

680
00:28:07,200 --> 00:28:13,760
steps um and this has been called back

681
00:28:10,760 --> 00:28:16,320
propagation through time uh since uh

682
00:28:13,760 --> 00:28:18,679
these were originally invented so

683
00:28:16,320 --> 00:28:21,720
basically what it looks like is because

684
00:28:18,679 --> 00:28:25,600
the parameters for this RNN function are

685
00:28:21,720 --> 00:28:27,120
shared uh they'll essentially be updated

686
00:28:25,600 --> 00:28:29,480
they'll only be updated once but they're

687
00:28:27,120 --> 00:28:32,640
updated from like four different

688
00:28:29,480 --> 00:28:32,640
positions in this network

689
00:28:34,120 --> 00:28:38,440
essentially yeah and this is the same

690
00:28:36,120 --> 00:28:40,559
for all sequence uh sequence models that

691
00:28:38,440 --> 00:28:43,519
I'm going to talk about

692
00:28:40,559 --> 00:28:45,360
today um another variety of models that

693
00:28:43,519 --> 00:28:47,559
people use are bidirectional rnns and

694
00:28:45,360 --> 00:28:49,880
these are uh used when you want to you

695
00:28:47,559 --> 00:28:52,960
know do something like sequence labeling

696
00:28:49,880 --> 00:28:54,399
and so you just uh run two rnns you want

697
00:28:52,960 --> 00:28:56,279
run one from the beginning one from the

698
00:28:54,399 --> 00:28:59,399
end and concatenate them together like

699
00:28:56,279 --> 00:28:59,399
this make predictions

700
00:29:01,200 --> 00:29:08,200
cool uh any questions yeah if you run

701
00:29:05,559 --> 00:29:09,960
the does that change your

702
00:29:08,200 --> 00:29:11,679
complexity does this change the

703
00:29:09,960 --> 00:29:13,000
complexity it doesn't change the ASM

704
00:29:11,679 --> 00:29:16,519
totic complexity because you're

705
00:29:13,000 --> 00:29:18,320
multiplying by two uh and like Big O

706
00:29:16,519 --> 00:29:21,559
notation doesn't care if you multiply by

707
00:29:18,320 --> 00:29:23,880
a constant but it it does double the Ty

708
00:29:21,559 --> 00:29:23,880
that it would

709
00:29:24,080 --> 00:29:28,080
do cool any

710
00:29:26,320 --> 00:29:32,799
other

711
00:29:28,080 --> 00:29:35,720
okay let's go forward um another problem

712
00:29:32,799 --> 00:29:37,240
that is particularly Salient in rnns and

713
00:29:35,720 --> 00:29:40,440
part of the reason why attention models

714
00:29:37,240 --> 00:29:42,000
are so useful is Vanishing gradients but

715
00:29:40,440 --> 00:29:43,880
you should be aware of this regardless

716
00:29:42,000 --> 00:29:46,799
of whether like no matter which model

717
00:29:43,880 --> 00:29:48,799
you're using and um thinking about it

718
00:29:46,799 --> 00:29:50,720
very carefully is actually a really good

719
00:29:48,799 --> 00:29:52,399
way to design better architectures if

720
00:29:50,720 --> 00:29:54,000
you're going to be designing uh

721
00:29:52,399 --> 00:29:56,039
designing

722
00:29:54,000 --> 00:29:58,000
architectures so basically the problem

723
00:29:56,039 --> 00:29:59,399
with Vanishing gradients is like let's

724
00:29:58,000 --> 00:30:01,799
say we have a prediction task where

725
00:29:59,399 --> 00:30:03,960
we're calculating a regression we're

726
00:30:01,799 --> 00:30:05,519
inputting a whole bunch of tokens and

727
00:30:03,960 --> 00:30:08,080
then calculating a regression at the

728
00:30:05,519 --> 00:30:12,840
very end using a square air loss

729
00:30:08,080 --> 00:30:16,360
function if we do something like this uh

730
00:30:12,840 --> 00:30:17,919
the problem is if we have a standard RNN

731
00:30:16,360 --> 00:30:21,279
when we do back

732
00:30:17,919 --> 00:30:25,480
propop we'll have a big gradient

733
00:30:21,279 --> 00:30:27,000
probably for the first RNN unit here but

734
00:30:25,480 --> 00:30:30,120
every time because we're running this

735
00:30:27,000 --> 00:30:33,679
through through some sort of

736
00:30:30,120 --> 00:30:37,080
nonlinearity if we for example if our

737
00:30:33,679 --> 00:30:39,240
nonlinearity is a t h function uh the

738
00:30:37,080 --> 00:30:42,000
gradient of the tan H function looks a

739
00:30:39,240 --> 00:30:42,000
little bit like

740
00:30:42,120 --> 00:30:50,000
this and um here I if I am not mistaken

741
00:30:47,200 --> 00:30:53,480
this Peaks at at one and everywhere else

742
00:30:50,000 --> 00:30:56,919
at zero and so because this is peing at

743
00:30:53,480 --> 00:30:58,679
one everywhere else at zero let's say um

744
00:30:56,919 --> 00:31:01,360
we have an input way over here like

745
00:30:58,679 --> 00:31:03,080
minus minus 3 or something like that if

746
00:31:01,360 --> 00:31:04,760
we have that that basically destroys our

747
00:31:03,080 --> 00:31:10,760
gradient our gradient disappears for

748
00:31:04,760 --> 00:31:13,559
that particular unit um and you know

749
00:31:10,760 --> 00:31:15,399
maybe one thing that you might say is oh

750
00:31:13,559 --> 00:31:17,039
well you know if this is getting so

751
00:31:15,399 --> 00:31:19,320
small because this only goes up to one

752
00:31:17,039 --> 00:31:22,960
let's do like 100 time t

753
00:31:19,320 --> 00:31:24,880
h as our uh as our activation function

754
00:31:22,960 --> 00:31:26,600
we'll do 100 time tan H and so now this

755
00:31:24,880 --> 00:31:28,279
goes up to 100 and now our gradients are

756
00:31:26,600 --> 00:31:30,080
not going to disapp here but then you

757
00:31:28,279 --> 00:31:31,720
have the the opposite problem you have

758
00:31:30,080 --> 00:31:34,760
exploding gradients where it goes up by

759
00:31:31,720 --> 00:31:36,360
100 every time uh it gets unmanageable

760
00:31:34,760 --> 00:31:40,000
and destroys your gradient descent

761
00:31:36,360 --> 00:31:41,720
itself so basically we have uh we have

762
00:31:40,000 --> 00:31:43,200
this problem because if you apply a

763
00:31:41,720 --> 00:31:45,639
function over and over again your

764
00:31:43,200 --> 00:31:47,240
gradient gets smaller and smaller every

765
00:31:45,639 --> 00:31:49,080
smaller and smaller bigger and bigger

766
00:31:47,240 --> 00:31:50,480
every time you do that and uh you have

767
00:31:49,080 --> 00:31:51,720
the vanishing gradient or exploding

768
00:31:50,480 --> 00:31:54,799
gradient

769
00:31:51,720 --> 00:31:56,919
problem um it's not just a problem with

770
00:31:54,799 --> 00:31:59,039
nonlinearities so it also happens when

771
00:31:56,919 --> 00:32:00,480
you do do your weight Matrix multiplies

772
00:31:59,039 --> 00:32:03,840
and other stuff like that basically

773
00:32:00,480 --> 00:32:05,960
anytime you modify uh the the input into

774
00:32:03,840 --> 00:32:07,720
a different output it will have a

775
00:32:05,960 --> 00:32:10,240
gradient and so it will either be bigger

776
00:32:07,720 --> 00:32:14,000
than one or less than

777
00:32:10,240 --> 00:32:16,000
one um so I mentioned this is a problem

778
00:32:14,000 --> 00:32:18,120
for rnns it's particularly a problem for

779
00:32:16,000 --> 00:32:20,799
rnns over long sequences but it's also a

780
00:32:18,120 --> 00:32:23,039
problem for any other model you use and

781
00:32:20,799 --> 00:32:24,960
the reason why this is important to know

782
00:32:23,039 --> 00:32:26,799
is if there's important information in

783
00:32:24,960 --> 00:32:29,000
your model finding a way that you can

784
00:32:26,799 --> 00:32:30,559
get a direct path from that important

785
00:32:29,000 --> 00:32:32,600
information to wherever you're making a

786
00:32:30,559 --> 00:32:34,440
prediction often is a way to improve

787
00:32:32,600 --> 00:32:39,120
your model

788
00:32:34,440 --> 00:32:41,159
um improve your model performance and on

789
00:32:39,120 --> 00:32:42,919
the contrary if there's unimportant

790
00:32:41,159 --> 00:32:45,320
information if there's information that

791
00:32:42,919 --> 00:32:47,159
you think is likely to be unimportant

792
00:32:45,320 --> 00:32:49,159
putting it farther away or making it a

793
00:32:47,159 --> 00:32:51,279
more indirect path so the model has to

794
00:32:49,159 --> 00:32:53,200
kind of work harder to use it is a good

795
00:32:51,279 --> 00:32:54,840
way to prevent the model from being

796
00:32:53,200 --> 00:32:57,679
distracted by like tons and tons of

797
00:32:54,840 --> 00:33:00,200
information um uh some of it

798
00:32:57,679 --> 00:33:03,960
which may be irrelevant so it's a good

799
00:33:00,200 --> 00:33:03,960
thing to know about in general for model

800
00:33:05,360 --> 00:33:13,080
design so um how did RNN solve this

801
00:33:09,559 --> 00:33:15,360
problem of uh of the vanishing gradient

802
00:33:13,080 --> 00:33:16,880
there is a method called long short-term

803
00:33:15,360 --> 00:33:20,360
memory

804
00:33:16,880 --> 00:33:22,840
um and the basic idea is to make

805
00:33:20,360 --> 00:33:24,360
additive connections between time

806
00:33:22,840 --> 00:33:29,919
steps

807
00:33:24,360 --> 00:33:32,799
and so addition is the

808
00:33:29,919 --> 00:33:36,399
only addition or kind of like the

809
00:33:32,799 --> 00:33:38,159
identity is the only thing that does not

810
00:33:36,399 --> 00:33:40,880
change the gradient it's guaranteed to

811
00:33:38,159 --> 00:33:43,279
not change the gradient because um the

812
00:33:40,880 --> 00:33:46,639
identity function is like f

813
00:33:43,279 --> 00:33:49,159
ofx equals X and if you take the

814
00:33:46,639 --> 00:33:51,480
derivative of this it's one so you're

815
00:33:49,159 --> 00:33:55,440
guaranteed to always have a gradient of

816
00:33:51,480 --> 00:33:57,360
one according to this function so um

817
00:33:55,440 --> 00:33:59,559
long shortterm memory makes sure that

818
00:33:57,360 --> 00:34:01,840
you have this additive uh input between

819
00:33:59,559 --> 00:34:04,600
time steps and this is what it looks

820
00:34:01,840 --> 00:34:05,919
like it's not super super important to

821
00:34:04,600 --> 00:34:09,119
understand everything that's going on

822
00:34:05,919 --> 00:34:12,200
here but just to explain it very quickly

823
00:34:09,119 --> 00:34:15,720
this uh C here is something called the

824
00:34:12,200 --> 00:34:20,520
memory cell it's passed on linearly like

825
00:34:15,720 --> 00:34:24,679
this and then um you have some gates the

826
00:34:20,520 --> 00:34:27,320
update gate is determining whether uh

827
00:34:24,679 --> 00:34:28,919
whether you update this hidden state or

828
00:34:27,320 --> 00:34:31,440
how much you update given this hidden

829
00:34:28,919 --> 00:34:34,480
State this input gate is deciding how

830
00:34:31,440 --> 00:34:36,760
much of the input you take in um and

831
00:34:34,480 --> 00:34:39,879
then the output gate is deciding how

832
00:34:36,760 --> 00:34:43,280
much of uh the output from the cell you

833
00:34:39,879 --> 00:34:45,599
uh you basically push out after using

834
00:34:43,280 --> 00:34:47,079
the cells so um it has these three gates

835
00:34:45,599 --> 00:34:48,760
that control the information flow and

836
00:34:47,079 --> 00:34:51,520
the model can learn to turn them on or

837
00:34:48,760 --> 00:34:53,720
off uh or something like that so uh

838
00:34:51,520 --> 00:34:55,679
that's the basic uh basic idea of the

839
00:34:53,720 --> 00:34:57,240
LSM and there's lots of other like

840
00:34:55,679 --> 00:34:59,359
variants of this like gated recurrent

841
00:34:57,240 --> 00:35:01,520
units that are a little bit simpler but

842
00:34:59,359 --> 00:35:03,920
the basic idea of an additive connection

843
00:35:01,520 --> 00:35:07,240
plus gating is uh something that appears

844
00:35:03,920 --> 00:35:07,240
a lot in many different types of

845
00:35:07,440 --> 00:35:14,240
architectures um any questions

846
00:35:12,079 --> 00:35:15,760
here another thing I should mention that

847
00:35:14,240 --> 00:35:19,200
I just realized I don't have on my

848
00:35:15,760 --> 00:35:24,480
slides but it's a good thing to know is

849
00:35:19,200 --> 00:35:29,040
that this is also used in uh deep

850
00:35:24,480 --> 00:35:32,440
networks and uh multi-layer

851
00:35:29,040 --> 00:35:32,440
networks and so

852
00:35:34,240 --> 00:35:39,520
basically lstms uh this is

853
00:35:39,720 --> 00:35:45,359
time lstms have this additive connection

854
00:35:43,359 --> 00:35:47,599
between the member eel where you're

855
00:35:45,359 --> 00:35:50,079
always

856
00:35:47,599 --> 00:35:53,119
adding um adding this into to whatever

857
00:35:50,079 --> 00:35:53,119
input you

858
00:35:54,200 --> 00:36:00,720
get and then you you get an input and

859
00:35:57,000 --> 00:36:00,720
you add this in you get an

860
00:36:00,839 --> 00:36:07,000
input and so this this makes sure you

861
00:36:03,440 --> 00:36:09,640
pass your gradients forward in

862
00:36:07,000 --> 00:36:11,720
time there's also uh something called

863
00:36:09,640 --> 00:36:13,000
residual connections which I think a lot

864
00:36:11,720 --> 00:36:14,319
of people have heard of if you've done a

865
00:36:13,000 --> 00:36:16,000
deep learning class or something like

866
00:36:14,319 --> 00:36:18,079
that but if you haven't uh they're a

867
00:36:16,000 --> 00:36:20,599
good thing to know residual connections

868
00:36:18,079 --> 00:36:22,440
are if you run your input through

869
00:36:20,599 --> 00:36:25,720
multiple

870
00:36:22,440 --> 00:36:28,720
layers like let's say you have a block

871
00:36:25,720 --> 00:36:28,720
here

872
00:36:36,480 --> 00:36:41,280
let's let's call this an RNN for now

873
00:36:38,560 --> 00:36:44,280
because we know um we know about RNN

874
00:36:41,280 --> 00:36:44,280
already so

875
00:36:45,119 --> 00:36:49,560
RNN so this this connection here is

876
00:36:48,319 --> 00:36:50,920
called the residual connection and

877
00:36:49,560 --> 00:36:55,240
basically it's adding an additive

878
00:36:50,920 --> 00:36:57,280
connection before and after layers so um

879
00:36:55,240 --> 00:36:58,640
this allows you to pass information from

880
00:36:57,280 --> 00:37:00,880
the very beginning of a network to the

881
00:36:58,640 --> 00:37:03,520
very end of a network um through

882
00:37:00,880 --> 00:37:05,480
multiple layers and it also is there to

883
00:37:03,520 --> 00:37:08,800
help prevent the gradient finishing

884
00:37:05,480 --> 00:37:11,520
problem so like in a way you can view uh

885
00:37:08,800 --> 00:37:14,560
you can view lstms what lstms are doing

886
00:37:11,520 --> 00:37:15,800
is preventing loss of gradient in time

887
00:37:14,560 --> 00:37:17,280
and these are preventing loss of

888
00:37:15,800 --> 00:37:19,480
gradient as you go through like multiple

889
00:37:17,280 --> 00:37:21,119
layers of the network and this is super

890
00:37:19,480 --> 00:37:24,079
standard this is used in all like

891
00:37:21,119 --> 00:37:25,599
Transformer models and llama and GPT and

892
00:37:24,079 --> 00:37:31,200
whatever

893
00:37:25,599 --> 00:37:31,200
else cool um any other questions about

894
00:37:32,760 --> 00:37:39,079
that okay cool um so next I'd like to go

895
00:37:36,880 --> 00:37:41,760
into convolution um one one thing I

896
00:37:39,079 --> 00:37:44,760
should mention is rnns or RNN style

897
00:37:41,760 --> 00:37:46,920
models are used extensively in very long

898
00:37:44,760 --> 00:37:48,160
sequence modeling and we're going to

899
00:37:46,920 --> 00:37:50,440
talk more about like actual

900
00:37:48,160 --> 00:37:52,640
architectures that people use uh to do

901
00:37:50,440 --> 00:37:55,119
this um usually in combination with

902
00:37:52,640 --> 00:37:57,720
attention based models uh but they're

903
00:37:55,119 --> 00:38:01,800
used in very long sequence modeling

904
00:37:57,720 --> 00:38:05,640
convolutions tend to be used in um a lot

905
00:38:01,800 --> 00:38:07,160
in speech and image processing uh and

906
00:38:05,640 --> 00:38:10,880
the reason why they're used a lot in

907
00:38:07,160 --> 00:38:13,560
speech and image processing is

908
00:38:10,880 --> 00:38:16,800
because when we're processing

909
00:38:13,560 --> 00:38:18,599
language uh we have like

910
00:38:16,800 --> 00:38:22,720
um

911
00:38:18,599 --> 00:38:22,720
this is

912
00:38:23,599 --> 00:38:29,400
wonderful like this is wonderful is

913
00:38:26,599 --> 00:38:33,319
three tokens in language but if we look

914
00:38:29,400 --> 00:38:36,960
at it in speech it's going to be

915
00:38:33,319 --> 00:38:36,960
like many many

916
00:38:37,560 --> 00:38:46,079
frames so kind of

917
00:38:41,200 --> 00:38:47,680
the semantics of language is already

918
00:38:46,079 --> 00:38:48,960
kind of like if you look at a single

919
00:38:47,680 --> 00:38:51,599
token you already get something

920
00:38:48,960 --> 00:38:52,839
semantically meaningful um but in

921
00:38:51,599 --> 00:38:54,560
contrast if you're looking at like

922
00:38:52,839 --> 00:38:56,000
speech or you're looking at pixels and

923
00:38:54,560 --> 00:38:57,400
images or something like that you're not

924
00:38:56,000 --> 00:39:00,359
going to get something semantically

925
00:38:57,400 --> 00:39:01,920
meaningful uh so uh convolution is used

926
00:39:00,359 --> 00:39:03,359
a lot in that case and also you could

927
00:39:01,920 --> 00:39:06,079
create a convolutional model over

928
00:39:03,359 --> 00:39:08,599
characters as well

929
00:39:06,079 --> 00:39:10,599
um so what is convolution in the first

930
00:39:08,599 --> 00:39:13,319
place um as I mentioned before basically

931
00:39:10,599 --> 00:39:16,359
you take the local window uh around an

932
00:39:13,319 --> 00:39:19,680
input and you run it through um

933
00:39:16,359 --> 00:39:22,079
basically a model and a a good way to

934
00:39:19,680 --> 00:39:24,400
think about it is it's essentially a

935
00:39:22,079 --> 00:39:26,440
feed forward Network where you can

936
00:39:24,400 --> 00:39:28,240
catenate uh all of the surrounding

937
00:39:26,440 --> 00:39:30,280
vectors together and run them through a

938
00:39:28,240 --> 00:39:34,400
linear transform like this so you can

939
00:39:30,280 --> 00:39:34,400
Cate XT minus XT XT

940
00:39:35,880 --> 00:39:43,040
plus1 convolution can also be used in

941
00:39:39,440 --> 00:39:45,400
Auto regressive models and normally like

942
00:39:43,040 --> 00:39:48,079
we think of it like this so we think

943
00:39:45,400 --> 00:39:50,640
that we're taking the previous one the

944
00:39:48,079 --> 00:39:53,839
current one and the next one and making

945
00:39:50,640 --> 00:39:54,960
a prediction based on this but this

946
00:39:53,839 --> 00:39:56,440
would be good for something like

947
00:39:54,960 --> 00:39:57,720
sequence labeling but it's not good for

948
00:39:56,440 --> 00:39:59,040
for something like language modeling

949
00:39:57,720 --> 00:40:01,400
because in language modeling we can't

950
00:39:59,040 --> 00:40:05,200
look at the future right but there's a

951
00:40:01,400 --> 00:40:07,280
super simple uh solution to this which

952
00:40:05,200 --> 00:40:11,280
is you have a convolution that just

953
00:40:07,280 --> 00:40:13,720
looks at the past basically um and

954
00:40:11,280 --> 00:40:15,319
predicts the next word based on the the

955
00:40:13,720 --> 00:40:16,760
you know current word in the past so

956
00:40:15,319 --> 00:40:19,520
here you would be predicting the word

957
00:40:16,760 --> 00:40:21,040
movie um this is actually essentially

958
00:40:19,520 --> 00:40:23,839
equivalent to the feed forward language

959
00:40:21,040 --> 00:40:25,880
model that I talked about last time uh

960
00:40:23,839 --> 00:40:27,240
so you can also think of that as a

961
00:40:25,880 --> 00:40:30,599
convolution

962
00:40:27,240 --> 00:40:32,119
a convolutional language model um so

963
00:40:30,599 --> 00:40:33,359
when whenever you say feed forward or

964
00:40:32,119 --> 00:40:36,160
convolutional language model they're

965
00:40:33,359 --> 00:40:38,880
basically the same uh modulo some uh

966
00:40:36,160 --> 00:40:42,359
some details about striding and stuff

967
00:40:38,880 --> 00:40:42,359
which I'm going to talk about the class

968
00:40:43,000 --> 00:40:49,359
today cool um I covered convolution very

969
00:40:47,400 --> 00:40:51,440
briefly because it's also the least used

970
00:40:49,359 --> 00:40:53,400
of the three uh sequence modeling things

971
00:40:51,440 --> 00:40:55,400
in NLP nowadays but um are there any

972
00:40:53,400 --> 00:40:58,319
questions there or can I just run into

973
00:40:55,400 --> 00:40:58,319
attention

974
00:40:59,119 --> 00:41:04,040
okay cool I'll go into attention next so

975
00:41:02,400 --> 00:41:06,400
uh the basic idea about

976
00:41:04,040 --> 00:41:11,119
attention um

977
00:41:06,400 --> 00:41:12,839
is that we encode uh each token and the

978
00:41:11,119 --> 00:41:14,440
sequence into a

979
00:41:12,839 --> 00:41:19,119
vector

980
00:41:14,440 --> 00:41:21,640
um or so we we have input an input

981
00:41:19,119 --> 00:41:24,240
sequence that we'd like to encode over

982
00:41:21,640 --> 00:41:27,800
and we perform a linear combination of

983
00:41:24,240 --> 00:41:30,640
the vectors weighted by attention weight

984
00:41:27,800 --> 00:41:33,359
and there's two varieties of attention

985
00:41:30,640 --> 00:41:35,160
uh that are good to know about the first

986
00:41:33,359 --> 00:41:37,440
one is cross

987
00:41:35,160 --> 00:41:40,040
atten where each element in a sequence

988
00:41:37,440 --> 00:41:41,960
attends to elements of another sequence

989
00:41:40,040 --> 00:41:44,280
and this is widely used in encoder

990
00:41:41,960 --> 00:41:47,359
decoder models where you have one

991
00:41:44,280 --> 00:41:50,319
encoder and you have a separate decoder

992
00:41:47,359 --> 00:41:51,880
um these models the popular models that

993
00:41:50,319 --> 00:41:55,119
are like this that people still use a

994
00:41:51,880 --> 00:41:57,480
lot are T5 uh is a example of an encoder

995
00:41:55,119 --> 00:42:00,760
decoder model or embar is another

996
00:41:57,480 --> 00:42:03,160
example of encoder decoder model um but

997
00:42:00,760 --> 00:42:07,880
basically the uh The Way Cross attention

998
00:42:03,160 --> 00:42:10,359
works is we have for example an English

999
00:42:07,880 --> 00:42:14,079
uh sentence here and we want to

1000
00:42:10,359 --> 00:42:17,560
translate it into uh into a Japanese

1001
00:42:14,079 --> 00:42:23,040
sentence and so when we output the first

1002
00:42:17,560 --> 00:42:25,119
word we would mostly uh upweight this or

1003
00:42:23,040 --> 00:42:26,800
sorry we have a we have a Japanese

1004
00:42:25,119 --> 00:42:29,119
sentence and we would like to translated

1005
00:42:26,800 --> 00:42:31,680
into an English sentence for example so

1006
00:42:29,119 --> 00:42:35,160
when we generate the first word in

1007
00:42:31,680 --> 00:42:38,400
Japanese means this so in order to

1008
00:42:35,160 --> 00:42:40,079
Output the first word we would first uh

1009
00:42:38,400 --> 00:42:43,559
do a weighted sum of all of the

1010
00:42:40,079 --> 00:42:46,240
embeddings of the Japanese sentence and

1011
00:42:43,559 --> 00:42:49,359
we would focus probably most on this

1012
00:42:46,240 --> 00:42:51,920
word up here C because it corresponds to

1013
00:42:49,359 --> 00:42:51,920
the word

1014
00:42:53,160 --> 00:42:59,800
this in the next step of generating an

1015
00:42:55,960 --> 00:43:01,319
out output uh we would uh attend to

1016
00:42:59,800 --> 00:43:04,119
different words because different words

1017
00:43:01,319 --> 00:43:07,680
correspond to is so you would attend to

1018
00:43:04,119 --> 00:43:11,040
which corresponds to is um when you

1019
00:43:07,680 --> 00:43:12,599
output n actually there's no word in the

1020
00:43:11,040 --> 00:43:16,839
Japanese sentence that correspon to and

1021
00:43:12,599 --> 00:43:18,720
so you might get a very like blob like

1022
00:43:16,839 --> 00:43:21,319
uh in attention weight that doesn't look

1023
00:43:18,720 --> 00:43:23,319
very uh that looks very smooth not very

1024
00:43:21,319 --> 00:43:25,119
peaky and then when you do example you'd

1025
00:43:23,319 --> 00:43:27,880
have strong attention on uh on the word

1026
00:43:25,119 --> 00:43:29,400
that corresponds to example

1027
00:43:27,880 --> 00:43:31,599
there's also self

1028
00:43:29,400 --> 00:43:33,480
attention and um self attention

1029
00:43:31,599 --> 00:43:36,000
basically what it does is each element

1030
00:43:33,480 --> 00:43:38,640
in a sequence attends to elements of the

1031
00:43:36,000 --> 00:43:40,240
same sequence and so this is a good way

1032
00:43:38,640 --> 00:43:43,359
of doing sequence encoding just like we

1033
00:43:40,240 --> 00:43:46,280
used rnns by rnns uh convolutional

1034
00:43:43,359 --> 00:43:47,559
neural networks and so um the reason why

1035
00:43:46,280 --> 00:43:50,119
you would want to do something like this

1036
00:43:47,559 --> 00:43:52,760
just to give an example let's say we

1037
00:43:50,119 --> 00:43:54,280
wanted to run this we wanted to encode

1038
00:43:52,760 --> 00:43:56,920
the English sentence before doing

1039
00:43:54,280 --> 00:44:00,040
something like translation into Japanese

1040
00:43:56,920 --> 00:44:01,559
and if we did that um this maybe we

1041
00:44:00,040 --> 00:44:02,960
don't need to attend to a whole lot of

1042
00:44:01,559 --> 00:44:06,440
other things because it's kind of clear

1043
00:44:02,960 --> 00:44:08,920
what this means but um

1044
00:44:06,440 --> 00:44:10,880
is the way you would translate it would

1045
00:44:08,920 --> 00:44:12,280
be rather heavily dependent on what the

1046
00:44:10,880 --> 00:44:13,640
other words in the sentence so you might

1047
00:44:12,280 --> 00:44:17,280
want to attend to all the other words in

1048
00:44:13,640 --> 00:44:20,559
the sentence say oh this is is co

1049
00:44:17,280 --> 00:44:22,839
cooccurring with this and example and so

1050
00:44:20,559 --> 00:44:24,440
if that's the case then well we would

1051
00:44:22,839 --> 00:44:26,920
need to translate it in this way or we'

1052
00:44:24,440 --> 00:44:28,960
need to handle it in this way and that's

1053
00:44:26,920 --> 00:44:29,880
exactly the same for you know any other

1054
00:44:28,960 --> 00:44:32,720
sort of

1055
00:44:29,880 --> 00:44:35,880
disambiguation uh style

1056
00:44:32,720 --> 00:44:37,720
task so uh yeah we do something similar

1057
00:44:35,880 --> 00:44:39,040
like this so basically cross attention

1058
00:44:37,720 --> 00:44:42,520
is attending to a different sequence

1059
00:44:39,040 --> 00:44:42,520
self attention is attending to the same

1060
00:44:42,680 --> 00:44:46,559
sequence so how do we do this

1061
00:44:44,960 --> 00:44:48,200
mechanistically in the first place so

1062
00:44:46,559 --> 00:44:51,480
like let's say We're translating from

1063
00:44:48,200 --> 00:44:52,880
Japanese to English um we would have uh

1064
00:44:51,480 --> 00:44:55,960
and we're doing it with an encoder

1065
00:44:52,880 --> 00:44:57,480
decoder model where we have already ENC

1066
00:44:55,960 --> 00:45:00,640
coded the

1067
00:44:57,480 --> 00:45:02,920
input sequence and now we're generating

1068
00:45:00,640 --> 00:45:05,240
the output sequence with a for example a

1069
00:45:02,920 --> 00:45:09,880
recurrent neural network um and so if

1070
00:45:05,240 --> 00:45:12,400
that's the case we have uh I I hate uh

1071
00:45:09,880 --> 00:45:14,440
like this and we want to predict the

1072
00:45:12,400 --> 00:45:17,280
next word so what we would do is we

1073
00:45:14,440 --> 00:45:19,480
would take the current state

1074
00:45:17,280 --> 00:45:21,480
here and uh we use something called a

1075
00:45:19,480 --> 00:45:22,760
query vector and the query Vector is

1076
00:45:21,480 --> 00:45:24,880
essentially the vector that we want to

1077
00:45:22,760 --> 00:45:28,720
use to decide what to attend

1078
00:45:24,880 --> 00:45:31,800
to we then have key vectors and the key

1079
00:45:28,720 --> 00:45:35,319
vectors are the vectors that we would

1080
00:45:31,800 --> 00:45:37,480
like to use to decide which ones we

1081
00:45:35,319 --> 00:45:40,720
should be attending

1082
00:45:37,480 --> 00:45:42,040
to and then for each query key pair we

1083
00:45:40,720 --> 00:45:45,319
calculate a

1084
00:45:42,040 --> 00:45:48,319
weight and we do it like this um this

1085
00:45:45,319 --> 00:45:50,680
gear here is some function that takes in

1086
00:45:48,319 --> 00:45:53,200
the uh query vector and the key vector

1087
00:45:50,680 --> 00:45:55,599
and outputs a weight and notably we use

1088
00:45:53,200 --> 00:45:57,559
the same function every single time this

1089
00:45:55,599 --> 00:46:00,960
is really important again because like

1090
00:45:57,559 --> 00:46:03,760
RNN that allows us to extrapolate

1091
00:46:00,960 --> 00:46:05,960
unlimited length sequences because uh we

1092
00:46:03,760 --> 00:46:08,280
only have one set of you know we only

1093
00:46:05,960 --> 00:46:10,359
have one function no matter how long the

1094
00:46:08,280 --> 00:46:13,200
sequence gets so we can just apply it

1095
00:46:10,359 --> 00:46:15,839
over and over and over

1096
00:46:13,200 --> 00:46:17,920
again uh once we calculate these values

1097
00:46:15,839 --> 00:46:20,839
we normalize so that they add up to one

1098
00:46:17,920 --> 00:46:22,559
using the softmax function and um

1099
00:46:20,839 --> 00:46:27,800
basically in this case that would be

1100
00:46:22,559 --> 00:46:27,800
like 0.76 uh etc etc oops

1101
00:46:28,800 --> 00:46:33,559
so step number two is once we have this

1102
00:46:32,280 --> 00:46:37,839
uh these

1103
00:46:33,559 --> 00:46:40,160
attention uh values here notably these

1104
00:46:37,839 --> 00:46:41,359
values aren't really probabilities uh

1105
00:46:40,160 --> 00:46:42,800
despite the fact that they're between

1106
00:46:41,359 --> 00:46:44,240
zero and one and they add up to one

1107
00:46:42,800 --> 00:46:47,440
because all we're doing is we're using

1108
00:46:44,240 --> 00:46:50,480
them to uh to combine together uh

1109
00:46:47,440 --> 00:46:51,800
multiple vectors so I we don't really

1110
00:46:50,480 --> 00:46:53,319
normally call them attention

1111
00:46:51,800 --> 00:46:54,680
probabilities or anything like that I

1112
00:46:53,319 --> 00:46:56,319
just call them attention values or

1113
00:46:54,680 --> 00:46:59,680
normalized attention values

1114
00:46:56,319 --> 00:47:03,760
is um but once we have these uh

1115
00:46:59,680 --> 00:47:05,760
attention uh attention weights we have

1116
00:47:03,760 --> 00:47:07,200
value vectors and these value vectors

1117
00:47:05,760 --> 00:47:10,000
are the vectors that we would actually

1118
00:47:07,200 --> 00:47:12,319
like to combine together to get the uh

1119
00:47:10,000 --> 00:47:14,000
encoding here and so we take these

1120
00:47:12,319 --> 00:47:17,559
vectors we do a weighted some of the

1121
00:47:14,000 --> 00:47:21,200
vectors and get a final final sum

1122
00:47:17,559 --> 00:47:22,920
here and we can take this uh some and

1123
00:47:21,200 --> 00:47:26,920
use it in any part of the model that we

1124
00:47:22,920 --> 00:47:29,079
would like um and so is very broad it

1125
00:47:26,920 --> 00:47:31,200
can be used in any way now the most

1126
00:47:29,079 --> 00:47:33,240
common way to use it is just have lots

1127
00:47:31,200 --> 00:47:35,000
of self attention layers like in

1128
00:47:33,240 --> 00:47:37,440
something in a Transformer but um you

1129
00:47:35,000 --> 00:47:40,160
can also use it in decoder or other

1130
00:47:37,440 --> 00:47:42,920
things like that as

1131
00:47:40,160 --> 00:47:45,480
well this is an actual graphical example

1132
00:47:42,920 --> 00:47:47,319
from the original attention paper um I'm

1133
00:47:45,480 --> 00:47:50,000
going to give some other examples from

1134
00:47:47,319 --> 00:47:52,480
Transformers in the next class but

1135
00:47:50,000 --> 00:47:55,400
basically you can see that the attention

1136
00:47:52,480 --> 00:47:57,559
weights uh for this English to French I

1137
00:47:55,400 --> 00:48:00,520
think it's English French translation

1138
00:47:57,559 --> 00:48:02,920
task basically um overlap with what you

1139
00:48:00,520 --> 00:48:04,440
would expect uh if you can read English

1140
00:48:02,920 --> 00:48:06,599
and French it's kind of the words that

1141
00:48:04,440 --> 00:48:09,319
are semantically similar to each other

1142
00:48:06,599 --> 00:48:12,920
um it even learns to do this reordering

1143
00:48:09,319 --> 00:48:14,880
uh in an appropriate way here and all of

1144
00:48:12,920 --> 00:48:16,720
this is completely unsupervised so you

1145
00:48:14,880 --> 00:48:18,079
never actually give the model

1146
00:48:16,720 --> 00:48:19,440
information about what it should be

1147
00:48:18,079 --> 00:48:21,559
attending to it's all learned through

1148
00:48:19,440 --> 00:48:23,520
gradient descent and the model learns to

1149
00:48:21,559 --> 00:48:27,640
do this by making the embeddings of the

1150
00:48:23,520 --> 00:48:27,640
key and query vectors closer together

1151
00:48:28,440 --> 00:48:33,240
cool

1152
00:48:30,000 --> 00:48:33,240
um any

1153
00:48:33,800 --> 00:48:40,040
questions okay so um next I'd like to go

1154
00:48:38,440 --> 00:48:41,680
a little bit into how we actually

1155
00:48:40,040 --> 00:48:43,599
calculate the attention score function

1156
00:48:41,680 --> 00:48:44,839
so that's the little gear that I had on

1157
00:48:43,599 --> 00:48:50,280
my

1158
00:48:44,839 --> 00:48:53,559
uh my slide before so here Q is a query

1159
00:48:50,280 --> 00:48:56,440
and K is the key um the original

1160
00:48:53,559 --> 00:48:58,400
attention paper used a multi-layer layer

1161
00:48:56,440 --> 00:49:00,119
uh a multi-layer neural network to

1162
00:48:58,400 --> 00:49:02,440
calculate this so basically what it did

1163
00:49:00,119 --> 00:49:05,319
is it concatenated the query and key

1164
00:49:02,440 --> 00:49:08,000
Vector together multiplied it by a

1165
00:49:05,319 --> 00:49:12,240
weight Matrix calculated a tan H and

1166
00:49:08,000 --> 00:49:15,040
then ran it through uh a weight

1167
00:49:12,240 --> 00:49:19,799
Vector so this

1168
00:49:15,040 --> 00:49:22,480
is essentially very expressive

1169
00:49:19,799 --> 00:49:24,799
um uh it's flexible it's often good with

1170
00:49:22,480 --> 00:49:27,960
large data but it adds extra parameters

1171
00:49:24,799 --> 00:49:30,359
and uh computation time uh to your

1172
00:49:27,960 --> 00:49:31,559
calculations here so it's not as widely

1173
00:49:30,359 --> 00:49:34,359
used

1174
00:49:31,559 --> 00:49:37,799
anymore the uh other thing which was

1175
00:49:34,359 --> 00:49:41,599
proposed by long ad all is a bilinear

1176
00:49:37,799 --> 00:49:43,200
function um and a bilinear function

1177
00:49:41,599 --> 00:49:45,920
basically what it does is it has your

1178
00:49:43,200 --> 00:49:48,319
key Vector it has your query vector and

1179
00:49:45,920 --> 00:49:51,440
it has a matrix in between them like

1180
00:49:48,319 --> 00:49:53,000
this and uh then you calculate uh you

1181
00:49:51,440 --> 00:49:54,520
calculate the

1182
00:49:53,000 --> 00:49:56,680
alut

1183
00:49:54,520 --> 00:49:59,880
so

1184
00:49:56,680 --> 00:50:03,200
this is uh nice because it basically um

1185
00:49:59,880 --> 00:50:05,760
Can Transform uh the key and

1186
00:50:03,200 --> 00:50:08,760
query uh together

1187
00:50:05,760 --> 00:50:08,760
here

1188
00:50:09,119 --> 00:50:13,559
um people have also experimented with

1189
00:50:11,760 --> 00:50:16,079
DOT product and the dot product is

1190
00:50:13,559 --> 00:50:19,839
basically query times

1191
00:50:16,079 --> 00:50:23,480
key uh query transpose times key or

1192
00:50:19,839 --> 00:50:25,760
query. key this is okay but the problem

1193
00:50:23,480 --> 00:50:27,280
with this is then the query vector and

1194
00:50:25,760 --> 00:50:30,160
the key vectors have to be in exactly

1195
00:50:27,280 --> 00:50:31,920
the same space and that's kind of too

1196
00:50:30,160 --> 00:50:34,799
hard of a constraint so it doesn't scale

1197
00:50:31,920 --> 00:50:38,000
very well if you're um if you're working

1198
00:50:34,799 --> 00:50:40,839
hard uh if you're uh like training on

1199
00:50:38,000 --> 00:50:45,400
lots of data um then the scaled dot

1200
00:50:40,839 --> 00:50:47,880
product um the scale dot product here uh

1201
00:50:45,400 --> 00:50:50,079
one problem is that the scale of the dot

1202
00:50:47,880 --> 00:50:53,680
product increases as the dimensions get

1203
00:50:50,079 --> 00:50:55,880
larger and so there's a fix to scale by

1204
00:50:53,680 --> 00:50:58,839
the square root of the length of one of

1205
00:50:55,880 --> 00:51:00,680
the vectors um and so basically you're

1206
00:50:58,839 --> 00:51:04,559
multiplying uh you're taking the dot

1207
00:51:00,680 --> 00:51:06,559
product but you're dividing by the uh

1208
00:51:04,559 --> 00:51:09,359
the square root of the length of one of

1209
00:51:06,559 --> 00:51:11,839
the vectors uh does anyone have an idea

1210
00:51:09,359 --> 00:51:13,599
why you might take the square root here

1211
00:51:11,839 --> 00:51:16,920
if you've taken a machine

1212
00:51:13,599 --> 00:51:20,000
learning uh or maybe statistics class

1213
00:51:16,920 --> 00:51:20,000
you might have a an

1214
00:51:20,599 --> 00:51:26,599
idea any any ideas yeah it normalization

1215
00:51:24,720 --> 00:51:29,079
to make sure

1216
00:51:26,599 --> 00:51:32,760
because otherwise it will impact the

1217
00:51:29,079 --> 00:51:35,640
result because we want normalize one yes

1218
00:51:32,760 --> 00:51:37,920
so we do we do want to normalize it um

1219
00:51:35,640 --> 00:51:40,000
and so that's the reason why we divide

1220
00:51:37,920 --> 00:51:41,920
by the length um and that prevents it

1221
00:51:40,000 --> 00:51:43,839
from getting too large

1222
00:51:41,920 --> 00:51:45,920
specifically does anyone have an idea

1223
00:51:43,839 --> 00:51:49,440
why you take the square root here as

1224
00:51:45,920 --> 00:51:49,440
opposed to dividing just by the length

1225
00:51:52,400 --> 00:51:59,480
overall so um this is this is pretty

1226
00:51:55,400 --> 00:52:01,720
tough and actually uh we I didn't know

1227
00:51:59,480 --> 00:52:04,359
one of the last times I did this class

1228
00:52:01,720 --> 00:52:06,640
uh and had to actually go look for it

1229
00:52:04,359 --> 00:52:09,000
but basically the reason why is because

1230
00:52:06,640 --> 00:52:11,400
if you um if you have a whole bunch of

1231
00:52:09,000 --> 00:52:12,720
random variables so let's say you have a

1232
00:52:11,400 --> 00:52:14,040
whole bunch of random variables no

1233
00:52:12,720 --> 00:52:15,240
matter what kind they are as long as

1234
00:52:14,040 --> 00:52:19,680
they're from the same distribution

1235
00:52:15,240 --> 00:52:19,680
they're IID and you add them all

1236
00:52:20,160 --> 00:52:25,720
together um then the variance I believe

1237
00:52:23,200 --> 00:52:27,760
yeah the variance of this variant

1238
00:52:25,720 --> 00:52:31,119
standard deviation maybe standard

1239
00:52:27,760 --> 00:52:33,319
deviation of this goes uh goes up uh

1240
00:52:31,119 --> 00:52:35,640
square root uh yeah I think standard

1241
00:52:33,319 --> 00:52:38,880
deviation goes

1242
00:52:35,640 --> 00:52:41,040
up dividing by something that would

1243
00:52:38,880 --> 00:52:44,040
divide by this the standard deviation

1244
00:52:41,040 --> 00:52:48,240
here so it's made like normalizing by

1245
00:52:44,040 --> 00:52:51,040
that so um it's a it's that's actually I

1246
00:52:48,240 --> 00:52:53,359
don't think explicitly explained and the

1247
00:52:51,040 --> 00:52:54,720
uh attention is all you need paper uh

1248
00:52:53,359 --> 00:52:57,920
the vasani paper where they introduce

1249
00:52:54,720 --> 00:53:01,079
this but that's basic idea um in terms

1250
00:52:57,920 --> 00:53:03,839
of what people use most widely nowadays

1251
00:53:01,079 --> 00:53:07,680
um they

1252
00:53:03,839 --> 00:53:07,680
are basically doing

1253
00:53:24,160 --> 00:53:27,160
this

1254
00:53:30,280 --> 00:53:34,880
so they're taking the the hidden state

1255
00:53:33,000 --> 00:53:36,599
from the keys and multiplying it by a

1256
00:53:34,880 --> 00:53:39,440
matrix the hidden state by the queries

1257
00:53:36,599 --> 00:53:41,680
and multiplying it by a matrix um this

1258
00:53:39,440 --> 00:53:46,559
is what is done in uh in

1259
00:53:41,680 --> 00:53:50,280
Transformers and the uh and then they're

1260
00:53:46,559 --> 00:53:54,160
using this to um they're normalizing it

1261
00:53:50,280 --> 00:53:57,160
by this uh square root here

1262
00:53:54,160 --> 00:53:57,160
and

1263
00:53:59,440 --> 00:54:05,040
so this is essentially a bilinear

1264
00:54:02,240 --> 00:54:07,680
model um it's a bilinear model that is

1265
00:54:05,040 --> 00:54:09,119
normalized uh they call it uh scale do

1266
00:54:07,680 --> 00:54:11,119
product detention but actually because

1267
00:54:09,119 --> 00:54:15,520
they have these weight matrices uh it's

1268
00:54:11,119 --> 00:54:18,839
a bilinear model so um that's the the

1269
00:54:15,520 --> 00:54:18,839
most standard thing to be used

1270
00:54:20,200 --> 00:54:24,079
nowadays cool any any questions about

1271
00:54:22,520 --> 00:54:27,079
this

1272
00:54:24,079 --> 00:54:27,079
part

1273
00:54:28,240 --> 00:54:36,559
okay so um finally when you actually

1274
00:54:32,280 --> 00:54:36,559
train the model um as I mentioned

1275
00:54:41,960 --> 00:54:45,680
before right at the very

1276
00:54:48,040 --> 00:54:52,400
beginning

1277
00:54:49,839 --> 00:54:55,760
we when we're training an autor

1278
00:54:52,400 --> 00:54:57,400
regressive model we don't want to be

1279
00:54:55,760 --> 00:54:59,799
referring to the Future to things in the

1280
00:54:57,400 --> 00:55:01,240
future um because then you know

1281
00:54:59,799 --> 00:55:03,079
basically we'd be cheating and we'd have

1282
00:55:01,240 --> 00:55:04,599
a nonprobabilistic model it wouldn't be

1283
00:55:03,079 --> 00:55:08,960
good when we actually have to generate

1284
00:55:04,599 --> 00:55:12,119
left to right um and

1285
00:55:08,960 --> 00:55:15,720
so we essentially want to prevent

1286
00:55:12,119 --> 00:55:17,480
ourselves from using information from

1287
00:55:15,720 --> 00:55:20,319
the

1288
00:55:17,480 --> 00:55:22,839
future

1289
00:55:20,319 --> 00:55:24,240
and in an unconditioned model we want to

1290
00:55:22,839 --> 00:55:27,400
prevent ourselves from using any

1291
00:55:24,240 --> 00:55:29,680
information in the feature here um in a

1292
00:55:27,400 --> 00:55:31,520
conditioned model we're okay with doing

1293
00:55:29,680 --> 00:55:33,480
kind of bir

1294
00:55:31,520 --> 00:55:35,880
directional conditioning here to

1295
00:55:33,480 --> 00:55:37,359
calculate the representations but we're

1296
00:55:35,880 --> 00:55:40,440
not okay with doing it on the target

1297
00:55:37,359 --> 00:55:40,440
side so basically what we

1298
00:55:44,240 --> 00:55:50,960
do basically what we do is we create a

1299
00:55:47,920 --> 00:55:52,400
mask that prevents us from attending to

1300
00:55:50,960 --> 00:55:54,559
any of the information in the future

1301
00:55:52,400 --> 00:55:56,440
when we're uh predicting when we're

1302
00:55:54,559 --> 00:56:00,799
calculating the representations of the

1303
00:55:56,440 --> 00:56:04,880
the current thing uh word and

1304
00:56:00,799 --> 00:56:08,280
technically how we do this is we have

1305
00:56:04,880 --> 00:56:08,280
the attention

1306
00:56:09,079 --> 00:56:13,799
values uh like

1307
00:56:11,680 --> 00:56:15,480
2.1

1308
00:56:13,799 --> 00:56:17,880
attention

1309
00:56:15,480 --> 00:56:19,920
0.3 and

1310
00:56:17,880 --> 00:56:22,480
attention uh

1311
00:56:19,920 --> 00:56:24,960
0.5 or something like

1312
00:56:22,480 --> 00:56:27,480
that these are eventually going to be

1313
00:56:24,960 --> 00:56:29,799
fed through the soft Max to calculate

1314
00:56:27,480 --> 00:56:32,119
the attention values that we use to do

1315
00:56:29,799 --> 00:56:33,680
the waiting so what we do is any ones we

1316
00:56:32,119 --> 00:56:36,160
don't want to attend to we just add

1317
00:56:33,680 --> 00:56:39,799
negative infinity or add a very large

1318
00:56:36,160 --> 00:56:42,119
negative number so we uh cross that out

1319
00:56:39,799 --> 00:56:44,000
and set this the negative infinity and

1320
00:56:42,119 --> 00:56:45,440
so then when we take the softb basically

1321
00:56:44,000 --> 00:56:47,839
the value goes to zero and we don't

1322
00:56:45,440 --> 00:56:49,359
attend to it so um this is called the

1323
00:56:47,839 --> 00:56:53,240
attention mask and you'll see it when

1324
00:56:49,359 --> 00:56:53,240
you have to implement

1325
00:56:53,440 --> 00:56:56,880
attention cool

1326
00:56:57,039 --> 00:57:00,200
any any questions about

1327
00:57:02,079 --> 00:57:08,599
this okay great um so next I'd like to

1328
00:57:05,839 --> 00:57:11,039
go to Applications of sequence models um

1329
00:57:08,599 --> 00:57:13,200
there's a bunch of ways that you can use

1330
00:57:11,039 --> 00:57:16,160
sequence models of any variety I wrote

1331
00:57:13,200 --> 00:57:18,400
RNN here arbitrarily but it could be

1332
00:57:16,160 --> 00:57:21,720
convolution or Transformer or anything

1333
00:57:18,400 --> 00:57:23,559
else so the first one is encoding

1334
00:57:21,720 --> 00:57:26,839
sequences

1335
00:57:23,559 --> 00:57:29,240
um and essentially if you do it with an

1336
00:57:26,839 --> 00:57:31,559
RNN this is one way you can encode a

1337
00:57:29,240 --> 00:57:35,799
sequence basically you take the

1338
00:57:31,559 --> 00:57:36,960
last uh value here and you use it to uh

1339
00:57:35,799 --> 00:57:40,559
encode the

1340
00:57:36,960 --> 00:57:42,720
output this can be used for any sort of

1341
00:57:40,559 --> 00:57:45,839
uh like binary or multiclass prediction

1342
00:57:42,720 --> 00:57:48,280
problem it's also right now used very

1343
00:57:45,839 --> 00:57:50,920
widely in sentence representations for

1344
00:57:48,280 --> 00:57:54,200
retrieval uh so for example you build a

1345
00:57:50,920 --> 00:57:55,520
big retrieval index uh with these

1346
00:57:54,200 --> 00:57:57,920
vectors

1347
00:57:55,520 --> 00:57:59,480
and then you do a vector near you also

1348
00:57:57,920 --> 00:58:02,119
in quote a query and you do a vector

1349
00:57:59,480 --> 00:58:04,760
nearest neighbor search to look up uh

1350
00:58:02,119 --> 00:58:06,760
the most similar sentence here so this

1351
00:58:04,760 --> 00:58:10,160
is uh these are two applications where

1352
00:58:06,760 --> 00:58:13,440
you use something like this right on

1353
00:58:10,160 --> 00:58:15,520
this slide I wrote that you use the last

1354
00:58:13,440 --> 00:58:17,359
Vector here but actually a lot of the

1355
00:58:15,520 --> 00:58:20,039
time it's also a good idea to just take

1356
00:58:17,359 --> 00:58:22,599
the mean of the vectors or take the max

1357
00:58:20,039 --> 00:58:26,640
of all of the vectors

1358
00:58:22,599 --> 00:58:29,119
uh in fact I would almost I would almost

1359
00:58:26,640 --> 00:58:30,520
say that that's usually a better choice

1360
00:58:29,119 --> 00:58:32,760
if you're doing any sort of thing where

1361
00:58:30,520 --> 00:58:35,359
you need a single Vector unless your

1362
00:58:32,760 --> 00:58:38,200
model has been specifically trained to

1363
00:58:35,359 --> 00:58:41,480
have good like output vectors uh from

1364
00:58:38,200 --> 00:58:44,359
the final Vector here so um you could

1365
00:58:41,480 --> 00:58:46,880
also just take the the mean of all of

1366
00:58:44,359 --> 00:58:46,880
the purple

1367
00:58:48,240 --> 00:58:52,960
ones um another thing you can do is

1368
00:58:50,280 --> 00:58:54,359
encode tokens for sequence labeling Um

1369
00:58:52,960 --> 00:58:56,200
this can also be used for language

1370
00:58:54,359 --> 00:58:58,280
modeling and what do I mean it can be

1371
00:58:56,200 --> 00:59:00,039
used for language

1372
00:58:58,280 --> 00:59:03,319
modeling

1373
00:59:00,039 --> 00:59:06,599
basically you can view this as first

1374
00:59:03,319 --> 00:59:09,200
running along sequence encoding and then

1375
00:59:06,599 --> 00:59:12,319
after that making all of the predictions

1376
00:59:09,200 --> 00:59:15,240
um it's also a good thing to know

1377
00:59:12,319 --> 00:59:18,440
computationally because um often you can

1378
00:59:15,240 --> 00:59:20,720
do sequence encoding uh kind of all in

1379
00:59:18,440 --> 00:59:22,440
parallel and yeah actually I said I was

1380
00:59:20,720 --> 00:59:23,359
going to mention I said I was going to

1381
00:59:22,440 --> 00:59:25,079
mention that but I don't think I

1382
00:59:23,359 --> 00:59:27,319
actually have a slide about it but um

1383
00:59:25,079 --> 00:59:29,720
one important thing about rnn's compared

1384
00:59:27,319 --> 00:59:33,079
to convolution or Transformers uh sorry

1385
00:59:29,720 --> 00:59:34,839
convolution or attention is rnns in

1386
00:59:33,079 --> 00:59:37,440
order to calculate this RNN you need to

1387
00:59:34,839 --> 00:59:39,599
wait for this RNN to finish so it's

1388
00:59:37,440 --> 00:59:41,200
sequential and you need to go like here

1389
00:59:39,599 --> 00:59:43,480
and then here and then here and then

1390
00:59:41,200 --> 00:59:45,720
here and then here and that's a pretty

1391
00:59:43,480 --> 00:59:48,200
big bottleneck because uh things like

1392
00:59:45,720 --> 00:59:50,760
gpus or tpus they're actually really

1393
00:59:48,200 --> 00:59:52,839
good at doing a bunch of things at once

1394
00:59:50,760 --> 00:59:56,440
and so attention even though its ASM

1395
00:59:52,839 --> 00:59:57,400
totic complexity is worse o of n squ uh

1396
00:59:56,440 --> 00:59:59,319
just because you don't have that

1397
00:59:57,400 --> 01:00:01,680
bottleneck of doing things sequentially

1398
00:59:59,319 --> 01:00:03,640
it can be way way faster on a GPU

1399
01:00:01,680 --> 01:00:04,960
because you're not wasting your time

1400
01:00:03,640 --> 01:00:07,640
waiting for the previous thing to be

1401
01:00:04,960 --> 01:00:11,039
calculated so that's actually why uh

1402
01:00:07,640 --> 01:00:13,520
Transformers are so fast

1403
01:00:11,039 --> 01:00:14,599
um uh Transformers and attention models

1404
01:00:13,520 --> 01:00:17,160
are so

1405
01:00:14,599 --> 01:00:21,119
fast

1406
01:00:17,160 --> 01:00:23,079
um another thing to note so that's one

1407
01:00:21,119 --> 01:00:25,039
of the big reasons why attention models

1408
01:00:23,079 --> 01:00:27,359
are so popular nowadays because fast to

1409
01:00:25,039 --> 01:00:30,200
calculate on Modern Hardware another

1410
01:00:27,359 --> 01:00:33,520
reason why attention models are popular

1411
01:00:30,200 --> 01:00:34,799
nowadays does anyone have a um does

1412
01:00:33,520 --> 01:00:37,280
anyone have an

1413
01:00:34,799 --> 01:00:38,839
idea uh about another reason it's based

1414
01:00:37,280 --> 01:00:41,200
on how easy they are to learn and

1415
01:00:38,839 --> 01:00:43,680
there's a reason why and that reason why

1416
01:00:41,200 --> 01:00:46,240
has to do with

1417
01:00:43,680 --> 01:00:48,520
um that reason why has to do with uh

1418
01:00:46,240 --> 01:00:49,400
something I introduced in this lecture

1419
01:00:48,520 --> 01:00:52,039
uh

1420
01:00:49,400 --> 01:00:54,720
earlier I'll give a

1421
01:00:52,039 --> 01:00:58,079
hint gradients yeah more more

1422
01:00:54,720 --> 01:01:00,480
specifically what what's nice about

1423
01:00:58,079 --> 01:01:02,920
attention with respect to gradients or

1424
01:01:00,480 --> 01:01:02,920
Vanishing

1425
01:01:04,119 --> 01:01:07,319
gradients any

1426
01:01:07,680 --> 01:01:15,160
ideas let's say we have a really long

1427
01:01:10,160 --> 01:01:17,839
sentence it's like X1 X2 X3

1428
01:01:15,160 --> 01:01:21,799
X4 um

1429
01:01:17,839 --> 01:01:26,440
X200 over here and in order to predict

1430
01:01:21,799 --> 01:01:26,440
X200 you need to pay attention to X3

1431
01:01:27,359 --> 01:01:29,640
any

1432
01:01:33,079 --> 01:01:37,359
ideas another another hint how many

1433
01:01:35,599 --> 01:01:38,960
nonlinearities do you have to pass

1434
01:01:37,359 --> 01:01:41,440
through in order to pass that

1435
01:01:38,960 --> 01:01:44,839
information from X3 to

1436
01:01:41,440 --> 01:01:48,839
X200 in a recurrent Network um in a

1437
01:01:44,839 --> 01:01:48,839
recurrent Network or

1438
01:01:51,920 --> 01:01:57,160
attention netw should be

1439
01:01:54,960 --> 01:02:00,680
197 yeah in a recurrent Network it's

1440
01:01:57,160 --> 01:02:03,480
basically 197 or may maybe 196 I haven't

1441
01:02:00,680 --> 01:02:06,319
paid attention but every time every time

1442
01:02:03,480 --> 01:02:08,319
you pass it to the hidden

1443
01:02:06,319 --> 01:02:10,200
state it has to go through a

1444
01:02:08,319 --> 01:02:13,240
nonlinearity so it goes through like

1445
01:02:10,200 --> 01:02:17,119
1907 nonlinearities and even if you're

1446
01:02:13,240 --> 01:02:19,680
using an lstm um it's still the lstm

1447
01:02:17,119 --> 01:02:21,559
hidden cell is getting information added

1448
01:02:19,680 --> 01:02:23,400
to it and subtracted to it and other

1449
01:02:21,559 --> 01:02:24,960
things like that so it's still a bit

1450
01:02:23,400 --> 01:02:27,880
tricky

1451
01:02:24,960 --> 01:02:27,880
um what about

1452
01:02:28,119 --> 01:02:35,160
attention yeah basically one time so

1453
01:02:31,520 --> 01:02:39,319
attention um in the next layer here

1454
01:02:35,160 --> 01:02:41,119
you're passing it all the way you're

1455
01:02:39,319 --> 01:02:45,000
passing all of the information directly

1456
01:02:41,119 --> 01:02:46,480
in and the only qualifying thing is that

1457
01:02:45,000 --> 01:02:47,760
your weight has to be good it has to

1458
01:02:46,480 --> 01:02:49,079
find a good attention weight so that

1459
01:02:47,760 --> 01:02:50,920
it's actually paying attention to that

1460
01:02:49,079 --> 01:02:53,039
information so this is actually

1461
01:02:50,920 --> 01:02:54,400
discussed in the vaswani at all

1462
01:02:53,039 --> 01:02:57,359
attention is all you need paper that

1463
01:02:54,400 --> 01:02:59,920
introduced Transformers um convolutions

1464
01:02:57,359 --> 01:03:03,640
are kind of in the middle so like let's

1465
01:02:59,920 --> 01:03:06,400
say you have a convolution of length 10

1466
01:03:03,640 --> 01:03:09,880
um and then you have two layers of it um

1467
01:03:06,400 --> 01:03:09,880
if you have a convolution of length

1468
01:03:10,200 --> 01:03:15,880
10 or yeah let's say you have a

1469
01:03:12,559 --> 01:03:18,520
convolution of length 10 you would need

1470
01:03:15,880 --> 01:03:19,520
basically you would pass from 10

1471
01:03:18,520 --> 01:03:21,720
previous

1472
01:03:19,520 --> 01:03:23,319
ones and then you would pass again from

1473
01:03:21,720 --> 01:03:27,359
10 previous ones and then you would have

1474
01:03:23,319 --> 01:03:29,160
to go through like 16 or like I guess

1475
01:03:27,359 --> 01:03:31,279
almost 20 layers of convolution in order

1476
01:03:29,160 --> 01:03:34,720
to pass that information along so it's

1477
01:03:31,279 --> 01:03:39,200
kind of in the middle of RNs in uh in

1478
01:03:34,720 --> 01:03:43,480
lsms uh sorry RNN in attention

1479
01:03:39,200 --> 01:03:47,359
Ms Yeah question so regarding how you

1480
01:03:43,480 --> 01:03:51,319
have to wait for one r& the next one can

1481
01:03:47,359 --> 01:03:53,000
you inflence on one RNN once it's done

1482
01:03:51,319 --> 01:03:54,839
even though the next one's competing off

1483
01:03:53,000 --> 01:03:58,400
that one

1484
01:03:54,839 --> 01:04:01,160
yes yeah you can you can do

1485
01:03:58,400 --> 01:04:03,880
inference you could is well so as long

1486
01:04:01,160 --> 01:04:03,880
as

1487
01:04:05,599 --> 01:04:10,640
the as long as the output doesn't affect

1488
01:04:08,079 --> 01:04:14,000
the next input so in this

1489
01:04:10,640 --> 01:04:17,119
case in this case because of language

1490
01:04:14,000 --> 01:04:19,400
modeling or generation is because the

1491
01:04:17,119 --> 01:04:21,000
output doesn't affect the ne uh because

1492
01:04:19,400 --> 01:04:22,440
the output affects the next input if

1493
01:04:21,000 --> 01:04:26,680
you're predicting the output you have to

1494
01:04:22,440 --> 01:04:28,920
weigh if you know the output already um

1495
01:04:26,680 --> 01:04:30,599
if you know the output already you could

1496
01:04:28,920 --> 01:04:33,599
make the prediction at the same time

1497
01:04:30,599 --> 01:04:34,799
miscalculating this next hidden State um

1498
01:04:33,599 --> 01:04:36,200
so if you're just calculating the

1499
01:04:34,799 --> 01:04:38,559
probability you could do that and that's

1500
01:04:36,200 --> 01:04:40,880
actually where Transformers or attention

1501
01:04:38,559 --> 01:04:44,839
models shine attention models actually

1502
01:04:40,880 --> 01:04:46,000
aren't great for Generation Um and the

1503
01:04:44,839 --> 01:04:49,279
reason why they're not great for

1504
01:04:46,000 --> 01:04:52,279
generation is because they're

1505
01:04:49,279 --> 01:04:52,279
um

1506
01:04:52,799 --> 01:04:57,680
like when you're you're generating the

1507
01:04:55,039 --> 01:04:59,200
next token you still need to wait you

1508
01:04:57,680 --> 01:05:00,559
can't calculate in parallel because you

1509
01:04:59,200 --> 01:05:03,039
need to generate the next token before

1510
01:05:00,559 --> 01:05:04,839
you can encode the next uh the previous

1511
01:05:03,039 --> 01:05:07,119
sorry need to generate the next token

1512
01:05:04,839 --> 01:05:08,680
before you can encode it so you can't do

1513
01:05:07,119 --> 01:05:10,359
everything in parallel so Transformers

1514
01:05:08,680 --> 01:05:15,039
for generation are actually

1515
01:05:10,359 --> 01:05:16,559
slow and um there are models uh I don't

1516
01:05:15,039 --> 01:05:18,520
know if people are using them super

1517
01:05:16,559 --> 01:05:22,200
widely now but there were actually

1518
01:05:18,520 --> 01:05:23,640
transform uh language model sorry

1519
01:05:22,200 --> 01:05:26,319
machine translation model set we in

1520
01:05:23,640 --> 01:05:28,279
production they had a really big strong

1521
01:05:26,319 --> 01:05:34,359
Transformer encoder and then they had a

1522
01:05:28,279 --> 01:05:34,359
tiny fast RNN decoder um

1523
01:05:35,440 --> 01:05:40,960
and and if you want a actual

1524
01:05:52,000 --> 01:05:59,440
reference there's there's

1525
01:05:55,079 --> 01:05:59,440
this deep encoder shellow

1526
01:05:59,559 --> 01:06:05,520
decoder um and then there's also the the

1527
01:06:03,079 --> 01:06:07,599
Maran machine translation toolkit that

1528
01:06:05,520 --> 01:06:11,119
supports uh supports those types of

1529
01:06:07,599 --> 01:06:13,839
things as well so um it's also the

1530
01:06:11,119 --> 01:06:16,200
reason why uh if you're using if you're

1531
01:06:13,839 --> 01:06:18,839
using uh like the GPT models through the

1532
01:06:16,200 --> 01:06:21,680
API that decoding is more expensive

1533
01:06:18,839 --> 01:06:21,680
right like

1534
01:06:22,119 --> 01:06:27,960
encoding I forget exactly is it 0.03

1535
01:06:26,279 --> 01:06:30,839
cents for 1,000 tokens for encoding and

1536
01:06:27,960 --> 01:06:33,039
0.06 cents for 1,000 tokens for decoding

1537
01:06:30,839 --> 01:06:34,799
in like gp4 or something like this the

1538
01:06:33,039 --> 01:06:36,839
reason why is precisely that just

1539
01:06:34,799 --> 01:06:37,760
because it's so much more expensive to

1540
01:06:36,839 --> 01:06:41,599
to run the

1541
01:06:37,760 --> 01:06:45,160
decoder um cool I have a few final

1542
01:06:41,599 --> 01:06:47,039
things also about efficiency so um these

1543
01:06:45,160 --> 01:06:50,720
go back to the efficiency things that I

1544
01:06:47,039 --> 01:06:52,279
talked about last time um handling mini

1545
01:06:50,720 --> 01:06:54,440
batching so what do we have to do when

1546
01:06:52,279 --> 01:06:56,359
we're handling mini batching if we were

1547
01:06:54,440 --> 01:06:59,440
handling mini batching in feed forward

1548
01:06:56,359 --> 01:07:02,880
networks it's actually relatively easy

1549
01:06:59,440 --> 01:07:04,880
um because we all of our computations

1550
01:07:02,880 --> 01:07:06,400
are the same shape so we just

1551
01:07:04,880 --> 01:07:09,359
concatenate them all together into a big

1552
01:07:06,400 --> 01:07:11,000
tensor and run uh run over it uh we saw

1553
01:07:09,359 --> 01:07:12,599
mini batching makes things much faster

1554
01:07:11,000 --> 01:07:15,160
but mini batching and sequence modeling

1555
01:07:12,599 --> 01:07:17,240
is harder than in feed forward networks

1556
01:07:15,160 --> 01:07:20,240
um one reason is in rnns each word

1557
01:07:17,240 --> 01:07:22,680
depends on the previous word um also

1558
01:07:20,240 --> 01:07:26,359
because sequences are of various

1559
01:07:22,680 --> 01:07:30,279
lengths so so what we do to handle this

1560
01:07:26,359 --> 01:07:33,480
is uh we do padding and masking uh

1561
01:07:30,279 --> 01:07:35,680
so we can do padding like this uh so we

1562
01:07:33,480 --> 01:07:37,279
just add an extra token at the end to

1563
01:07:35,680 --> 01:07:40,440
make all of the sequences at the same

1564
01:07:37,279 --> 01:07:44,480
length um if we are doing an encoder

1565
01:07:40,440 --> 01:07:47,160
decoder style model uh where we have an

1566
01:07:44,480 --> 01:07:48,440
input and then we want to generate all

1567
01:07:47,160 --> 01:07:50,640
the outputs based on the input one of

1568
01:07:48,440 --> 01:07:54,920
the easy things is to add pads to the

1569
01:07:50,640 --> 01:07:56,520
beginning um and then so yeah it doesn't

1570
01:07:54,920 --> 01:07:58,000
really matter but you can add pads to

1571
01:07:56,520 --> 01:07:59,440
the beginning so they're all starting at

1572
01:07:58,000 --> 01:08:03,079
the same place especially if you're

1573
01:07:59,440 --> 01:08:05,799
using RNN style models um then we

1574
01:08:03,079 --> 01:08:08,920
calculate the loss over the output for

1575
01:08:05,799 --> 01:08:11,000
example we multiply the loss by a mask

1576
01:08:08,920 --> 01:08:13,480
to remove the loss over the tokens that

1577
01:08:11,000 --> 01:08:16,880
we don't care about and we take the sum

1578
01:08:13,480 --> 01:08:19,120
of these and so luckily most of this is

1579
01:08:16,880 --> 01:08:20,719
implemented in for example ptch or

1580
01:08:19,120 --> 01:08:22,279
huging face Transformers already so you

1581
01:08:20,719 --> 01:08:23,560
don't need to worry about it but it is a

1582
01:08:22,279 --> 01:08:24,799
good idea to know what's going on under

1583
01:08:23,560 --> 01:08:28,560
the hood if you want to implement

1584
01:08:24,799 --> 01:08:32,440
anything unusual and also um it's good

1585
01:08:28,560 --> 01:08:35,600
to know for the following reason also

1586
01:08:32,440 --> 01:08:38,799
which is bucketing and

1587
01:08:35,600 --> 01:08:40,319
sorting so if we use sentences of vastly

1588
01:08:38,799 --> 01:08:43,359
different lengths and we put them in the

1589
01:08:40,319 --> 01:08:46,640
same mini batch this can uh waste a

1590
01:08:43,359 --> 01:08:48,000
really large amount of computation so

1591
01:08:46,640 --> 01:08:50,759
like let's say we're processing

1592
01:08:48,000 --> 01:08:52,480
documents or movie reviews or something

1593
01:08:50,759 --> 01:08:54,799
like that and you have a most movie

1594
01:08:52,480 --> 01:08:57,719
reviews are like

1595
01:08:54,799 --> 01:09:00,080
10 words long but you have one movie

1596
01:08:57,719 --> 01:09:02,319
review in your mini batch of uh a

1597
01:09:00,080 --> 01:09:04,359
thousand words so basically what that

1598
01:09:02,319 --> 01:09:08,279
means is you're padding most of your

1599
01:09:04,359 --> 01:09:11,120
sequences 990 times to process 10

1600
01:09:08,279 --> 01:09:12,120
sequences which is like a lot of waste

1601
01:09:11,120 --> 01:09:14,000
right because you're running them all

1602
01:09:12,120 --> 01:09:16,799
through your GPU and other things like

1603
01:09:14,000 --> 01:09:19,080
that so one way to remedy this is to

1604
01:09:16,799 --> 01:09:22,719
sort sentences so similarly length

1605
01:09:19,080 --> 01:09:27,480
sentences are in the same batch so you

1606
01:09:22,719 --> 01:09:29,920
uh you first sort before building all of

1607
01:09:27,480 --> 01:09:31,640
your batches and then uh that makes it

1608
01:09:29,920 --> 01:09:32,960
so that similarly sized ones are the

1609
01:09:31,640 --> 01:09:35,239
same

1610
01:09:32,960 --> 01:09:37,040
batch this goes into the problem that I

1611
01:09:35,239 --> 01:09:39,359
mentioned before but only in passing

1612
01:09:37,040 --> 01:09:42,440
which is uh let's say you're calculating

1613
01:09:39,359 --> 01:09:44,199
your batch based on the number of

1614
01:09:42,440 --> 01:09:47,679
sequences that you're

1615
01:09:44,199 --> 01:09:51,400
processing if you say Okay I want 64

1616
01:09:47,679 --> 01:09:53,359
sequences in my mini batch um if most of

1617
01:09:51,400 --> 01:09:55,159
the time those 64 sequences are are 10

1618
01:09:53,359 --> 01:09:57,480
tokens that's fine but then when you get

1619
01:09:55,159 --> 01:10:01,440
the One Mini batch that has a thousand

1620
01:09:57,480 --> 01:10:02,760
tokens in each sentence or each sequence

1621
01:10:01,440 --> 01:10:04,920
um suddenly you're going to run out of

1622
01:10:02,760 --> 01:10:07,800
GPU memory and you're like training is

1623
01:10:04,920 --> 01:10:08,920
going to crash right which is you really

1624
01:10:07,800 --> 01:10:10,440
don't want that to happen when you

1625
01:10:08,920 --> 01:10:12,440
started running your homework assignment

1626
01:10:10,440 --> 01:10:15,560
and then went to bed and then wake up

1627
01:10:12,440 --> 01:10:18,440
and it crashed you know uh 15 minutes

1628
01:10:15,560 --> 01:10:21,040
into Computing or something so uh this

1629
01:10:18,440 --> 01:10:23,440
is an important thing to be aware of

1630
01:10:21,040 --> 01:10:26,760
practically uh again this can be solved

1631
01:10:23,440 --> 01:10:29,239
by a lot of toolkits like I know fer uh

1632
01:10:26,760 --> 01:10:30,840
does it and hugging face does it if you

1633
01:10:29,239 --> 01:10:33,159
set the appropriate settings but it's

1634
01:10:30,840 --> 01:10:36,239
something you should be aware of um

1635
01:10:33,159 --> 01:10:37,880
another note is that if you do this it's

1636
01:10:36,239 --> 01:10:41,280
reducing the randomness in your

1637
01:10:37,880 --> 01:10:42,880
distribution of data so um stochastic

1638
01:10:41,280 --> 01:10:44,520
gradient descent is really heavily

1639
01:10:42,880 --> 01:10:47,480
reliant on the fact that your ordering

1640
01:10:44,520 --> 01:10:49,440
of data is randomized or at least it's a

1641
01:10:47,480 --> 01:10:52,159
distributed appropriately so it's

1642
01:10:49,440 --> 01:10:56,840
something to definitely be aware of um

1643
01:10:52,159 --> 01:10:59,560
so uh this is a good thing to to think

1644
01:10:56,840 --> 01:11:01,400
about another really useful thing to

1645
01:10:59,560 --> 01:11:03,800
think about is strided

1646
01:11:01,400 --> 01:11:05,440
architectures um strided architectures

1647
01:11:03,800 --> 01:11:07,520
appear in rnns they appear in

1648
01:11:05,440 --> 01:11:10,080
convolution they appear in trans

1649
01:11:07,520 --> 01:11:12,320
Transformers or attention based models

1650
01:11:10,080 --> 01:11:15,199
um they're called different things in

1651
01:11:12,320 --> 01:11:18,159
each of them so in rnns they're called

1652
01:11:15,199 --> 01:11:21,280
pyramidal rnns in convolution they're

1653
01:11:18,159 --> 01:11:22,400
called strided architectures and in

1654
01:11:21,280 --> 01:11:25,080
attention they're called sparse

1655
01:11:22,400 --> 01:11:27,440
attention usually they all actually kind

1656
01:11:25,080 --> 01:11:30,800
of mean the same thing um and basically

1657
01:11:27,440 --> 01:11:33,440
what they mean is you don't you have a

1658
01:11:30,800 --> 01:11:37,040
multi-layer model and when you have a

1659
01:11:33,440 --> 01:11:40,920
multi-layer model you don't process

1660
01:11:37,040 --> 01:11:43,920
every input uh from the uh from the

1661
01:11:40,920 --> 01:11:45,560
previous layer so here's an example um

1662
01:11:43,920 --> 01:11:47,840
like let's say you have a whole bunch of

1663
01:11:45,560 --> 01:11:50,199
inputs um each of the inputs is

1664
01:11:47,840 --> 01:11:53,159
processed in the first layer in some way

1665
01:11:50,199 --> 01:11:56,639
but in the second layer you actually

1666
01:11:53,159 --> 01:12:01,520
input for example uh two inputs to the

1667
01:11:56,639 --> 01:12:03,560
RNN but you you skip so you have one

1668
01:12:01,520 --> 01:12:05,440
state that corresponds to state number

1669
01:12:03,560 --> 01:12:06,840
one and two another state that

1670
01:12:05,440 --> 01:12:08,440
corresponds to state number two and

1671
01:12:06,840 --> 01:12:10,920
three another state that corresponds to

1672
01:12:08,440 --> 01:12:13,280
state number three and four so what that

1673
01:12:10,920 --> 01:12:15,199
means is you can gradually decrease the

1674
01:12:13,280 --> 01:12:18,199
number like the length of the sequence

1675
01:12:15,199 --> 01:12:20,719
every time you process so uh this is a

1676
01:12:18,199 --> 01:12:22,360
really useful thing that to do if you're

1677
01:12:20,719 --> 01:12:25,480
processing very long sequences so you

1678
01:12:22,360 --> 01:12:25,480
should be aware of it

1679
01:12:27,440 --> 01:12:34,120
cool um everything

1680
01:12:30,639 --> 01:12:36,920
okay okay the final thing is truncated

1681
01:12:34,120 --> 01:12:39,239
back propagation through time and uh

1682
01:12:36,920 --> 01:12:41,000
truncated back propagation Through Time

1683
01:12:39,239 --> 01:12:43,560
what this is doing is basically you do

1684
01:12:41,000 --> 01:12:46,120
back propop over shorter segments but

1685
01:12:43,560 --> 01:12:47,840
you initialize with the state from the

1686
01:12:46,120 --> 01:12:51,040
previous

1687
01:12:47,840 --> 01:12:52,440
segment and the way this works is uh

1688
01:12:51,040 --> 01:12:56,080
like for example if you're running an

1689
01:12:52,440 --> 01:12:57,600
RNN uh you would run the RNN over the

1690
01:12:56,080 --> 01:12:59,400
previous segment maybe it's length four

1691
01:12:57,600 --> 01:13:02,120
maybe it's length 400 it doesn't really

1692
01:12:59,400 --> 01:13:04,520
matter but it's uh coherently length

1693
01:13:02,120 --> 01:13:06,360
segment and then when you do the next

1694
01:13:04,520 --> 01:13:08,840
segment what you do is you only pass the

1695
01:13:06,360 --> 01:13:12,960
hidden state but you throw away the rest

1696
01:13:08,840 --> 01:13:16,360
of the previous computation graph and

1697
01:13:12,960 --> 01:13:18,040
then walk through uh like this uh so you

1698
01:13:16,360 --> 01:13:22,159
won't actually be updating the

1699
01:13:18,040 --> 01:13:24,080
parameters of this based on the result

1700
01:13:22,159 --> 01:13:25,800
the lost from this but you're still

1701
01:13:24,080 --> 01:13:28,159
passing the information so this can use

1702
01:13:25,800 --> 01:13:30,400
the information for the previous state

1703
01:13:28,159 --> 01:13:32,239
so this is an example from RNN this is

1704
01:13:30,400 --> 01:13:35,159
used pretty widely in RNN but there's

1705
01:13:32,239 --> 01:13:38,000
also a lot of Transformer architectures

1706
01:13:35,159 --> 01:13:39,400
that do things like this um the original

1707
01:13:38,000 --> 01:13:41,000
one is something called Transformer

1708
01:13:39,400 --> 01:13:44,560
Excel that was actually created here at

1709
01:13:41,000 --> 01:13:46,560
CMU but this is also um used in the new

1710
01:13:44,560 --> 01:13:48,719
mistol models and other things like this

1711
01:13:46,560 --> 01:13:51,719
as well so um it's something that's

1712
01:13:48,719 --> 01:13:54,719
still very much alive and well nowadays

1713
01:13:51,719 --> 01:13:56,320
as well

1714
01:13:54,719 --> 01:13:57,840
cool um that's all I have for today are

1715
01:13:56,320 --> 01:13:59,760
there any questions people want to ask

1716
01:13:57,840 --> 01:14:02,760
before we wrap

1717
01:13:59,760 --> 01:14:02,760
up

1718
01:14:12,840 --> 01:14:20,000
yeah doesent yeah so for condition

1719
01:14:16,960 --> 01:14:25,040
prediction what is Source X and Target y

1720
01:14:20,000 --> 01:14:26,520
um I think I kind of maybe carried over

1721
01:14:25,040 --> 01:14:28,679
uh some terminology from machine

1722
01:14:26,520 --> 01:14:31,400
translation uh by accident maybe it

1723
01:14:28,679 --> 01:14:34,080
should be input X and output y uh that

1724
01:14:31,400 --> 01:14:36,600
would be a better way to put it and so

1725
01:14:34,080 --> 01:14:38,080
uh it could be anything for translation

1726
01:14:36,600 --> 01:14:39,560
it's like something in the source

1727
01:14:38,080 --> 01:14:42,600
language and something in the target

1728
01:14:39,560 --> 01:14:44,520
language so like English and Japanese um

1729
01:14:42,600 --> 01:14:47,280
if it's just a regular language model it

1730
01:14:44,520 --> 01:14:50,560
could be something like a prompt and the

1731
01:14:47,280 --> 01:14:55,280
output so for

1732
01:14:50,560 --> 01:14:55,280
UNC y example that

1733
01:14:57,400 --> 01:15:01,400
yeah so for unconditioned prediction

1734
01:14:59,760 --> 01:15:03,840
that could just be straight up language

1735
01:15:01,400 --> 01:15:07,040
modeling for example so um language

1736
01:15:03,840 --> 01:15:11,840
modeling with no not necessarily any

1737
01:15:07,040 --> 01:15:11,840
problems okay thanks and anything

1738
01:15:12,440 --> 01:15:17,880
else okay great thanks a lot I'm happy

1739
01:15:14,639 --> 01:15:17,880
to take questions

1740
01:15:18,639 --> 01:15:21,639
to