CMU Advanced NLP 2024 (3) Language Modeling/transcript.vtt

WEBVTT

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so this time I'm going to be talking

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about language modeling uh obviously

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language modeling is a big topic and I'm

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not going to be able to cover it all in

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one class but this is kind of the basics

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of uh what does it mean to build a

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language model what is a language model

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how do we evaluate language models and

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other stuff like that and around the end

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I'm going to talk a little bit about

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efficiently implementing things in

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neural networks it's not directly

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related to language models but it's very

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important to know how to do uh to solve

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your assignments so I'll cover both

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is

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cool okay so the first thing I'd like to

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talk about is generative versus

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discriminative models and the reason why

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is up until now we've been talking about

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discriminative models and these are

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models uh that are mainly designed to

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calculate the probability of a latent

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trait uh given the data and so this is

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uh P of Y given X where Y is the lat and

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trait we want to calculate and X is uh

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the input data that we're calculating it

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over so just review from last class what

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was X from last class from the example

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in L

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class

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anybody yeah some text yeah and then

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what was

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why it shouldn't be too

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hard yeah it was a category or a

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sentiment label precisely in the

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sentiment analysis tasks so so um a

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generative model on the other hand is a

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model that calculates the probability of

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data itself and is not specifically

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conditional and there's a couple of

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varieties um this isn't like super

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standard terminology I just uh wrote it

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myself but here we have a standalone

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probability of P of X and we can also

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calculate the joint probability P of X

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and Y

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so probabilistic language models

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basically what they do is they calculate

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this uh probability usually uh we think

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of it as a standalone probability of P

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of X where X is something like a

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sentence or a

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document and it's a generative model

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that calculates the probability of

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language recently the definition of

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language model has expanded a little bit

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so now

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um people also call things that

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calculate the probability of text and

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images as like multimodal language

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models or uh what are some of the other

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ones yeah I think that's the main the

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main exception to this rule usually

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usually it's calculating either of text

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or over text in some multimodal data but

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for now we're going to

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consider

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um then there's kind of two fundamental

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operations that we perform with LMS

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almost everything else we do with LMS

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can be considered like one of these two

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types of things the first thing is calc

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scoring sentences or calculating the

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probability of

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sentences and this

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is uh for example if we calculate the

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probability of Jane went to the store uh

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this would have a high probability

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ideally um and if we have this kind of

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word salid like this this would be given

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a low probability uh according to a

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English language model if we had a

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Chinese language model ideally it would

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also probably give low probability first

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sentence too because it's a language

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model of natural Chinese and not of

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natural English so there's also

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different types of language models

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depending on the type of data you play

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in

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the another thing I can do is generate

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sentences and we'll talk more about the

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different methods for generating

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sentences but typically they fall into

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one of two categories one is sampling

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like this where you try to sample a

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sentence from the probability

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distribution of the language model

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possibly with some modifications to the

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probability

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distribution um the other thing which I

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didn't write on the slide is uh finding

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the highest scoring sentence according

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to the language model um and we do both

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of those

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S so more concretely how can we apply

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these these can be applied to answer

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questions so for example um if we have a

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multiple choice question we can score

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possible multiple choice answers and uh

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the way we do this is we calculate

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we first

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take uh like we have

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like

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um

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where is

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CMU

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located um

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that's and actually maybe promete this

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all again to an a here and then we say X

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X1 is equal to

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this and then we have X2 which is

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Q

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where is

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CMU

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located

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a um what's something

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plausible

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uh what was

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it okay now now you're going to make it

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tricky and make me talk about when we

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have multiple right answers and how we

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evaluate and stuff let let's ignore that

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for now it's say New

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York it's not located in New York is

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it

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okay let's say

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Birmingham hopefully there's no CMU

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affiliate in Birmingham I think we're

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we're pretty so um and then you would

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just calculate the probability of X1 and

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the probability of X2 X3 X4 Etc and um

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then pick the highest saring one and

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actually um there's a famous

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there's a famous uh leaderboard for

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language models that probably a lot of

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people know about it's called the open

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llm

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leaderboard and a lot of these tasks

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here basically correspond to doing

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something like that like hel swag is

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kind of a multiple choice uh is a

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multiple choice question answering thing

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about common sense where they calculate

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it by scoring uh scoring the

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outputs so that's a very common way to

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use language

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models um another thing is generating a

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continuation of a question prompt so

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basically this is when you uh

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sample and so what you would do is you

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would prompt the

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model with this uh X here and then you

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would ask it to generate either the most

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likely uh completion or generate um

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sample multiple completions to get the

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answer so this is very common uh people

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are very familiar with this there's lots

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of other uh things you can do though so

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um you can classify text and there's a

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couple ways you can do this uh one way

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you can do this is um like let's say we

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have a sentiment sentence

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here

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um you can say uh

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this is

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gr and then you can say um

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star

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rating five or something like that and

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then you could also have star rating

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four star rating three star rating two

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star rating one and calculate the

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probability of all of these and find

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which one has the highest probability so

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this is a a common way you can do things

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another thing you can do which is kind

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of interesting and um there are papers

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on this but they're kind of

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underexplored is you can do like star

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rating

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five and then

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generate generate the output um and so

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that basically says Okay I I want a

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positive sentence now I'm going to score

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the actual review and see whether that

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matches my like conception of a positive

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sentence and there's a few uh papers

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that do

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this

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um let

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me

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this is a kind of older one and then

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there's another more recent one by Sean

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Min I believe um uh but they demonstrate

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how you can do both generative and

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discriminative classification in this

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way so that's another thing that you can

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do uh with language

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models and then the other thing you can

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do is you can generate the label given a

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classification proc so you you say this

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is is great star rating and then

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generate five

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whatever finally um you can do things

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like correct a grammar so uh for example

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if you score the probability of each

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word and you find words that are really

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low probability then you can uh replace

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them with higher probability words um or

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you could ask a model please paraphrase

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this output and it will paraphrase it

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into something that gives you uh you

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know that has better gra so basically

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like as I said language models are very

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diverse um and they can do a ton of

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different things but most of them boil

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down to doing one of these two

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operations scoring or

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generating any questions

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s

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okay so next I I want to talk about a

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specific type of language models uh Auto

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regressive language models and auto

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regressive language models are language

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models that specifically calculate this

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probability um in a fashion where you

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calculate the probability of one token

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and then you calculate the probability

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of the next token given the previous

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token the probability of the third token

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G given the previous two tokens almost

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always this happens left to right um or

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start to finish um and so this is the

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next token here this is a context where

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usually um the context is the previous

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tokens Can anyone think of a time when

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you might want to do

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right to left instead of left to

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right yeah language that's from right to

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yeah that's actually exactly what I what

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I was looking for so if you have a

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language that's written from right to

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left actually uh things like uh Arabic

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and Hebrew are written right to left so

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um both of those are

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chronologically like earlier to later

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because you know if if you're thinking

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about how people speak um the the first

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word that an English speaker speaks is

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on the left just because that's the way

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you write it but the first word that an

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Arabic speaker speaks is on the the

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right because chronologically that's uh

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that's how it works um there's other

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reasons why you might want to do right

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to left but uh it's not really that left

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to right is important it's that like

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start to finish is important in spoken

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language so um one thing I should

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mention here is that this is just a rule

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of probability that if you have multiple

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variables and you're calculating the

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joint probability of variables the

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probability of all of the variables

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together is equal to this probability

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here so we're not making any

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approximations we're not making any

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compromises in order to do this but it

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all hinges on whether we can predict

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this probability um accurately uh

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actually another question does anybody

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know why we do this decomposition why

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don't we just try to predict the

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probability of x

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directly any

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ideas uh of big X sorry uh why don't we

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try to calculate the probability of this

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is great directly without deated the

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IND that

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possibility it could be word salid if

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you did it in a in a particular way yes

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um so that that's a good point

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yeah yeah so for example we talked about

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um uh we'll talk about

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models um or I I mentioned this briefly

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last time you can mention it in more

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detail this time but this is great we

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probably have never seen this before

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right so if we predict only things that

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we've seen before if we only assign a

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non-zero probability to the things we've

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seen before there's going to be lots of

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sentences that we've never seen before

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it makes it

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supercars um that that's basically close

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to what I wanted to say so um the reason

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why we don't typically do it with um

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predicting the whole sentence directly

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is because if we think about the size of

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the classification problem we need to

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solve in order to predict the next word

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it's a v uh where V is the size of the

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vocabulary but the size of the

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classification problem that we need to

00:13:33.120 --> 00:13:38.040
um we need to solve if we predict

00:13:35.399 --> 00:13:40.079
everything directly is V to the N where

00:13:38.040 --> 00:13:42.240
n is the length of the sequence and

00:13:40.079 --> 00:13:45.240
that's just huge the vocabulary is so

00:13:42.240 --> 00:13:48.440
big that it's hard to kind of uh know

00:13:45.240 --> 00:13:51.000
how we handle that so basically by doing

00:13:48.440 --> 00:13:53.160
this sort of decomposition we decompose

00:13:51.000 --> 00:13:56.440
this into uh

00:13:53.160 --> 00:13:58.120
n um prediction problems of size V and

00:13:56.440 --> 00:13:59.519
that's kind of just a lot more

00:13:58.120 --> 00:14:03.079
manageable for from the point of view of

00:13:59.519 --> 00:14:06.000
how we train uh know how we train

00:14:03.079 --> 00:14:09.399
models um that being said there are

00:14:06.000 --> 00:14:11.360
other Alternatives um something very

00:14:09.399 --> 00:14:13.920
widely known uh very widely used is

00:14:11.360 --> 00:14:16.440
called a MK language model um a mast

00:14:13.920 --> 00:14:19.480
language model is something like Bert or

00:14:16.440 --> 00:14:21.680
debera or Roberta or all of these models

00:14:19.480 --> 00:14:25.000
that you might have heard if you've been

00:14:21.680 --> 00:14:28.279
in MLP for more than two years I guess

00:14:25.000 --> 00:14:30.680
um and basically what they do is they

00:14:28.279 --> 00:14:30.680
predict

00:14:32.199 --> 00:14:37.480
uh they like mask out this word and they

00:14:34.839 --> 00:14:39.480
predict the middle word so they mask out

00:14:37.480 --> 00:14:41.440
is and then try to predict that given

00:14:39.480 --> 00:14:45.320
all the other words the problem with

00:14:41.440 --> 00:14:48.959
these models is uh twofold number one

00:14:45.320 --> 00:14:51.880
they don't actually give you a uh good

00:14:48.959 --> 00:14:55.399
probability here uh like a a properly

00:14:51.880 --> 00:14:57.800
formed probability here

00:14:55.399 --> 00:14:59.160
because this is true only as long as

00:14:57.800 --> 00:15:01.920
you're only conditioning on things that

00:14:59.160 --> 00:15:03.480
you've previously generated so that

00:15:01.920 --> 00:15:04.839
they're not actually true language

00:15:03.480 --> 00:15:06.920
models from the point of view of being

00:15:04.839 --> 00:15:10.040
able to easily predict the probability

00:15:06.920 --> 00:15:11.399
of a sequence um and also it's hard to

00:15:10.040 --> 00:15:13.399
generate from them because you need to

00:15:11.399 --> 00:15:15.440
generate in some order and mass language

00:15:13.399 --> 00:15:17.600
models don't specify economical orders

00:15:15.440 --> 00:15:19.120
so they're good for some things like

00:15:17.600 --> 00:15:21.720
calculating representations of the

00:15:19.120 --> 00:15:22.920
output but they're not useful uh they're

00:15:21.720 --> 00:15:25.240
not as useful for

00:15:22.920 --> 00:15:26.880
Generation Um there's also energy based

00:15:25.240 --> 00:15:28.759
language models which basically create a

00:15:26.880 --> 00:15:30.000
scoring function that's not necessarily

00:15:28.759 --> 00:15:31.279
left to right or right to left or

00:15:30.000 --> 00:15:33.120
anything like that but that's very

00:15:31.279 --> 00:15:34.639
Advanced um if you're interested in them

00:15:33.120 --> 00:15:36.319
I can talk more about them that we'll

00:15:34.639 --> 00:15:38.920
skip

00:15:36.319 --> 00:15:41.600
them and um also all of the language

00:15:38.920 --> 00:15:45.639
models that you hear about nowadays GPT

00:15:41.600 --> 00:15:48.800
uh llama whatever else are all other

00:15:45.639 --> 00:15:52.880
models cool so I'm going to go into the

00:15:48.800 --> 00:15:52.880
very um any questions about that

00:15:57.600 --> 00:16:00.600
yeah

00:16:00.680 --> 00:16:04.160
yeah so in Mass language models the

00:16:02.680 --> 00:16:06.000
question was in Mass language models

00:16:04.160 --> 00:16:08.360
couldn't you just mask out the last

00:16:06.000 --> 00:16:10.759
token and predict that sure you could do

00:16:08.360 --> 00:16:13.079
that but there it's just not trained

00:16:10.759 --> 00:16:14.720
that way so it won't do a very good job

00:16:13.079 --> 00:16:16.880
if you always trained it that way it's

00:16:14.720 --> 00:16:18.160
an autor regressive language model so

00:16:16.880 --> 00:16:22.240
you're you're back to where you were in

00:16:18.160 --> 00:16:24.800
the first place um cool so now we I'll

00:16:22.240 --> 00:16:26.399
talk about unigram language models and

00:16:24.800 --> 00:16:29.319
so the simplest language models are

00:16:26.399 --> 00:16:33.560
count-based unigram language models and

00:16:29.319 --> 00:16:35.319
the way they work is um basically we

00:16:33.560 --> 00:16:38.519
want to calculate this probability

00:16:35.319 --> 00:16:41.240
conditioned on all the previous ones and

00:16:38.519 --> 00:16:42.360
the way we do this is we just say

00:16:41.240 --> 00:16:45.680
actually we're not going to worry about

00:16:42.360 --> 00:16:48.759
the order at all and we're just going to

00:16:45.680 --> 00:16:52.240
uh predict the probability of the next

00:16:48.759 --> 00:16:55.279
word uh independently of all the other

00:16:52.240 --> 00:16:57.519
words so if you have something like this

00:16:55.279 --> 00:16:59.720
it's actually extremely easy to predict

00:16:57.519 --> 00:17:02.480
the probability of this word and the way

00:16:59.720 --> 00:17:04.280
you do this is you just count up the

00:17:02.480 --> 00:17:08.360
number of times this word appeared in

00:17:04.280 --> 00:17:10.480
the training data set and divide by the

00:17:08.360 --> 00:17:12.559
uh divide by the total number of words

00:17:10.480 --> 00:17:14.240
in the pring data set and now you have a

00:17:12.559 --> 00:17:15.959
language model this is like language

00:17:14.240 --> 00:17:17.760
model 101 it's the easiest possible

00:17:15.959 --> 00:17:19.520
language model you can write in you know

00:17:17.760 --> 00:17:21.120
three lines of python

00:17:19.520 --> 00:17:25.039
basically

00:17:21.120 --> 00:17:28.480
um so it has a few problems uh the first

00:17:25.039 --> 00:17:31.120
problem with this language model is um

00:17:28.480 --> 00:17:32.960
handling unknown words so what happens

00:17:31.120 --> 00:17:38.679
if you have a word that you've never

00:17:32.960 --> 00:17:41.000
seen before um in this language model

00:17:38.679 --> 00:17:42.240
here what is the probability of any

00:17:41.000 --> 00:17:44.720
sequence that has a word that you've

00:17:42.240 --> 00:17:47.440
never seen before yeah the probability

00:17:44.720 --> 00:17:49.240
of the sequence gets zero so there might

00:17:47.440 --> 00:17:51.120
not be such a big problem for generating

00:17:49.240 --> 00:17:52.480
things from the language model because

00:17:51.120 --> 00:17:54.520
you know maybe it's fine if you only

00:17:52.480 --> 00:17:55.960
generate words that you've seen before

00:17:54.520 --> 00:17:57.679
uh but it is definitely a problem of

00:17:55.960 --> 00:17:59.720
scoring things with the language model

00:17:57.679 --> 00:18:02.039
and it's also a problem of uh for

00:17:59.720 --> 00:18:04.440
something like translation if you get an

00:18:02.039 --> 00:18:05.840
unknown word uh when you're translating

00:18:04.440 --> 00:18:07.799
something then you would like to be able

00:18:05.840 --> 00:18:11.320
to translate it reasonably but you can't

00:18:07.799 --> 00:18:13.799
do that so um that's an issue so how do

00:18:11.320 --> 00:18:15.840
we how do we fix this um there's a

00:18:13.799 --> 00:18:17.640
couple options the first option is to

00:18:15.840 --> 00:18:19.440
segment to characters and subwords and

00:18:17.640 --> 00:18:21.720
this is now the preferred option that

00:18:19.440 --> 00:18:24.360
most people use nowadays uh just run

00:18:21.720 --> 00:18:26.840
sentence piece segment your vocabulary

00:18:24.360 --> 00:18:28.400
and you're all set you're you'll now no

00:18:26.840 --> 00:18:29.679
longer have any unknown words because

00:18:28.400 --> 00:18:30.840
all the unknown words get split into

00:18:29.679 --> 00:18:33.559
shorter

00:18:30.840 --> 00:18:36.240
units there's also other options that

00:18:33.559 --> 00:18:37.919
you can use if you're uh very interested

00:18:36.240 --> 00:18:41.280
in or serious about this and want to

00:18:37.919 --> 00:18:43.720
handle this like uh as part of a

00:18:41.280 --> 00:18:45.960
research project or something like this

00:18:43.720 --> 00:18:48.520
and uh the way you can do this is you

00:18:45.960 --> 00:18:50.120
can build an unknown word model and an

00:18:48.520 --> 00:18:52.200
unknown word model basically what it

00:18:50.120 --> 00:18:54.520
does is it uh predicts the probability

00:18:52.200 --> 00:18:56.200
of unknown words using characters and

00:18:54.520 --> 00:18:59.559
then it models the probability of words

00:18:56.200 --> 00:19:01.159
using words and so now you can you have

00:18:59.559 --> 00:19:02.559
kind of like a hierarchical model where

00:19:01.159 --> 00:19:03.919
you first try to predict words and then

00:19:02.559 --> 00:19:06.720
if you can't predict words you predict

00:19:03.919 --> 00:19:08.960
unknown words so this isn't us as widely

00:19:06.720 --> 00:19:11.520
anymore but it's worth thinking about uh

00:19:08.960 --> 00:19:11.520
or knowing

00:19:11.840 --> 00:19:20.880
about okay uh so a second detail um a

00:19:17.200 --> 00:19:22.799
parameter uh so parameterizing in log

00:19:20.880 --> 00:19:25.880
space

00:19:22.799 --> 00:19:28.400
so the um multiplication of

00:19:25.880 --> 00:19:29.840
probabilities can be reexpressed is the

00:19:28.400 --> 00:19:31.840
addition of log

00:19:29.840 --> 00:19:34.159
probabilities uh so this is really

00:19:31.840 --> 00:19:35.720
important and this is widely used in all

00:19:34.159 --> 00:19:37.520
language models whether they're unigram

00:19:35.720 --> 00:19:39.640
language models or or neural language

00:19:37.520 --> 00:19:41.799
models there's actually a very simple

00:19:39.640 --> 00:19:45.440
reason why we why we do it this way does

00:19:41.799 --> 00:19:45.440
anybody uh know the

00:19:46.440 --> 00:19:52.679
answer what would happen if we

00:19:48.280 --> 00:19:56.720
multiplied uh let's say uh 30 30 tokens

00:19:52.679 --> 00:20:00.360
worth of probabilities together um

00:19:56.720 --> 00:20:02.120
yeah uh yeah too too small um so

00:20:00.360 --> 00:20:06.120
basically the problem is numerical

00:20:02.120 --> 00:20:07.520
underflow um so modern computers if if

00:20:06.120 --> 00:20:08.840
we weren't doing this on a computer and

00:20:07.520 --> 00:20:11.240
we were just doing math it wouldn't

00:20:08.840 --> 00:20:14.280
matter at all um but because we're doing

00:20:11.240 --> 00:20:17.280
it on a computer uh we

00:20:14.280 --> 00:20:17.280
have

00:20:20.880 --> 00:20:26.000
ours we have our

00:20:23.000 --> 00:20:26.000
32bit

00:20:27.159 --> 00:20:30.159
float

00:20:32.320 --> 00:20:37.720
where we have uh the exponent in the the

00:20:35.799 --> 00:20:40.159
fraction over here so the largest the

00:20:37.720 --> 00:20:41.960
exponent can get is limited by the

00:20:40.159 --> 00:20:45.880
number of exponent bits that we have in

00:20:41.960 --> 00:20:48.039
a 32-bit float and um if that's the case

00:20:45.880 --> 00:20:52.480
I forget exactly how large it is it's

00:20:48.039 --> 00:20:53.440
like yeah something like 30 minus 38 is

00:20:52.480 --> 00:20:56.640
that

00:20:53.440 --> 00:20:58.520
right yeah but anyway like if the number

00:20:56.640 --> 00:21:00.640
gets too small you'll underflow it goes

00:20:58.520 --> 00:21:02.400
to zero and you'll get a zero

00:21:00.640 --> 00:21:05.720
probability despite the fact that it's

00:21:02.400 --> 00:21:07.640
not actually zero so um that's usually

00:21:05.720 --> 00:21:09.440
why we do this it's also a little bit

00:21:07.640 --> 00:21:12.960
easier for people just to look at like

00:21:09.440 --> 00:21:15.200
minus 30 instead of looking to something

00:21:12.960 --> 00:21:19.960
something time 10 to the minus 30 or

00:21:15.200 --> 00:21:24.520
something so uh that is why we normally

00:21:19.960 --> 00:21:27.159
go um another thing that you can note is

00:21:24.520 --> 00:21:28.760
uh you can treat each of these in a

00:21:27.159 --> 00:21:31.360
unigram model you can treat each of

00:21:28.760 --> 00:21:37.039
these as parameters so we talked about

00:21:31.360 --> 00:21:39.640
parameters of a model uh like a um like

00:21:37.039 --> 00:21:41.120
a bag of words model and we can

00:21:39.640 --> 00:21:44.080
similarly treat these unigram

00:21:41.120 --> 00:21:47.760
probabilities as parameters so um how

00:21:44.080 --> 00:21:47.760
many parameters does a unigram model

00:21:48.080 --> 00:21:51.320
have any

00:21:57.039 --> 00:22:02.400
ideas

00:21:59.600 --> 00:22:04.440
yeah yeah exactly parameters equal to

00:22:02.400 --> 00:22:08.120
the size of the vocabulary so this one's

00:22:04.440 --> 00:22:10.880
easy and then we can go um we can go to

00:22:08.120 --> 00:22:13.880
the slightly less easy ones

00:22:10.880 --> 00:22:16.039
there so anyway this is a unigram model

00:22:13.880 --> 00:22:17.960
uh it's it's not too hard um you

00:22:16.039 --> 00:22:20.480
basically count up and divide and then

00:22:17.960 --> 00:22:22.720
you add the the probabilities here you

00:22:20.480 --> 00:22:25.440
could easily do it in a short Python

00:22:22.720 --> 00:22:28.400
program higher order engram models so

00:22:25.440 --> 00:22:31.600
higher order engram models um what these

00:22:28.400 --> 00:22:35.520
do is they essentially limit the context

00:22:31.600 --> 00:22:40.240
length to a length of N and then they

00:22:35.520 --> 00:22:42.600
count and divide so the way it works

00:22:40.240 --> 00:22:45.559
here maybe this is a little bit uh

00:22:42.600 --> 00:22:47.320
tricky but I can show an example so what

00:22:45.559 --> 00:22:49.840
we do is we count up the number of times

00:22:47.320 --> 00:22:51.320
we've seen this is an example and then

00:22:49.840 --> 00:22:53.480
we divide by the number of times we've

00:22:51.320 --> 00:22:55.960
seen this is n and that's the

00:22:53.480 --> 00:22:56.960
probability of example given the the

00:22:55.960 --> 00:22:58.720
previous

00:22:56.960 --> 00:23:00.559
coms

00:22:58.720 --> 00:23:02.039
so the problem with this is anytime we

00:23:00.559 --> 00:23:03.400
get a sequence that we've never seen

00:23:02.039 --> 00:23:04.960
before like we would like to model

00:23:03.400 --> 00:23:07.200
longer sequences to make this more

00:23:04.960 --> 00:23:08.600
accurate but anytime we've get a uh we

00:23:07.200 --> 00:23:10.720
get a sequence that we've never seen

00:23:08.600 --> 00:23:12.919
before um it will get a probability of

00:23:10.720 --> 00:23:15.919
zero similarly because this count on top

00:23:12.919 --> 00:23:19.919
of here will be zero so the way that uh

00:23:15.919 --> 00:23:22.640
engram language models work with this uh

00:23:19.919 --> 00:23:27.320
handle this is they have fall back to

00:23:22.640 --> 00:23:31.840
Shorter uh engram models so um this

00:23:27.320 --> 00:23:33.480
model sorry when I say NR uh n is the

00:23:31.840 --> 00:23:35.520
length of the context so this is a four

00:23:33.480 --> 00:23:37.679
gr model here because the top context is

00:23:35.520 --> 00:23:40.520
four so the photogram model would

00:23:37.679 --> 00:23:46.640
calculate this and then interpolate it

00:23:40.520 --> 00:23:48.640
like this with a um with a trigram model

00:23:46.640 --> 00:23:50.400
uh and then the trigram model itself

00:23:48.640 --> 00:23:51.720
would interpolate with the Byram model

00:23:50.400 --> 00:23:53.440
the Byram model would interpolate with

00:23:51.720 --> 00:23:56.880
the unram

00:23:53.440 --> 00:23:59.880
model oh this one oh

00:23:56.880 --> 00:23:59.880
okay

00:24:02.159 --> 00:24:05.440
um one

00:24:07.039 --> 00:24:12.320
second could you uh help get it from the

00:24:10.000 --> 00:24:12.320
lock

00:24:26.799 --> 00:24:29.799
box

00:24:43.640 --> 00:24:50.200
um okay sorry

00:24:46.880 --> 00:24:53.640
so getting bad

00:24:50.200 --> 00:24:56.640
here just

00:24:53.640 --> 00:24:56.640
actually

00:24:56.760 --> 00:25:02.559
okay uh oh wow that's a lot

00:25:02.960 --> 00:25:12.080
better cool okay so

00:25:08.279 --> 00:25:14.159
um so this is uh how we deal with the

00:25:12.080 --> 00:25:18.799
fact that models can

00:25:14.159 --> 00:25:23.919
be um models can be more precise but

00:25:18.799 --> 00:25:26.679
more sparse and less precise but less

00:25:23.919 --> 00:25:28.720
sparse this is also another concept that

00:25:26.679 --> 00:25:31.039
we're going to talk about more later uh

00:25:28.720 --> 00:25:33.240
in another class but this is a variety

00:25:31.039 --> 00:25:33.240
of

00:25:33.679 --> 00:25:38.440
ensembling where we have different

00:25:35.960 --> 00:25:40.360
models that are good at different things

00:25:38.440 --> 00:25:42.279
and we combine them together so this is

00:25:40.360 --> 00:25:44.760
the first instance that you would see of

00:25:42.279 --> 00:25:46.159
this there are other instances of this

00:25:44.760 --> 00:25:50.320
but the reason why I mentioned that this

00:25:46.159 --> 00:25:51.840
is a a variety of ensembling is actually

00:25:50.320 --> 00:25:55.520
you're probably not going to be using

00:25:51.840 --> 00:25:57.840
engram models super widely unless you

00:25:55.520 --> 00:26:00.520
really want to process huge data sets

00:25:57.840 --> 00:26:02.399
because that is one advantage of them

00:26:00.520 --> 00:26:03.960
but some of these smoothing methods

00:26:02.399 --> 00:26:05.720
actually might be interesting even if

00:26:03.960 --> 00:26:10.520
you're using other models and ensembling

00:26:05.720 --> 00:26:10.520
them together so

00:26:10.600 --> 00:26:15.679
the in order to decide this

00:26:13.679 --> 00:26:19.559
interpolation coefficient one way we can

00:26:15.679 --> 00:26:23.440
do it is just set a fixed um set a fixed

00:26:19.559 --> 00:26:26.039
amount of probability that we use for

00:26:23.440 --> 00:26:29.000
every um every time so we could say that

00:26:26.039 --> 00:26:32.000
we always set this Lambda to 0.8 and

00:26:29.000 --> 00:26:34.320
some always set this Lambda 1us Lambda

00:26:32.000 --> 00:26:36.559
to 0.2 and interpolate those two

00:26:34.320 --> 00:26:39.120
together but actually there's more

00:26:36.559 --> 00:26:42.240
sophisticated methods of doing this and

00:26:39.120 --> 00:26:44.080
so one way of doing this is uh called

00:26:42.240 --> 00:26:47.240
additive

00:26:44.080 --> 00:26:50.600
smoothing excuse me and the the way that

00:26:47.240 --> 00:26:54.039
additive smoothing works is um basically

00:26:50.600 --> 00:26:54.919
we add Alpha to the uh to the top and

00:26:54.039 --> 00:26:58.000
the

00:26:54.919 --> 00:27:02.159
bottom and the reason why this is slight

00:26:58.000 --> 00:27:06.279
different as is as our accounts get

00:27:02.159 --> 00:27:10.799
larger we start to approach the true

00:27:06.279 --> 00:27:10.799
distribution so just to give an

00:27:12.080 --> 00:27:19.480
example let's say we have uh the

00:27:17.640 --> 00:27:21.640
box

00:27:19.480 --> 00:27:26.279
is

00:27:21.640 --> 00:27:26.279
um let's say initially we

00:27:26.520 --> 00:27:29.520
have

00:27:31.159 --> 00:27:37.600
uh let let's say our Alpha is

00:27:33.840 --> 00:27:43.559
one so initially if we have

00:27:37.600 --> 00:27:47.320
nothing um if we have no no evidence for

00:27:43.559 --> 00:27:47.320
our sorry I I

00:27:49.720 --> 00:27:54.960
realize let's say this is

00:27:52.640 --> 00:27:56.840
our fallback

00:27:54.960 --> 00:27:59.240
distribution um where this is a

00:27:56.840 --> 00:28:01.880
probability of Z 0.5 this is a

00:27:59.240 --> 00:28:03.360
probability of 0.3 and this is a

00:28:01.880 --> 00:28:06.559
probability of

00:28:03.360 --> 00:28:09.919
0.2 so now let's talk about our byr

00:28:06.559 --> 00:28:13.399
model um and our byr

00:28:09.919 --> 00:28:18.000
model has counts which is the

00:28:13.399 --> 00:28:18.000
the the box and the

00:28:19.039 --> 00:28:24.480
is so if we do something like this then

00:28:22.720 --> 00:28:26.720
um initially we have no counts like

00:28:24.480 --> 00:28:28.159
let's say we we have no data uh about

00:28:26.720 --> 00:28:30.760
this distribution

00:28:28.159 --> 00:28:33.200
um our counts would be zero and our

00:28:30.760 --> 00:28:35.919
Alpha would be

00:28:33.200 --> 00:28:37.840
one and so we would just fall back to

00:28:35.919 --> 00:28:40.960
this distribution we just have like one

00:28:37.840 --> 00:28:43.320
times uh one times this distribution

00:28:40.960 --> 00:28:45.679
let's say we then we have one piece of

00:28:43.320 --> 00:28:48.640
evidence and once we have one piece of

00:28:45.679 --> 00:28:52.279
evidence now this would be

00:28:48.640 --> 00:28:53.960
0.33 um and this would uh be Alpha equal

00:28:52.279 --> 00:28:56.399
to 1 so we'd have

00:28:53.960 --> 00:28:58.679
0.5 *

00:28:56.399 --> 00:29:00.399
0.33

00:28:58.679 --> 00:29:04.039
uh and

00:29:00.399 --> 00:29:07.720
0.5 time

00:29:04.039 --> 00:29:10.840
0.3 uh is the probability of the Box

00:29:07.720 --> 00:29:12.840
because um basically we we have one

00:29:10.840 --> 00:29:14.720
piece of evidence and we are adding a

00:29:12.840 --> 00:29:17.080
count of one to the lower order

00:29:14.720 --> 00:29:18.320
distribution then if we increase our

00:29:17.080 --> 00:29:24.159
count

00:29:18.320 --> 00:29:24.159
here um now we rely more

00:29:24.880 --> 00:29:30.960
strongly sorry that that would be wrong

00:29:27.720 --> 00:29:32.399
so so now we rely more strongly on the

00:29:30.960 --> 00:29:33.880
higher order distribution because we

00:29:32.399 --> 00:29:37.039
have more evidence for the higher order

00:29:33.880 --> 00:29:39.610
distribution so basically in this case

00:29:37.039 --> 00:29:41.240
um the probability

00:29:39.610 --> 00:29:44.559
[Music]

00:29:41.240 --> 00:29:48.200
of Lambda which I showed

00:29:44.559 --> 00:29:52.000
before is equal to the the sum of the

00:29:48.200 --> 00:29:54.200
counts plus um the sum of the counts

00:29:52.000 --> 00:29:56.480
over the sum of the counts plus

00:29:54.200 --> 00:29:58.159
Ali so as the sum of the counts gets

00:29:56.480 --> 00:30:00.240
larger you rely on the higher order

00:29:58.159 --> 00:30:01.640
distribution is the sum of the counts is

00:30:00.240 --> 00:30:02.760
if the sum of the counts is smaller you

00:30:01.640 --> 00:30:04.320
rely more on the lower order

00:30:02.760 --> 00:30:06.720
distribution so the more evidence you

00:30:04.320 --> 00:30:11.640
have the more you rely on so that's the

00:30:06.720 --> 00:30:11.640
basic idea behind these smoothing things

00:30:11.679 --> 00:30:16.679
um there's also a number of other

00:30:14.519 --> 00:30:18.760
varieties called uh

00:30:16.679 --> 00:30:20.799
discounting so uh the discount

00:30:18.760 --> 00:30:23.679
hyperparameter basically you subtract

00:30:20.799 --> 00:30:26.080
this off um uh you subtract this from

00:30:23.679 --> 00:30:27.840
the count so you would subtract like 0.5

00:30:26.080 --> 00:30:32.679
from each of the counts that you it's

00:30:27.840 --> 00:30:36.279
just empirically this is a better match

00:30:32.679 --> 00:30:38.600
for the fact that um natural language

00:30:36.279 --> 00:30:40.039
has a very longtailed distribution um

00:30:38.600 --> 00:30:41.600
you can kind of do the math and show

00:30:40.039 --> 00:30:43.720
that that works and that's actually in

00:30:41.600 --> 00:30:46.080
this um in this paper if you're

00:30:43.720 --> 00:30:49.880
interested in looking at more details of

00:30:46.080 --> 00:30:51.519
that um and then kind of the

00:30:49.880 --> 00:30:53.440
stateoftheart in language modeling

00:30:51.519 --> 00:30:56.600
before neural language models came out

00:30:53.440 --> 00:30:59.919
was this kesser smoothing and what it

00:30:56.600 --> 00:31:02.440
does is it discounts but it also

00:30:59.919 --> 00:31:04.480
modifies the lower order distribution so

00:31:02.440 --> 00:31:07.200
in the lower order distribution you

00:31:04.480 --> 00:31:09.039
basically um modify the counts with

00:31:07.200 --> 00:31:11.919
respect to how many times that word has

00:31:09.039 --> 00:31:13.519
appeared in new contexts with the IDE

00:31:11.919 --> 00:31:16.360
idea being that you only use the lower

00:31:13.519 --> 00:31:18.880
order distribution when you have uh new

00:31:16.360 --> 00:31:21.200
contexts um and so you can kind of Be

00:31:18.880 --> 00:31:23.600
Clever

00:31:21.200 --> 00:31:25.399
About You Can Be Clever about how you

00:31:23.600 --> 00:31:27.639
build this distribution based on the

00:31:25.399 --> 00:31:29.360
fact that you're only using it in the

00:31:27.639 --> 00:31:31.320
case when this distribution is not very

00:31:29.360 --> 00:31:33.960
Rel

00:31:31.320 --> 00:31:36.080
so I I would spend a lot more time

00:31:33.960 --> 00:31:37.960
teaching this when uh engram models were

00:31:36.080 --> 00:31:39.840
kind of the thing uh that people were

00:31:37.960 --> 00:31:41.960
using but now I'm going to go over them

00:31:39.840 --> 00:31:43.600
very quickly so you know don't worry if

00:31:41.960 --> 00:31:46.559
you weren't able to follow all the

00:31:43.600 --> 00:31:47.960
details but the basic um the basic thing

00:31:46.559 --> 00:31:49.279
take away from this is number one these

00:31:47.960 --> 00:31:51.639
are the methods that people use for

00:31:49.279 --> 00:31:53.440
engram language models number two if

00:31:51.639 --> 00:31:55.720
you're thinking about combining language

00:31:53.440 --> 00:31:57.519
models together in some way through you

00:31:55.720 --> 00:31:59.279
know ensembling their probability or

00:31:57.519 --> 00:32:00.480
something like this this is something

00:31:59.279 --> 00:32:02.279
that you should think about a little bit

00:32:00.480 --> 00:32:03.679
more carefully because like some

00:32:02.279 --> 00:32:05.240
language models might be good in some

00:32:03.679 --> 00:32:07.440
context other language models might be

00:32:05.240 --> 00:32:09.440
good in other contexts so you would need

00:32:07.440 --> 00:32:11.799
to think about that when you're doing um

00:32:09.440 --> 00:32:18.200
when you're combining the model

00:32:11.799 --> 00:32:18.200
that cool um any any questions about

00:32:19.080 --> 00:32:24.840
this Okay

00:32:21.159 --> 00:32:27.840
cool so there's a lot of problems that

00:32:24.840 --> 00:32:30.760
we have to deal with um when were

00:32:27.840 --> 00:32:32.600
creating engram models and that actually

00:32:30.760 --> 00:32:35.279
kind of motivated the reason why we

00:32:32.600 --> 00:32:36.639
moved to neural language models the

00:32:35.279 --> 00:32:38.720
first one is similar to what I talked

00:32:36.639 --> 00:32:40.519
about last time with text classification

00:32:38.720 --> 00:32:42.600
um that they can't share strength among

00:32:40.519 --> 00:32:45.159
similar words like bought and

00:32:42.600 --> 00:32:46.919
purchase um another thing is that they

00:32:45.159 --> 00:32:49.440
can't easily condition on context with

00:32:46.919 --> 00:32:51.240
intervening words so engram models if

00:32:49.440 --> 00:32:52.799
you have a rare word in your context

00:32:51.240 --> 00:32:54.320
immediately start falling back to the

00:32:52.799 --> 00:32:56.799
unigram distribution and they end up

00:32:54.320 --> 00:32:58.720
being very bad so uh that was another

00:32:56.799 --> 00:33:01.000
issue

00:32:58.720 --> 00:33:04.760
and they couldn't handle long distance

00:33:01.000 --> 00:33:09.080
um dependencies so if this was beyond

00:33:04.760 --> 00:33:10.559
the engram context that they would uh be

00:33:09.080 --> 00:33:14.320
handling then you wouldn't be able to

00:33:10.559 --> 00:33:15.840
manage this so actually before neural

00:33:14.320 --> 00:33:18.000
language models became a really big

00:33:15.840 --> 00:33:19.960
thing uh people came up with a bunch of

00:33:18.000 --> 00:33:22.760
individual solutions for this in order

00:33:19.960 --> 00:33:24.440
to solve the problems but actually it

00:33:22.760 --> 00:33:26.679
wasn't that these Solutions didn't work

00:33:24.440 --> 00:33:29.159
at all it was just that engineering all

00:33:26.679 --> 00:33:30.519
of them together was so hard that nobody

00:33:29.159 --> 00:33:32.120
actually ever did that and so they

00:33:30.519 --> 00:33:35.120
relied on just engram models out of the

00:33:32.120 --> 00:33:37.600
box and that wasn't scalable so it's

00:33:35.120 --> 00:33:39.279
kind of a funny example of how like

00:33:37.600 --> 00:33:42.000
actually neural networks despite all the

00:33:39.279 --> 00:33:43.559
pain that they cause in some areas are a

00:33:42.000 --> 00:33:47.120
much better engineering solution to

00:33:43.559 --> 00:33:51.279
solve all the issues that previous

00:33:47.120 --> 00:33:53.159
method cool um so when they use uh Eng

00:33:51.279 --> 00:33:54.799
grab models neural language models

00:33:53.159 --> 00:33:56.559
achieve better performance but Eng grab

00:33:54.799 --> 00:33:58.440
models are very very fast to estimate

00:33:56.559 --> 00:33:59.880
and apply you can even estimate them

00:33:58.440 --> 00:34:04.399
completely in

00:33:59.880 --> 00:34:07.720
parallel um engram models also I I don't

00:34:04.399 --> 00:34:10.399
know if this is necessarily

00:34:07.720 --> 00:34:13.200
A a thing that

00:34:10.399 --> 00:34:15.079
you a reason to use engram language

00:34:13.200 --> 00:34:17.720
models but it is a reason to think a

00:34:15.079 --> 00:34:20.320
little bit critically about uh neural

00:34:17.720 --> 00:34:22.720
language models which is neural language

00:34:20.320 --> 00:34:24.320
models actually can be worse than engram

00:34:22.720 --> 00:34:26.679
language models at modeling very low

00:34:24.320 --> 00:34:28.480
frequency phenomenas so engram language

00:34:26.679 --> 00:34:29.960
model can learn from a single example

00:34:28.480 --> 00:34:32.119
they only need a single example of

00:34:29.960 --> 00:34:36.879
anything before the probability of that

00:34:32.119 --> 00:34:38.639
continuation goes up very high um and uh

00:34:36.879 --> 00:34:41.359
but neural language models actually can

00:34:38.639 --> 00:34:43.599
forget or not memorize uh appropriately

00:34:41.359 --> 00:34:46.280
from single examples so they can be

00:34:43.599 --> 00:34:48.040
better at that um there's a toolkit the

00:34:46.280 --> 00:34:49.919
standard toolkit for estimating engram

00:34:48.040 --> 00:34:54.359
language models is called KLM it's kind

00:34:49.919 --> 00:34:57.599
of frighteningly fast um and so people

00:34:54.359 --> 00:35:00.400
have been uh saying like I've seen some

00:34:57.599 --> 00:35:01.599
jokes which are like job postings that

00:35:00.400 --> 00:35:04.040
say people who have been working on

00:35:01.599 --> 00:35:05.880
large language models uh for we want

00:35:04.040 --> 00:35:07.359
people who have been 10 years of

00:35:05.880 --> 00:35:09.240
experience working on large language

00:35:07.359 --> 00:35:11.960
models or something like that and a lot

00:35:09.240 --> 00:35:13.440
of people are saying wait nobody has 10

00:35:11.960 --> 00:35:16.400
years of experience working on large

00:35:13.440 --> 00:35:18.160
language models well Kenneth hfield who

00:35:16.400 --> 00:35:19.440
created KLM does have 10 years of

00:35:18.160 --> 00:35:22.800
experience working on large language

00:35:19.440 --> 00:35:24.599
models because he was estimating uh

00:35:22.800 --> 00:35:27.720
seven gr

00:35:24.599 --> 00:35:30.320
bottles um seven models with a

00:35:27.720 --> 00:35:35.040
vocabulary of let's say

00:35:30.320 --> 00:35:37.720
100,000 on um you know web text so how

00:35:35.040 --> 00:35:41.119
many parameters is at that's more than

00:35:37.720 --> 00:35:44.320
any you know large neural language model

00:35:41.119 --> 00:35:45.640
that we have nowadays so um they they

00:35:44.320 --> 00:35:47.520
have a lot of these parameters are

00:35:45.640 --> 00:35:49.400
sparse they're zero counts so obviously

00:35:47.520 --> 00:35:52.160
you don't uh you don't memorize all of

00:35:49.400 --> 00:35:55.040
them but uh

00:35:52.160 --> 00:35:57.800
yeah cool um another thing that maybe I

00:35:55.040 --> 00:35:59.359
should mention like so this doesn't

00:35:57.800 --> 00:36:01.960
sound completely outdated there was a

00:35:59.359 --> 00:36:05.400
really good paper

00:36:01.960 --> 00:36:08.400
recently that used the fact that engrams

00:36:05.400 --> 00:36:08.400
are

00:36:11.079 --> 00:36:17.319
so uses effect that engram models are so

00:36:14.280 --> 00:36:18.960
scalable it's this paper um it's called

00:36:17.319 --> 00:36:21.079
Data selection for language models via

00:36:18.960 --> 00:36:22.359
importance rese sampling and one

00:36:21.079 --> 00:36:24.359
interesting thing that they do in this

00:36:22.359 --> 00:36:28.920
paper is that they don't

00:36:24.359 --> 00:36:31.560
actually um they don't

00:36:28.920 --> 00:36:32.800
actually use neural models in any way

00:36:31.560 --> 00:36:34.920
despite the fact that they use the

00:36:32.800 --> 00:36:36.880
downstream data that they sample in

00:36:34.920 --> 00:36:41.319
order to calculate neural models but

00:36:36.880 --> 00:36:42.880
they run engram models over um over lots

00:36:41.319 --> 00:36:47.359
and lots of data and then they fit a

00:36:42.880 --> 00:36:50.000
gaussian distribution to the enr model

00:36:47.359 --> 00:36:51.520
counts basically uh in order to select

00:36:50.000 --> 00:36:53.040
the data in the reason why they do this

00:36:51.520 --> 00:36:55.280
is they want to do this over the entire

00:36:53.040 --> 00:36:56.760
web and running a neural model over the

00:36:55.280 --> 00:36:58.920
entire web would be too expensive so

00:36:56.760 --> 00:37:00.319
they use angr models instead so that's

00:36:58.920 --> 00:37:02.359
just an example of something in the

00:37:00.319 --> 00:37:04.920
modern context where keeping this in

00:37:02.359 --> 00:37:04.920
mind is a good

00:37:08.200 --> 00:37:14.000
idea okay I'd like to move to the next

00:37:10.960 --> 00:37:15.319
part so a language model evaluation uh

00:37:14.000 --> 00:37:17.200
this is important to know I'm not going

00:37:15.319 --> 00:37:19.079
to talk about language model evaluation

00:37:17.200 --> 00:37:20.599
on other tasks I'm only going to talk

00:37:19.079 --> 00:37:23.800
right now about language model

00:37:20.599 --> 00:37:26.280
evaluation on the task of language

00:37:23.800 --> 00:37:29.079
modeling and there's a number of metrics

00:37:26.280 --> 00:37:30.680
that we use for the task of language

00:37:29.079 --> 00:37:32.720
modeling evaluating language models on

00:37:30.680 --> 00:37:35.560
the task of language modeling the first

00:37:32.720 --> 00:37:38.480
one is log likelihood and basically uh

00:37:35.560 --> 00:37:40.160
the way we calculate log likelihood is

00:37:38.480 --> 00:37:41.640
uh sorry there's an extra parenthesis

00:37:40.160 --> 00:37:45.480
here but the way we calculate log

00:37:41.640 --> 00:37:47.160
likelihood is we get a test set that

00:37:45.480 --> 00:37:50.400
ideally has not been included in our

00:37:47.160 --> 00:37:52.520
training data and we take all of the

00:37:50.400 --> 00:37:54.200
documents or sentences in the test set

00:37:52.520 --> 00:37:57.040
we calculate the log probability of all

00:37:54.200 --> 00:37:59.520
of them uh we don't actually use this

00:37:57.040 --> 00:38:02.640
super broadly to evaluate models and the

00:37:59.520 --> 00:38:04.200
reason why is because this number is

00:38:02.640 --> 00:38:05.720
very dependent on the size of the data

00:38:04.200 --> 00:38:07.119
set so if you have a larger data set

00:38:05.720 --> 00:38:08.720
this number will be larger if you have a

00:38:07.119 --> 00:38:10.960
smaller data set this number will be

00:38:08.720 --> 00:38:14.040
smaller so the more common thing to do

00:38:10.960 --> 00:38:15.839
is per word uh log likelihood and per

00:38:14.040 --> 00:38:19.800
word log likelihood is basically

00:38:15.839 --> 00:38:22.760
dividing the um dividing the log

00:38:19.800 --> 00:38:25.520
probability of the entire corpus with uh

00:38:22.760 --> 00:38:28.359
the number of words that you have in the

00:38:25.520 --> 00:38:31.000
corpus

00:38:28.359 --> 00:38:34.599
um it's also common for papers to report

00:38:31.000 --> 00:38:36.359
negative log likelihood uh where because

00:38:34.599 --> 00:38:37.800
that's used as a loss and there lower is

00:38:36.359 --> 00:38:40.440
better so you just need to be careful

00:38:37.800 --> 00:38:42.560
about which one is being

00:38:40.440 --> 00:38:43.880
reported so this is pretty common I

00:38:42.560 --> 00:38:45.400
think most people are are somewhat

00:38:43.880 --> 00:38:49.040
familiar with

00:38:45.400 --> 00:38:49.800
this another thing that you might see is

00:38:49.040 --> 00:38:53.079
uh

00:38:49.800 --> 00:38:55.000
entropy and uh specifically this is

00:38:53.079 --> 00:38:57.319
often called cross entropy because

00:38:55.000 --> 00:38:59.880
you're calculating

00:38:57.319 --> 00:39:01.599
the you're estimating the model on a

00:38:59.880 --> 00:39:05.079
training data set and then evaluating it

00:39:01.599 --> 00:39:08.400
on a separate data set uh so uh on the

00:39:05.079 --> 00:39:12.200
test data set and this is calcul often

00:39:08.400 --> 00:39:14.640
or usually calculated as log 2 um of the

00:39:12.200 --> 00:39:17.119
probability divided by the number of

00:39:14.640 --> 00:39:18.760
words or units in the Corpus does anyone

00:39:17.119 --> 00:39:23.839
know why this is log

00:39:18.760 --> 00:39:23.839
two as opposed to a normal uh

00:39:25.440 --> 00:39:31.319
log

00:39:28.440 --> 00:39:31.319
anyone yeah

00:39:33.119 --> 00:39:38.720
so yeah so it's calculating as bits um

00:39:36.760 --> 00:39:43.160
and this is kind of

00:39:38.720 --> 00:39:45.240
a um this is kind of a historical thing

00:39:43.160 --> 00:39:47.119
and it's not super super important for

00:39:45.240 --> 00:39:51.800
language models but it's actually pretty

00:39:47.119 --> 00:39:54.599
interesting uh to to think about and so

00:39:51.800 --> 00:39:57.480
actually any probabilistic distribution

00:39:54.599 --> 00:40:00.040
can also be used for data compression

00:39:57.480 --> 00:40:03.319
um and so you know when you're running a

00:40:00.040 --> 00:40:05.000
zip file or you're running gzip or bz2

00:40:03.319 --> 00:40:07.359
or something like that uh you're

00:40:05.000 --> 00:40:09.240
compressing a file into a smaller file

00:40:07.359 --> 00:40:12.000
and any language model can also be used

00:40:09.240 --> 00:40:15.280
to compress a SM file into a smaller

00:40:12.000 --> 00:40:17.119
file um and so the way it does this is

00:40:15.280 --> 00:40:19.200
if you have more likely

00:40:17.119 --> 00:40:20.960
sequences uh for example more likely

00:40:19.200 --> 00:40:25.079
sentences or more likely documents you

00:40:20.960 --> 00:40:26.920
can press them into a a shorter uh

00:40:25.079 --> 00:40:29.440
output and

00:40:26.920 --> 00:40:29.440
kind of

00:40:29.640 --> 00:40:33.800
the

00:40:31.480 --> 00:40:35.720
ideal I I think it's pretty safe to say

00:40:33.800 --> 00:40:37.920
ideal because I think you can't get a

00:40:35.720 --> 00:40:42.920
better method for compression than this

00:40:37.920 --> 00:40:45.000
uh if I unless I'm uh you know not well

00:40:42.920 --> 00:40:46.800
versed enough in information Theory but

00:40:45.000 --> 00:40:49.240
I I think this is basically the ideal

00:40:46.800 --> 00:40:51.960
method for data compression and the way

00:40:49.240 --> 00:40:54.640
it works is um I have a figure up here

00:40:51.960 --> 00:40:58.800
but I'd like to recreate it here which

00:40:54.640 --> 00:41:02.640
is let's say we have a vocabulary of

00:40:58.800 --> 00:41:07.200
a um which has

00:41:02.640 --> 00:41:08.800
50% and then we have a vocabulary uh B

00:41:07.200 --> 00:41:11.560
which is

00:41:08.800 --> 00:41:14.040
33% and a vocabulary

00:41:11.560 --> 00:41:18.520
C

00:41:14.040 --> 00:41:18.520
uh yeah C which is about

00:41:18.640 --> 00:41:25.640
17% and so if you have a single token

00:41:22.960 --> 00:41:26.839
sequence um if you have a single token

00:41:25.640 --> 00:41:30.880
sequence

00:41:26.839 --> 00:41:30.880
what you do is you can

00:41:31.319 --> 00:41:38.800
see divide this into zero and one so if

00:41:36.400 --> 00:41:40.680
your single token sequence is a you can

00:41:38.800 --> 00:41:42.760
just put zero and you'll be done

00:41:40.680 --> 00:41:46.800
encoding it if your single token

00:41:42.760 --> 00:41:51.920
sequence is B

00:41:46.800 --> 00:41:56.520
then um one overlaps with b and c so now

00:41:51.920 --> 00:42:00.920
you need to further split this up into

00:41:56.520 --> 00:42:00.920
uh o and one and you can see

00:42:04.880 --> 00:42:11.440
that let make sure I did that right yeah

00:42:08.359 --> 00:42:11.440
you can you can see

00:42:15.599 --> 00:42:25.720
that one zero is entirely encompassed by

00:42:19.680 --> 00:42:29.200
uh by B so now B is one Z and C uh C is

00:42:25.720 --> 00:42:32.359
not L encompassed by that so you would

00:42:29.200 --> 00:42:39.240
need to further break this up and say

00:42:32.359 --> 00:42:41.880
it's Z one here and now one one

00:42:39.240 --> 00:42:45.520
one is encompassed by this so you would

00:42:41.880 --> 00:42:48.680
get uh you would get C if it was 111 and

00:42:45.520 --> 00:42:51.119
so every every sequence that started

00:42:48.680 --> 00:42:53.000
with zero would start out with a every

00:42:51.119 --> 00:42:54.960
sequence that started out with one zero

00:42:53.000 --> 00:42:57.200
would start with b and every sequence

00:42:54.960 --> 00:43:02.079
that started with 11 one1

00:42:57.200 --> 00:43:04.920
start um and so then you can look at the

00:43:02.079 --> 00:43:06.960
next word and let's say we're using a

00:43:04.920 --> 00:43:09.839
unigram model if we're using a unigram

00:43:06.960 --> 00:43:12.960
model for the next uh the next token

00:43:09.839 --> 00:43:18.200
let's say the next token is C

00:43:12.960 --> 00:43:23.640
so now the next token being C we already

00:43:18.200 --> 00:43:27.920
have B and now we take we subdivide

00:43:23.640 --> 00:43:33.040
B into

00:43:27.920 --> 00:43:35.720
a BC ba a BB and BC and then we find the

00:43:33.040 --> 00:43:40.720
next binary sequence that is entirely

00:43:35.720 --> 00:43:44.000
encompassed by uh BC by this like

00:43:40.720 --> 00:43:45.359
interval and so the moment we find a a

00:43:44.000 --> 00:43:48.520
binary sequence that's entirely

00:43:45.359 --> 00:43:50.599
encompassed by the interval uh then that

00:43:48.520 --> 00:43:53.400
is the the sequence that we can use to

00:43:50.599 --> 00:43:54.640
represent that SC and so um if you're

00:43:53.400 --> 00:43:56.520
interested in this you can look up the

00:43:54.640 --> 00:44:00.400
arithmetic coding on on wikip it's

00:43:56.520 --> 00:44:02.079
pretty fascinating but basically um here

00:44:00.400 --> 00:44:04.040
this is showing the example of the

00:44:02.079 --> 00:44:07.160
unigram model where the probabilities

00:44:04.040 --> 00:44:10.240
don't change based on the context but

00:44:07.160 --> 00:44:13.000
what if we knew that

00:44:10.240 --> 00:44:15.599
c had a really high probability of

00:44:13.000 --> 00:44:22.160
following B so if that's the case now we

00:44:15.599 --> 00:44:24.559
have like a a b c here um like based on

00:44:22.160 --> 00:44:25.880
our our byr model or neural language

00:44:24.559 --> 00:44:29.319
model or something like that so now this

00:44:25.880 --> 00:44:31.240
is interval is much much larger so it's

00:44:29.319 --> 00:44:35.079
much more likely to entirely Encompass a

00:44:31.240 --> 00:44:39.720
shorter string and because of that the

00:44:35.079 --> 00:44:42.440
um the output can be much shorter and so

00:44:39.720 --> 00:44:45.760
if you use this arithmetic encoding um

00:44:42.440 --> 00:44:49.440
over a very long sequence of outputs

00:44:45.760 --> 00:44:52.440
your the length of the sequence that is

00:44:49.440 --> 00:44:56.000
needed to encode this uh this particular

00:44:52.440 --> 00:45:00.359
output is going to be essentially um the

00:44:56.000 --> 00:45:03.319
number of bits according to times the

00:45:00.359 --> 00:45:06.480
times the sequence so this is very

00:45:03.319 --> 00:45:10.000
directly connected to like compression

00:45:06.480 --> 00:45:13.160
and information Theory and stuff like

00:45:10.000 --> 00:45:15.359
that so that that's where entropy comes

00:45:13.160 --> 00:45:17.680
from uh are are there any questions

00:45:15.359 --> 00:45:17.680
about

00:45:19.319 --> 00:45:22.319
this

00:45:24.880 --> 00:45:28.119
yeah

00:45:26.800 --> 00:45:31.880
uh for

00:45:28.119 --> 00:45:34.319
c um so

00:45:31.880 --> 00:45:36.599
111 is

00:45:34.319 --> 00:45:37.920
because let me let me see if I can do

00:45:36.599 --> 00:45:40.559
this

00:45:37.920 --> 00:45:44.240
again

00:45:40.559 --> 00:45:44.240
so I had one

00:45:46.079 --> 00:45:54.520
one so here this interval is

00:45:50.920 --> 00:45:56.839
one this interval is one one this

00:45:54.520 --> 00:46:00.079
interval is 111

00:45:56.839 --> 00:46:03.520
and 111 is the first interval that is

00:46:00.079 --> 00:46:05.520
entirely overlapping with with c um and

00:46:03.520 --> 00:46:08.760
it's not one Z because one one Z is

00:46:05.520 --> 00:46:08.760
overlaping with b and

00:46:09.960 --> 00:46:13.599
c so which

00:46:14.280 --> 00:46:21.720
Cas so which case one

00:46:20.160 --> 00:46:24.800
Z

00:46:21.720 --> 00:46:26.319
one one one

00:46:24.800 --> 00:46:30.800
Z

00:46:26.319 --> 00:46:30.800
when would you use 110 to represent

00:46:32.119 --> 00:46:38.839
something it's a good question I guess

00:46:36.119 --> 00:46:40.599
maybe you wouldn't which seems a little

00:46:38.839 --> 00:46:43.280
bit wasteful

00:46:40.599 --> 00:46:46.160
so let me let me think about that I

00:46:43.280 --> 00:46:49.920
think um it might be the case that you

00:46:46.160 --> 00:46:52.319
just don't use it um

00:46:49.920 --> 00:46:53.559
but yeah I'll try to think about that a

00:46:52.319 --> 00:46:55.920
little bit more because it seems like

00:46:53.559 --> 00:46:59.200
you should use every bet string right so

00:46:55.920 --> 00:47:01.559
um yeah if anybody uh has has the answer

00:46:59.200 --> 00:47:05.160
I'd be happy to hear it otherwise I take

00:47:01.559 --> 00:47:07.079
you cool um so next thing is perplexity

00:47:05.160 --> 00:47:10.640
so this is another one that you see

00:47:07.079 --> 00:47:13.240
commonly and um so perplexity is

00:47:10.640 --> 00:47:16.880
basically two to the ENT uh two to the

00:47:13.240 --> 00:47:20.760
per word entropy or e to the uh negative

00:47:16.880 --> 00:47:24.880
word level log likelihood in log space

00:47:20.760 --> 00:47:28.240
um and so this uh T larger tends to be

00:47:24.880 --> 00:47:32.559
better I'd like to do a little exercise

00:47:28.240 --> 00:47:34.599
to see uh if this works so like let's

00:47:32.559 --> 00:47:39.079
say we have one a dog sees a squirrel it

00:47:34.599 --> 00:47:40.960
will usually um and can anyone guess the

00:47:39.079 --> 00:47:43.480
next word just yell it

00:47:40.960 --> 00:47:46.400
out bar

00:47:43.480 --> 00:47:47.400
okay uh what about that what about

00:47:46.400 --> 00:47:50.400
something

00:47:47.400 --> 00:47:50.400
else

00:47:52.640 --> 00:47:57.520
Chase Run

00:47:54.720 --> 00:48:00.800
Run

00:47:57.520 --> 00:48:00.800
okay John

00:48:01.960 --> 00:48:05.280
John anything

00:48:07.000 --> 00:48:10.400
else any other

00:48:11.280 --> 00:48:16.960
ones so basically what this shows is

00:48:13.640 --> 00:48:16.960
humans are really bad language

00:48:17.160 --> 00:48:24.079
models so uh interestingly every single

00:48:21.520 --> 00:48:26.559
one of the words you predicted here is a

00:48:24.079 --> 00:48:32.240
uh a regular verb

00:48:26.559 --> 00:48:35.200
um but in natural language model gpt2 uh

00:48:32.240 --> 00:48:38.079
the first thing it predicts is B uh

00:48:35.200 --> 00:48:40.440
which is kind of a like the Cula there's

00:48:38.079 --> 00:48:43.400
also start and that will be like start

00:48:40.440 --> 00:48:44.880
running start something um and humans

00:48:43.400 --> 00:48:46.400
actually are really bad at doing this

00:48:44.880 --> 00:48:49.079
are really bad at predicting next words

00:48:46.400 --> 00:48:51.760
we're not trained that way um and so uh

00:48:49.079 --> 00:48:54.319
we end up having these biases but anyway

00:48:51.760 --> 00:48:55.799
um the reason why I did this quiz was

00:48:54.319 --> 00:48:57.280
because that's essentially what

00:48:55.799 --> 00:49:01.160
perplexity

00:48:57.280 --> 00:49:02.680
means um and what what perplexity is is

00:49:01.160 --> 00:49:04.559
it's the number of times you'd have to

00:49:02.680 --> 00:49:07.000
sample from the probability distribution

00:49:04.559 --> 00:49:09.200
before you get the answer right so you

00:49:07.000 --> 00:49:11.160
were a little bit biased here because we

00:49:09.200 --> 00:49:13.359
were doing sampling without replacement

00:49:11.160 --> 00:49:15.480
so like nobody was actually picking a

00:49:13.359 --> 00:49:17.000
word that had already been said but it's

00:49:15.480 --> 00:49:18.319
essentially like if you guessed over and

00:49:17.000 --> 00:49:20.839
over and over again how many times would

00:49:18.319 --> 00:49:22.720
you need until you get it right and so

00:49:20.839 --> 00:49:25.119
here like if the actual answer was start

00:49:22.720 --> 00:49:27.480
the perplexity would be 4.66 so we'd

00:49:25.119 --> 00:49:30.240
expect language model to get it in uh

00:49:27.480 --> 00:49:34.400
four guesses uh between four and five

00:49:30.240 --> 00:49:38.559
guesses and you guys all did six so you

00:49:34.400 --> 00:49:41.599
lose um so uh another important thing to

00:49:38.559 --> 00:49:42.799
mention is evaluation in vocabulary uh

00:49:41.599 --> 00:49:44.880
so for fair

00:49:42.799 --> 00:49:47.319
comparison um make sure that the

00:49:44.880 --> 00:49:49.559
denominator is the same so uh if you're

00:49:47.319 --> 00:49:51.559
calculating the perplexity make sure

00:49:49.559 --> 00:49:53.359
that you're dividing by the same number

00:49:51.559 --> 00:49:55.799
uh every time you're dividing by words

00:49:53.359 --> 00:49:58.520
if it's uh the other paper or whatever

00:49:55.799 --> 00:50:00.680
is dividing by words or like let's say

00:49:58.520 --> 00:50:02.160
you're comparing llama to gp2 they have

00:50:00.680 --> 00:50:04.880
different tokenizers so they'll have

00:50:02.160 --> 00:50:07.040
different numbers of tokens so comparing

00:50:04.880 --> 00:50:10.880
uh with different denominators is not uh

00:50:07.040 --> 00:50:12.440
not fair um if you're allowing unknown

00:50:10.880 --> 00:50:14.559
words or characters so if you allow the

00:50:12.440 --> 00:50:17.640
model to not predict

00:50:14.559 --> 00:50:19.119
any token then you need to be fair about

00:50:17.640 --> 00:50:22.040
that

00:50:19.119 --> 00:50:25.160
too um so I'd like to go into a few

00:50:22.040 --> 00:50:27.960
Alternatives these are very similar to

00:50:25.160 --> 00:50:29.400
the Network classifiers and bag of words

00:50:27.960 --> 00:50:30.680
classifiers that I talked about before

00:50:29.400 --> 00:50:32.480
so I'm going to go through them rather

00:50:30.680 --> 00:50:35.480
quickly because I think you should get

00:50:32.480 --> 00:50:38.119
the basic idea but basically the

00:50:35.480 --> 00:50:40.000
alternative is uh featued models so we

00:50:38.119 --> 00:50:42.559
calculate features of to account based

00:50:40.000 --> 00:50:44.599
models as featued models so we calculate

00:50:42.559 --> 00:50:46.880
features of the context and based on the

00:50:44.599 --> 00:50:48.280
features calculate probabilities

00:50:46.880 --> 00:50:50.480
optimize the feature weights using

00:50:48.280 --> 00:50:53.839
gradient descent uh

00:50:50.480 --> 00:50:56.119
Etc and so for example if we have uh

00:50:53.839 --> 00:50:58.880
input giving a

00:50:56.119 --> 00:51:02.960
uh we calculate features so um we might

00:50:58.880 --> 00:51:05.400
look up uh the word identity of the two

00:51:02.960 --> 00:51:08.240
previous words look up the word identity

00:51:05.400 --> 00:51:11.000
of the word uh directly previous add a

00:51:08.240 --> 00:51:13.480
bias add them all together get scores

00:51:11.000 --> 00:51:14.960
and calculate probabilities where each

00:51:13.480 --> 00:51:16.920
Vector is the size of the output

00:51:14.960 --> 00:51:19.680
vocabulary and feature weights are

00:51:16.920 --> 00:51:21.799
optimized using SGD so this is basically

00:51:19.680 --> 00:51:24.240
a bag of words classifier but it's a

00:51:21.799 --> 00:51:27.200
multiclass bag of words classifier over

00:51:24.240 --> 00:51:28.960
the next token so it's very similar to

00:51:27.200 --> 00:51:30.839
our classification task before except

00:51:28.960 --> 00:51:33.160
now instead of having two classes we

00:51:30.839 --> 00:51:36.280
have you know 10,000 classes or 100,000

00:51:33.160 --> 00:51:38.480
classes oh yeah sorry very quick aside

00:51:36.280 --> 00:51:40.280
um these were actually invented by Rony

00:51:38.480 --> 00:51:41.440
Rosenfeld who's the head of the machine

00:51:40.280 --> 00:51:45.119
learning department at the end the

00:51:41.440 --> 00:51:47.799
machine learning Department uh so um 27

00:51:45.119 --> 00:51:50.760
years ago I guess so he has even more

00:51:47.799 --> 00:51:52.680
experience large language modeling than

00:51:50.760 --> 00:51:55.880
um

00:51:52.680 --> 00:51:58.599
cool so um the one difference with a bag

00:51:55.880 --> 00:52:02.119
of words classifier is

00:51:58.599 --> 00:52:05.480
um we we have

00:52:02.119 --> 00:52:07.640
biases um and we have the probability

00:52:05.480 --> 00:52:09.400
Vector given the previous word but

00:52:07.640 --> 00:52:11.720
instead of using a bag of words this

00:52:09.400 --> 00:52:15.440
actually is using uh How likely is it

00:52:11.720 --> 00:52:16.960
giving given two words previous so uh

00:52:15.440 --> 00:52:18.040
the feature design would be a little bit

00:52:16.960 --> 00:52:19.119
different and that would give you a

00:52:18.040 --> 00:52:22.920
total

00:52:19.119 --> 00:52:24.359
score um as a reminder uh last time we

00:52:22.920 --> 00:52:26.440
did a training algorithm where we

00:52:24.359 --> 00:52:27.480
calculated gradients loss function with

00:52:26.440 --> 00:52:29.960
respect to the

00:52:27.480 --> 00:52:32.319
parameters and uh we can use the chain

00:52:29.960 --> 00:52:33.839
Rule and back propagation and updates to

00:52:32.319 --> 00:52:36.400
move in the direction that increases

00:52:33.839 --> 00:52:39.040
enough so nothing extremely different

00:52:36.400 --> 00:52:42.640
from what we had for our

00:52:39.040 --> 00:52:44.240
B um similarly this solves some problems

00:52:42.640 --> 00:52:47.240
so this didn't solve the problem of

00:52:44.240 --> 00:52:49.119
sharing strength among similar words it

00:52:47.240 --> 00:52:50.839
did solve the problem of conditioning on

00:52:49.119 --> 00:52:52.839
context with intervening words because

00:52:50.839 --> 00:52:56.920
now we can condition directly on Doctor

00:52:52.839 --> 00:52:59.680
without having to um combine with

00:52:56.920 --> 00:53:01.200
gitrid um and it doesn't necessarily

00:52:59.680 --> 00:53:03.480
handle longdistance dependencies because

00:53:01.200 --> 00:53:05.240
we're still limited in our context with

00:53:03.480 --> 00:53:09.079
the model I just

00:53:05.240 --> 00:53:11.920
described so um if we so sorry back to

00:53:09.079 --> 00:53:13.480
neural networks is what I should say um

00:53:11.920 --> 00:53:15.160
so if we have a feedforward neural

00:53:13.480 --> 00:53:18.480
network language model the way this

00:53:15.160 --> 00:53:20.400
could work is instead of looking up

00:53:18.480 --> 00:53:23.079
discrete features uh like we had in a

00:53:20.400 --> 00:53:25.960
bag of words model uh we would look up

00:53:23.079 --> 00:53:27.400
dents embeddings and so we concatenate

00:53:25.960 --> 00:53:29.359
together these dense

00:53:27.400 --> 00:53:32.319
embeddings and based on the dense

00:53:29.359 --> 00:53:34.599
embeddings uh we do some sort of uh

00:53:32.319 --> 00:53:36.079
intermediate layer transforms to extract

00:53:34.599 --> 00:53:37.200
features like we did for our neural

00:53:36.079 --> 00:53:39.359
network based

00:53:37.200 --> 00:53:41.520
classifier um we multiply this by

00:53:39.359 --> 00:53:43.559
weights uh we have a bias and we

00:53:41.520 --> 00:53:46.559
calculate

00:53:43.559 --> 00:53:49.200
scores and uh then we take a soft Max to

00:53:46.559 --> 00:53:49.200
do

00:53:50.400 --> 00:53:55.799
classification so um this can calculate

00:53:53.359 --> 00:53:58.000
combination features uh like we we also

00:53:55.799 --> 00:54:02.280
used in our uh neural network based

00:53:58.000 --> 00:54:04.119
classifiers so um this could uh give us

00:54:02.280 --> 00:54:05.760
a positive number for example if the

00:54:04.119 --> 00:54:07.760
previous word is a determiner and the

00:54:05.760 --> 00:54:10.440
second previous word is a verb so that

00:54:07.760 --> 00:54:14.520
would be like uh in giving and then that

00:54:10.440 --> 00:54:14.520
would allow us upway to that particular

00:54:15.000 --> 00:54:19.559
examples um so this allows us to share

00:54:17.640 --> 00:54:21.640
strength in various places in our model

00:54:19.559 --> 00:54:23.520
which was also You Know instrumental in

00:54:21.640 --> 00:54:25.599
making our our neural network

00:54:23.520 --> 00:54:28.000
classifiers work for similar work and

00:54:25.599 --> 00:54:30.119
stuff and so these would be word

00:54:28.000 --> 00:54:32.160
embeddings so similar words get similar

00:54:30.119 --> 00:54:35.079
embeddings another really important

00:54:32.160 --> 00:54:38.480
thing is uh similar output words also

00:54:35.079 --> 00:54:41.839
get similar rows in The softmax Matrix

00:54:38.480 --> 00:54:44.440
and so here remember if you remember

00:54:41.839 --> 00:54:48.240
from last class this was a big Matrix

00:54:44.440 --> 00:54:50.400
where the size of the Matrix was the

00:54:48.240 --> 00:54:53.319
number of vocabulary items times the

00:54:50.400 --> 00:54:55.920
size of a word embedding this is also a

00:54:53.319 --> 00:54:58.319
matrix where this is

00:54:55.920 --> 00:55:02.200
the number of vocabulary items times the

00:54:58.319 --> 00:55:04.160
size of a context embedding gr and so

00:55:02.200 --> 00:55:06.160
these will also be similar because words

00:55:04.160 --> 00:55:08.280
that appear in similar contexts will

00:55:06.160 --> 00:55:11.920
also you know want similar embeddings so

00:55:08.280 --> 00:55:15.119
they get uploaded in at the same

00:55:11.920 --> 00:55:17.119
time and similar hidden States will have

00:55:15.119 --> 00:55:19.799
similar context so ideally like if you

00:55:17.119 --> 00:55:20.920
have giving a or delivering a or

00:55:19.799 --> 00:55:22.680
something like that those would be

00:55:20.920 --> 00:55:27.000
similar contexts so they would get

00:55:22.680 --> 00:55:27.000
similar purple embeddings out out of the

00:55:28.440 --> 00:55:31.599
so one trick that's widely used in

00:55:30.200 --> 00:55:34.960
language model that further takes

00:55:31.599 --> 00:55:38.799
advantage of this is uh tying

00:55:34.960 --> 00:55:44.160
embeddings so here what this does is

00:55:38.799 --> 00:55:48.280
sharing parameters between this um

00:55:44.160 --> 00:55:49.920
lookup Matrix here and this uh Matrix

00:55:48.280 --> 00:55:51.119
over here that we use for calculating

00:55:49.920 --> 00:55:56.200
the

00:55:51.119 --> 00:55:58.839
softmax and um the reason why this is

00:55:56.200 --> 00:56:00.559
useful is twofold number one it gives

00:55:58.839 --> 00:56:02.079
you essentially more training data to

00:56:00.559 --> 00:56:04.440
learn these embeddings because instead

00:56:02.079 --> 00:56:05.799
of learning the embeddings whenever a

00:56:04.440 --> 00:56:08.520
word is in

00:56:05.799 --> 00:56:10.599
context separately from learning the

00:56:08.520 --> 00:56:13.520
embeddings whenever a word is predicted

00:56:10.599 --> 00:56:15.480
you learn the the same embedding Matrix

00:56:13.520 --> 00:56:19.319
whenever the word is in the context or

00:56:15.480 --> 00:56:21.520
whatever it's predicted and so um that

00:56:19.319 --> 00:56:24.119
makes it more accurate to learn these uh

00:56:21.520 --> 00:56:26.960
embeddings well another thing is the

00:56:24.119 --> 00:56:31.119
embedding mat can actually be very large

00:56:26.960 --> 00:56:34.920
so like let's say we have aab of

00:56:31.119 --> 00:56:37.520
10 100,000 and we have an embedding a

00:56:34.920 --> 00:56:40.799
word embedding size of like 512 or

00:56:37.520 --> 00:56:45.319
something like that

00:56:40.799 --> 00:56:45.319
that's um 51 million

00:56:46.839 --> 00:56:52.440
parameters um and this doesn't sound

00:56:49.559 --> 00:56:55.520
like a lot of parameters at first but it

00:56:52.440 --> 00:56:57.880
actually is a lot to learn when um

00:56:55.520 --> 00:57:01.000
these get updated relatively

00:56:57.880 --> 00:57:03.400
infrequently uh because

00:57:01.000 --> 00:57:06.079
um these get updated relatively

00:57:03.400 --> 00:57:07.960
infrequently because they only are

00:57:06.079 --> 00:57:09.559
updated whenever that word or token

00:57:07.960 --> 00:57:12.319
actually appears in your training data

00:57:09.559 --> 00:57:14.119
so um this can be a good thing for

00:57:12.319 --> 00:57:16.319
parameter savings parameter efficiency

00:57:14.119 --> 00:57:16.319
as

00:57:16.440 --> 00:57:22.520
well um so this uh solves most of the

00:57:19.599 --> 00:57:24.319
problems here um but it doesn't solve

00:57:22.520 --> 00:57:26.839
the problem of longdistance dependencies

00:57:24.319 --> 00:57:29.839
because still limited by the overall

00:57:26.839 --> 00:57:31.359
length of uh the context that we're

00:57:29.839 --> 00:57:32.520
concatenating together here sure we

00:57:31.359 --> 00:57:35.760
could make that longer but that would

00:57:32.520 --> 00:57:37.200
make our model larger and um and bring

00:57:35.760 --> 00:57:39.720
various

00:57:37.200 --> 00:57:42.520
issues and so what I'm going to talk

00:57:39.720 --> 00:57:44.599
about in on thur day is how we solve

00:57:42.520 --> 00:57:47.559
this problem of modeling long contexts

00:57:44.599 --> 00:57:49.720
so how do we um build recurrent neural

00:57:47.559 --> 00:57:52.559
networks uh how do we build

00:57:49.720 --> 00:57:54.960
convolutional uh convolutional networks

00:57:52.559 --> 00:57:57.520
or how do we build attention based

00:57:54.960 --> 00:58:00.720
Transformer models and these are all

00:57:57.520 --> 00:58:02.119
options that are used um Transformers

00:58:00.720 --> 00:58:04.359
are kind of

00:58:02.119 --> 00:58:06.039
the the main thing that people use

00:58:04.359 --> 00:58:08.400
nowadays but there's a lot of versions

00:58:06.039 --> 00:58:11.880
of Transformers that borrow ideas from

00:58:08.400 --> 00:58:14.960
recurrent uh and convolutional models

00:58:11.880 --> 00:58:17.359
um recently a lot of long context models

00:58:14.960 --> 00:58:19.440
us use ideas from recurrent networks and

00:58:17.359 --> 00:58:22.160
a lot of for example speech models or

00:58:19.440 --> 00:58:24.160
things like or image models use ideas

00:58:22.160 --> 00:58:25.920
from convolutional networks so I think

00:58:24.160 --> 00:58:28.760
learning all but at the same time is a

00:58:25.920 --> 00:58:32.160
good idea in comparing

00:58:28.760 --> 00:58:34.319
them cool uh any any questions about

00:58:32.160 --> 00:58:35.799
this part I went through this kind of

00:58:34.319 --> 00:58:37.319
quickly because it's pretty similar to

00:58:35.799 --> 00:58:40.079
the the classification stuff that we

00:58:37.319 --> 00:58:42.680
covered last time but uh any any things

00:58:40.079 --> 00:58:42.680
that people want to

00:58:43.880 --> 00:58:49.039
ask okay so next I'm going to talk about

00:58:46.839 --> 00:58:51.559
a few other desiderata of language

00:58:49.039 --> 00:58:53.039
models so the next one is really really

00:58:51.559 --> 00:58:55.640
important it's a concept I want

00:58:53.039 --> 00:58:57.640
everybody to know I actually

00:58:55.640 --> 00:58:59.520
taught this informally up until this

00:58:57.640 --> 00:59:02.039
class but now I I actually made slides

00:58:59.520 --> 00:59:05.079
for it starting this time which is

00:59:02.039 --> 00:59:07.240
calibration so the idea of calibration

00:59:05.079 --> 00:59:10.200
is that the model quote unquote knows

00:59:07.240 --> 00:59:14.559
when it knows or the the fact that it is

00:59:10.200 --> 00:59:17.480
able to provide a a good answer um uh

00:59:14.559 --> 00:59:21.640
provide a good confidence in its answer

00:59:17.480 --> 00:59:23.640
and more formally this can be specified

00:59:21.640 --> 00:59:25.240
as

00:59:23.640 --> 00:59:27.799
the

00:59:25.240 --> 00:59:29.200
feature that the model probability of

00:59:27.799 --> 00:59:33.119
the answer matches the actual

00:59:29.200 --> 00:59:37.319
probability of getting it right um and

00:59:33.119 --> 00:59:37.319
so what this means

00:59:41.960 --> 00:59:47.480
is the

00:59:44.240 --> 00:59:51.839
probability of the

00:59:47.480 --> 00:59:51.839
answer um is

00:59:52.720 --> 00:59:59.880
correct given the fact that

00:59:56.319 --> 00:59:59.880
the model

01:00:00.160 --> 01:00:07.440
probability is equal to

01:00:03.640 --> 01:00:07.440
P is equal to

01:00:08.559 --> 01:00:12.760
ke

01:00:10.480 --> 01:00:15.319
so I know this is a little bit hard to

01:00:12.760 --> 01:00:18.240
parse I it always took me like a few

01:00:15.319 --> 01:00:21.720
seconds to parse before I uh like when I

01:00:18.240 --> 01:00:25.160
looked at it but basically if the model

01:00:21.720 --> 01:00:26.920
if the model says the probability of it

01:00:25.160 --> 01:00:29.440
being correct is

01:00:26.920 --> 01:00:33.559
0.7 then the probability that the answer

01:00:29.440 --> 01:00:35.960
is correct is actually 0.7 so um you

01:00:33.559 --> 01:00:41.520
know if it says uh the probability is

01:00:35.960 --> 01:00:41.520
0.7 100 times then it will be right 70

01:00:43.640 --> 01:00:52.160
times and so the way we formalize this

01:00:48.039 --> 01:00:55.200
um is is by this uh it was proposed by

01:00:52.160 --> 01:00:57.760
this seminal paper by gu it all in

01:00:55.200 --> 01:01:00.319
2017

01:00:57.760 --> 01:01:03.319
and

01:01:00.319 --> 01:01:05.520
unfortunately this data itself is hard

01:01:03.319 --> 01:01:08.119
to collect

01:01:05.520 --> 01:01:11.200
because the model probability is always

01:01:08.119 --> 01:01:13.359
different right and so if the model

01:01:11.200 --> 01:01:15.359
probability is like if the model

01:01:13.359 --> 01:01:20.480
probability was actually 0.7 that'd be

01:01:15.359 --> 01:01:22.000
nice but actually it's 0.793 to 6 8 5

01:01:20.480 --> 01:01:24.599
and you never get another example where

01:01:22.000 --> 01:01:26.319
the probability is exactly the same so

01:01:24.599 --> 01:01:28.280
what we do instead is we divide the

01:01:26.319 --> 01:01:30.240
model probabilities into buckets so we

01:01:28.280 --> 01:01:32.880
say the model probability is between 0

01:01:30.240 --> 01:01:36.599
and 0.1 we say the model probability is

01:01:32.880 --> 01:01:40.319
between 0.1 and 0.2 0.2 and 0.3 so we

01:01:36.599 --> 01:01:44.599
create buckets like this like these and

01:01:40.319 --> 01:01:46.520
then we looked at the model confidence

01:01:44.599 --> 01:01:52.839
the average model confidence within that

01:01:46.520 --> 01:01:55.000
bucket so maybe uh between 0.1 and 0 uh

01:01:52.839 --> 01:01:58.000
between 0 and 0.1 the model confidence

01:01:55.000 --> 01:02:00.920
on average is 0 055 or something like

01:01:58.000 --> 01:02:02.640
that so that would be this T here and

01:02:00.920 --> 01:02:05.079
then the accuracy is how often did it

01:02:02.640 --> 01:02:06.680
actually get a correct and this can be

01:02:05.079 --> 01:02:09.720
plotted in this thing called a

01:02:06.680 --> 01:02:15.039
reliability diagram and the reliability

01:02:09.720 --> 01:02:17.599
diagram basically um the the

01:02:15.039 --> 01:02:20.359
outputs uh

01:02:17.599 --> 01:02:26.359
here so this is

01:02:20.359 --> 01:02:26.359
um the this is the model

01:02:27.520 --> 01:02:34.119
yeah I think the red is the model

01:02:30.760 --> 01:02:36.400
um expected probability and then the

01:02:34.119 --> 01:02:40.559
blue uh the blue is the actual

01:02:36.400 --> 01:02:43.240
probability and then um

01:02:40.559 --> 01:02:45.160
the difference between the expected and

01:02:43.240 --> 01:02:47.160
the actual probability is kind of like

01:02:45.160 --> 01:02:48.359
the penalty there is how how poorly

01:02:47.160 --> 01:02:52.000
calibrated

01:02:48.359 --> 01:02:55.880
the and one really important thing to

01:02:52.000 --> 01:02:58.440
know is that calibration in accuracy are

01:02:55.880 --> 01:03:00.599
not necessarily they don't go hand inand

01:02:58.440 --> 01:03:02.359
uh they do to some extent but they don't

01:03:00.599 --> 01:03:06.440
uh they don't necessarily go hand in

01:03:02.359 --> 01:03:06.440
hand and

01:03:07.200 --> 01:03:14.319
the example on the left is a a bad model

01:03:11.200 --> 01:03:16.279
but a well calibrated so its accuracy is

01:03:14.319 --> 01:03:18.720
uh its error is

01:03:16.279 --> 01:03:20.000
44.9% um but it's well calibrated as you

01:03:18.720 --> 01:03:21.440
can see like when it says it knows the

01:03:20.000 --> 01:03:23.880
answer it knows the answer when it

01:03:21.440 --> 01:03:27.799
doesn't answer does this model on the

01:03:23.880 --> 01:03:30.000
other hand has better erir and um but

01:03:27.799 --> 01:03:31.880
worse calibration so the reason why is

01:03:30.000 --> 01:03:36.680
the model is very very confident all the

01:03:31.880 --> 01:03:39.640
time and usually what happens is um

01:03:36.680 --> 01:03:41.200
models that overfit to the data

01:03:39.640 --> 01:03:43.359
especially when you do early stopping on

01:03:41.200 --> 01:03:44.760
something like accuracy uh when you stop

01:03:43.359 --> 01:03:47.279
the training on something like accuracy

01:03:44.760 --> 01:03:49.960
will become very overconfident and uh

01:03:47.279 --> 01:03:52.599
give confidence estimates um that are in

01:03:49.960 --> 01:03:54.000
cor like this so this is important to

01:03:52.599 --> 01:03:56.079
know and the reason why it's important

01:03:54.000 --> 01:03:58.000
to know is actually because you know

01:03:56.079 --> 01:04:00.960
models are very good at making up things

01:03:58.000 --> 01:04:02.359
that aren't actually correct nowadays um

01:04:00.960 --> 01:04:04.920
and but if you have a really well

01:04:02.359 --> 01:04:07.760
calibrated model you could at least say

01:04:04.920 --> 01:04:09.920
with what confidence you have this

01:04:07.760 --> 01:04:12.760
working so how do you calculate the

01:04:09.920 --> 01:04:14.160
probability of an answer so H yeah sorry

01:04:12.760 --> 01:04:17.599
uh yes

01:04:14.160 --> 01:04:17.599
yes yeah please

01:04:17.799 --> 01:04:26.559
go the probability of percent or

01:04:23.200 --> 01:04:28.039
percent um usually this would be for a

01:04:26.559 --> 01:04:29.599
generated output because you want to

01:04:28.039 --> 01:04:32.559
know the the probability that the

01:04:29.599 --> 01:04:32.559
generated output is

01:04:53.160 --> 01:04:56.160
cor

01:05:01.079 --> 01:05:06.319
great that's what I'm about to talk

01:05:03.000 --> 01:05:07.839
about so perfect perfect question um so

01:05:06.319 --> 01:05:10.160
how do we calculate the answer

01:05:07.839 --> 01:05:13.279
probability or um how do we calculate

01:05:10.160 --> 01:05:15.039
the confidence in an answer um we're

01:05:13.279 --> 01:05:18.319
actually going to go into more detail

01:05:15.039 --> 01:05:20.760
about this um in a a later class but the

01:05:18.319 --> 01:05:23.200
first thing is probability of the answer

01:05:20.760 --> 01:05:25.799
and this is easy when there's a single

01:05:23.200 --> 01:05:29.079
answer um like if there's only one

01:05:25.799 --> 01:05:31.839
correct answer and you want your model

01:05:29.079 --> 01:05:34.160
to be solving math problems and you want

01:05:31.839 --> 01:05:38.319
it to return only the answer and nothing

01:05:34.160 --> 01:05:40.760
else if it returns anything else like it

01:05:38.319 --> 01:05:44.920
won't work then you can just use the

01:05:40.760 --> 01:05:47.119
probability of the answer but what

01:05:44.920 --> 01:05:49.559
if

01:05:47.119 --> 01:05:52.000
um what if there are multiple acceptable

01:05:49.559 --> 01:05:54.680
answers um and maybe a perfect example

01:05:52.000 --> 01:06:02.240
of that is like where is CMU located

01:05:54.680 --> 01:06:04.400
or um uh where where are we right now um

01:06:02.240 --> 01:06:06.960
if the answer is where are we right

01:06:04.400 --> 01:06:08.880
now um could be

01:06:06.960 --> 01:06:12.880
Pittsburgh could be

01:06:08.880 --> 01:06:12.880
CMU could be carnegy

01:06:16.200 --> 01:06:24.440
melon could be other other things like

01:06:18.760 --> 01:06:26.760
this right um and so another way that

01:06:24.440 --> 01:06:28.319
you can calculate the confidence is

01:06:26.760 --> 01:06:31.240
calculating the probability of the

01:06:28.319 --> 01:06:33.680
answer plus uh you know paraphrases of

01:06:31.240 --> 01:06:35.799
the answer or other uh other things like

01:06:33.680 --> 01:06:37.680
this and so then you would just sum the

01:06:35.799 --> 01:06:38.839
probability over all the qu like

01:06:37.680 --> 01:06:41.680
acceptable

01:06:38.839 --> 01:06:45.359
answers

01:06:41.680 --> 01:06:47.680
um another thing that you can do is um

01:06:45.359 --> 01:06:49.279
sample multiple outputs and count the

01:06:47.680 --> 01:06:51.000
number of times you get a particular

01:06:49.279 --> 01:06:54.440
answer this doesn't solve the problem of

01:06:51.000 --> 01:06:58.119
paraphrasing ex paraphrases existing but

01:06:54.440 --> 01:06:59.880
it does solve the problem of uh it does

01:06:58.119 --> 01:07:01.480
solve two problems sometimes there are

01:06:59.880 --> 01:07:05.240
language models where you can't get

01:07:01.480 --> 01:07:06.640
probabilities out of them um this is not

01:07:05.240 --> 01:07:08.680
so much of a problem anymore with the

01:07:06.640 --> 01:07:11.240
GPT models because they're reintroducing

01:07:08.680 --> 01:07:12.440
the ability to get probabilities but um

01:07:11.240 --> 01:07:13.720
there are some models where you can just

01:07:12.440 --> 01:07:16.279
sample from them and you can't get

01:07:13.720 --> 01:07:18.680
probabilities out but also more

01:07:16.279 --> 01:07:21.039
importantly um sometimes when you're

01:07:18.680 --> 01:07:23.000
using things like uh Chain of Thought

01:07:21.039 --> 01:07:26.520
reasoning which I'll talk about in more

01:07:23.000 --> 01:07:29.839
detail but basically it's like um please

01:07:26.520 --> 01:07:31.480
solve this math problem and explain

01:07:29.839 --> 01:07:33.480
explain your solution and then if it

01:07:31.480 --> 01:07:35.119
will do that it will generate you know a

01:07:33.480 --> 01:07:36.279
really long explanation of how it got to

01:07:35.119 --> 01:07:40.119
the solution and then it will give you

01:07:36.279 --> 01:07:41.640
the answer at the very end and so then

01:07:40.119 --> 01:07:44.960
you can't calculate the probability of

01:07:41.640 --> 01:07:47.720
the actual like answer itself because

01:07:44.960 --> 01:07:49.359
there's this long reasoning chain in

01:07:47.720 --> 01:07:51.960
between and you have like all these

01:07:49.359 --> 01:07:53.559
other all that other text there but what

01:07:51.960 --> 01:07:55.480
you can do is you can sample those

01:07:53.559 --> 01:07:56.920
reasoning chains 100 times and then see

01:07:55.480 --> 01:07:59.599
how many times you got a particular

01:07:56.920 --> 01:08:02.960
answer and that's actually a pretty um a

01:07:59.599 --> 01:08:06.079
Prett pretty reasonable way of uh

01:08:02.960 --> 01:08:09.000
getting a have

01:08:06.079 --> 01:08:11.200
yet this is my favorite one I I love how

01:08:09.000 --> 01:08:12.880
we can do this now it's just absolutely

01:08:11.200 --> 01:08:16.480
ridiculous but you could ask the model

01:08:12.880 --> 01:08:20.279
how confident it is and um it sometimes

01:08:16.480 --> 01:08:22.359
gives you a reasonable uh a reasonable

01:08:20.279 --> 01:08:24.600
answer um there's a really nice

01:08:22.359 --> 01:08:26.400
comparison of different methods uh in

01:08:24.600 --> 01:08:29.679
this paper which is also on on the

01:08:26.400 --> 01:08:31.960
website and basically long story short

01:08:29.679 --> 01:08:34.000
the conclusion from this paper is the

01:08:31.960 --> 01:08:35.640
sampling multiple outputs one is the

01:08:34.000 --> 01:08:36.839
best way to do it if you can't directly

01:08:35.640 --> 01:08:39.520
calculate

01:08:36.839 --> 01:08:41.359
probabilities um another thing that I'd

01:08:39.520 --> 01:08:42.600
like people to pay very close attention

01:08:41.359 --> 01:08:45.040
to is in the

01:08:42.600 --> 01:08:46.480
Generation Um in the generation class

01:08:45.040 --> 01:08:49.600
we're going to be talking about minimum

01:08:46.480 --> 01:08:52.600
based risk which is a Criterion for

01:08:49.600 --> 01:08:54.719
deciding how risky an output is and it's

01:08:52.600 --> 01:08:56.199
actually a really good uh confidence

01:08:54.719 --> 01:08:58.000
metric as well but I'm going to leave

01:08:56.199 --> 01:08:59.440
that till when we discuss it more detail

01:08:58.000 --> 01:09:02.759
with

01:08:59.440 --> 01:09:05.359
it um any any questions

01:09:02.759 --> 01:09:08.440
here okay

01:09:05.359 --> 01:09:10.480
cool um so the other Criterion uh this

01:09:08.440 --> 01:09:12.520
is just yet another Criterion that we

01:09:10.480 --> 01:09:15.239
would like language models to be good at

01:09:12.520 --> 01:09:17.600
um its efficiency and so basically the

01:09:15.239 --> 01:09:21.920
model is easy to run on limited Hardware

01:09:17.600 --> 01:09:25.400
by some you know uh metric of easy and

01:09:21.920 --> 01:09:29.319
some metrics that we like to talk about

01:09:25.400 --> 01:09:32.400
our parameter account so often you will

01:09:29.319 --> 01:09:34.239
see oh this is the best model under

01:09:32.400 --> 01:09:35.520
three billion parameters or this is the

01:09:34.239 --> 01:09:37.960
best model under seven billion

01:09:35.520 --> 01:09:39.600
parameters or um we trained a model with

01:09:37.960 --> 01:09:42.159
one trillion parameters or something

01:09:39.600 --> 01:09:44.719
like that you know

01:09:42.159 --> 01:09:46.839
uh the thing is parameter count doesn't

01:09:44.719 --> 01:09:49.640
really mean that much um from the point

01:09:46.839 --> 01:09:52.839
of view of like ease of using the model

01:09:49.640 --> 01:09:54.400
um unless you also think about other uh

01:09:52.839 --> 01:09:56.480
you know deser

01:09:54.400 --> 01:09:58.840
like just to give one example this is a

01:09:56.480 --> 01:10:00.880
parameter count um let's say you have a

01:09:58.840 --> 01:10:02.960
parameter count of 7 billion is that 7

01:10:00.880 --> 01:10:05.719
billion parameters at 32-bit Precision

01:10:02.960 --> 01:10:07.800
or is that 7 billion parameters at 4bit

01:10:05.719 --> 01:10:09.400
Precision um will make a huge difference

01:10:07.800 --> 01:10:12.960
in your memory footprint your speed

01:10:09.400 --> 01:10:14.920
other things like that um so some of the

01:10:12.960 --> 01:10:18.040
things that are more direct with respect

01:10:14.920 --> 01:10:19.800
to efficiency are memory usage um and

01:10:18.040 --> 01:10:22.440
there's two varieties of memory usage

01:10:19.800 --> 01:10:24.280
one is model uh model only memory usage

01:10:22.440 --> 01:10:27.120
so when you load loaded the model into

01:10:24.280 --> 01:10:29.120
memory uh how much space does it take

01:10:27.120 --> 01:10:31.159
and also Peak memory consumption when

01:10:29.120 --> 01:10:33.159
you run have run the model over a

01:10:31.159 --> 01:10:35.920
sequence of a certain length how much is

01:10:33.159 --> 01:10:40.040
it going to P so that's another

01:10:35.920 --> 01:10:43.000
thing another thing is latency um and

01:10:40.040 --> 01:10:46.440
with respect to latency this can be

01:10:43.000 --> 01:10:49.440
either how long does it take to start

01:10:46.440 --> 01:10:52.080
outputting the first token um and how

01:10:49.440 --> 01:10:54.840
long does it take to uh finish

01:10:52.080 --> 01:10:59.480
outputting uh a generation of a certain

01:10:54.840 --> 01:11:01.199
length and the first will have more to

01:10:59.480 --> 01:11:04.960
do with how long does it take to encode

01:11:01.199 --> 01:11:06.480
a sequence um which is usually faster

01:11:04.960 --> 01:11:09.080
than how long does it take to generate a

01:11:06.480 --> 01:11:11.360
sequence so this will have to do with

01:11:09.080 --> 01:11:13.000
like encoding time this will require

01:11:11.360 --> 01:11:15.880
encoding time of course but it will also

01:11:13.000 --> 01:11:15.880
require generation

01:11:16.280 --> 01:11:21.840
time also throughput so you know how

01:11:19.239 --> 01:11:23.679
much um how many sentences can you

01:11:21.840 --> 01:11:25.400
process in a certain amount of time so

01:11:23.679 --> 01:11:26.480
of these are kind of desad that you you

01:11:25.400 --> 01:11:29.000
would

01:11:26.480 --> 01:11:30.280
say um we're going to be talking about

01:11:29.000 --> 01:11:31.920
this more in the distillation and

01:11:30.280 --> 01:11:33.199
compression and generation algorithms

01:11:31.920 --> 01:11:35.640
classes so I won't go into a whole lot

01:11:33.199 --> 01:11:36.840
of detail about this but um it's just

01:11:35.640 --> 01:11:39.960
another thing that we want to be

01:11:36.840 --> 01:11:43.560
thinking about in addition to

01:11:39.960 --> 01:11:45.360
complexity um but since I'm I'm on the

01:11:43.560 --> 01:11:47.800
topic of efficiency I would like to talk

01:11:45.360 --> 01:11:49.480
just a little bit about it um in terms

01:11:47.800 --> 01:11:51.000
of especially things that will be useful

01:11:49.480 --> 01:11:53.600
for implementing your first

01:11:51.000 --> 01:11:55.840
assignment and uh one thing that every

01:11:53.600 --> 01:11:58.639
body should know about um if you've done

01:11:55.840 --> 01:11:59.920
any like deep learning with pytorch or

01:11:58.639 --> 01:12:02.639
something like this you already know

01:11:59.920 --> 01:12:05.880
about this probably but uh I think it's

01:12:02.639 --> 01:12:08.760
worth mentioning but basically mini

01:12:05.880 --> 01:12:12.120
batching or batching uh is uh very

01:12:08.760 --> 01:12:15.320
useful and the basic idea behind it is

01:12:12.120 --> 01:12:17.560
that on Modern Hardware if you do many

01:12:15.320 --> 01:12:20.520
of the same operations at once it's much

01:12:17.560 --> 01:12:24.320
faster than doing um

01:12:20.520 --> 01:12:25.480
like uh operations executively and

01:12:24.320 --> 01:12:27.280
that's especially the case if you're

01:12:25.480 --> 01:12:30.520
programming in an extremely slow

01:12:27.280 --> 01:12:33.239
programming language like python um I

01:12:30.520 --> 01:12:37.239
love python but it's slow I mean like

01:12:33.239 --> 01:12:38.719
there's no argument about that um and so

01:12:37.239 --> 01:12:40.520
what mini batching does is it combines

01:12:38.719 --> 01:12:43.600
together smaller operations into one big

01:12:40.520 --> 01:12:47.480
one and the basic idea uh for example if

01:12:43.600 --> 01:12:51.679
we want to calculate our um our linear

01:12:47.480 --> 01:12:56.560
layer with a t uh nonlinearity after it

01:12:51.679 --> 01:12:59.760
we will take several inputs X1 X2 X3

01:12:56.560 --> 01:13:02.040
concatenate them together and do a

01:12:59.760 --> 01:13:04.600
Matrix Matrix multiply instead of doing

01:13:02.040 --> 01:13:07.960
three Vector Matrix

01:13:04.600 --> 01:13:09.239
multiplies and so what we do is we take

01:13:07.960 --> 01:13:11.280
a whole bunch of examples we take like

01:13:09.239 --> 01:13:13.840
64 examples or something like that and

01:13:11.280 --> 01:13:18.000
we combine them together and calculate

01:13:13.840 --> 01:13:21.280
out thingsit one thing to know is that

01:13:18.000 --> 01:13:22.560
if you're working with sentences there's

01:13:21.280 --> 01:13:24.719
different ways you can calculate the

01:13:22.560 --> 01:13:27.360
size of your mini

01:13:24.719 --> 01:13:28.880
normally nowadays the thing that people

01:13:27.360 --> 01:13:30.400
do and the thing that I recommend is to

01:13:28.880 --> 01:13:31.679
calculate the size of your mini batches

01:13:30.400 --> 01:13:33.639
based on the number of tokens in the

01:13:31.679 --> 01:13:35.840
mini batch it used to be that you would

01:13:33.639 --> 01:13:39.719
do it based on the number of sequences

01:13:35.840 --> 01:13:43.800
but the the problem is um one like 50

01:13:39.719 --> 01:13:47.120
sequences of length like 100 is much

01:13:43.800 --> 01:13:49.480
more memory intensive than uh 50

01:13:47.120 --> 01:13:51.960
sequences of Link five and so you get

01:13:49.480 --> 01:13:53.920
these vastly varying these mini batches

01:13:51.960 --> 01:13:57.000
of vastly varying size and that's both

01:13:53.920 --> 01:13:59.800
bad for you know memory overflows and

01:13:57.000 --> 01:14:01.639
bad for um and bad for learning

01:13:59.800 --> 01:14:04.280
stability so I I definitely recommend

01:14:01.639 --> 01:14:06.880
doing it based on the number of

01:14:04.280 --> 01:14:09.080
comps uh another thing is gpus versus

01:14:06.880 --> 01:14:12.400
CPUs so

01:14:09.080 --> 01:14:14.600
um uh CPUs one way you can think of it

01:14:12.400 --> 01:14:17.320
is a CPUs kind of like a motorcycle it's

01:14:14.600 --> 01:14:19.600
very fast at picking up and doing a

01:14:17.320 --> 01:14:23.960
bunch of uh things very quickly

01:14:19.600 --> 01:14:26.600
accelerating uh into starting new uh new

01:14:23.960 --> 01:14:28.760
tasks a GPU is more like an airplane

01:14:26.600 --> 01:14:30.719
which uh you wait forever in line in

01:14:28.760 --> 01:14:33.360
security and

01:14:30.719 --> 01:14:34.800
then and then uh it takes a long time to

01:14:33.360 --> 01:14:40.400
get off the ground and start working but

01:14:34.800 --> 01:14:43.679
once it does it's extremely fast um and

01:14:40.400 --> 01:14:45.360
so if we do a simple example of how long

01:14:43.679 --> 01:14:47.600
does it take to do a Matrix Matrix

01:14:45.360 --> 01:14:49.040
multiply I calculated this a really long

01:14:47.600 --> 01:14:51.280
time ago it's probably horribly out of

01:14:49.040 --> 01:14:55.120
date now but the same general principle

01:14:51.280 --> 01:14:56.560
stands which is if we have have um the

01:14:55.120 --> 01:14:58.480
number of seconds that it takes to do a

01:14:56.560 --> 01:15:02.080
Matrix Matrix multiply doing one of size

01:14:58.480 --> 01:15:03.920
16 is actually faster on CPU because uh

01:15:02.080 --> 01:15:07.760
the overhead it takes to get started is

01:15:03.920 --> 01:15:10.880
very low but if you um once you start

01:15:07.760 --> 01:15:13.360
getting up to size like 128 by 128

01:15:10.880 --> 01:15:15.800
Matrix multiplies then doing it on GPU

01:15:13.360 --> 01:15:17.320
is faster and then um it's you know a

01:15:15.800 --> 01:15:19.679
100 times faster once you start getting

01:15:17.320 --> 01:15:21.600
up to very large matrices so um if

01:15:19.679 --> 01:15:24.000
you're dealing with very large networks

01:15:21.600 --> 01:15:26.800
handling a GPU is good

01:15:24.000 --> 01:15:30.159
um and this is the the speed up

01:15:26.800 --> 01:15:31.440
percentage um one thing I should mention

01:15:30.159 --> 01:15:34.239
is

01:15:31.440 --> 01:15:36.440
um compute with respect to like doing

01:15:34.239 --> 01:15:39.800
the assignments for this class if you

01:15:36.440 --> 01:15:43.199
have a relatively recent Mac you're kind

01:15:39.800 --> 01:15:44.760
of in luck because actually the gpus on

01:15:43.199 --> 01:15:47.239
the Mac are pretty fast and they're well

01:15:44.760 --> 01:15:48.960
integrated with um they're well

01:15:47.239 --> 01:15:52.080
integrated with pipor and other things

01:15:48.960 --> 01:15:53.440
like that so decently sized models maybe

01:15:52.080 --> 01:15:54.840
up to the size that you would need to

01:15:53.440 --> 01:15:57.840
run for assignment one or even

01:15:54.840 --> 01:16:00.880
assignment two might uh just run on your

01:15:57.840 --> 01:16:03.639
uh laptop computer um if you don't have

01:16:00.880 --> 01:16:05.280
a GPU uh that you have immediately

01:16:03.639 --> 01:16:06.760
accessible to you I we're going to

01:16:05.280 --> 01:16:08.400
recommend that you use collab where you

01:16:06.760 --> 01:16:10.120
can get a GPU uh for the first

01:16:08.400 --> 01:16:12.440
assignments and then we'll have plug

01:16:10.120 --> 01:16:15.159
reddits that you can use otherwise but

01:16:12.440 --> 01:16:16.800
um GPU is usually like something that

01:16:15.159 --> 01:16:18.440
you can get on the cloud or one that you

01:16:16.800 --> 01:16:21.080
have on your Mac or one that you have on

01:16:18.440 --> 01:16:24.600
your gaming computer or something like

01:16:21.080 --> 01:16:26.040
that um there's a few speed tricks that

01:16:24.600 --> 01:16:30.000
you should know for efficient GPU

01:16:26.040 --> 01:16:32.480
operations so um one mistake that people

01:16:30.000 --> 01:16:35.880
make when creating models is they repeat

01:16:32.480 --> 01:16:38.080
operations over and over again and um

01:16:35.880 --> 01:16:40.600
you don't want to be doing this so like

01:16:38.080 --> 01:16:43.239
for example um this is multiplying a

01:16:40.600 --> 01:16:45.320
matrix by a constant multiple times and

01:16:43.239 --> 01:16:46.880
if you're just using out of thee box pie

01:16:45.320 --> 01:16:49.280
torch this would be really bad because

01:16:46.880 --> 01:16:50.400
you'd be repeating the operation uh when

01:16:49.280 --> 01:16:52.679
it's not

01:16:50.400 --> 01:16:54.480
necessary um you can also reduce the

01:16:52.679 --> 01:16:57.360
number of operations that you need to

01:16:54.480 --> 01:17:00.320
use so uh use Matrix Matrix multiplies

01:16:57.360 --> 01:17:03.080
instead of Matrix Vector

01:17:00.320 --> 01:17:07.920
multiplies and another thing is uh

01:17:03.080 --> 01:17:10.719
reducing CPU GPU data movement and um so

01:17:07.920 --> 01:17:12.360
when you do try to move memory um when

01:17:10.719 --> 01:17:17.080
you do try to move memory try to do it

01:17:12.360 --> 01:17:20.040
as early as possible and as uh and as

01:17:17.080 --> 01:17:22.199
few times as possible and the reason why

01:17:20.040 --> 01:17:24.199
you want to move things early or start

01:17:22.199 --> 01:17:25.920
operations early is many GPU operations

01:17:24.199 --> 01:17:27.159
are asynchronous so you can start the

01:17:25.920 --> 01:17:28.800
operation and it will run in the

01:17:27.159 --> 01:17:33.120
background while other things are

01:17:28.800 --> 01:17:36.080
processing so um it's a good idea to try

01:17:33.120 --> 01:17:39.840
to um to optimize and you can also use

01:17:36.080 --> 01:17:42.360
your python profiler or um envidia GPU

01:17:39.840 --> 01:17:43.679
profilers to try to optimize these

01:17:42.360 --> 01:17:46.520
things as

01:17:43.679 --> 01:17:49.840
well cool that's all I have uh we're

01:17:46.520 --> 01:17:49.840
right at time