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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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00:11:57,800 --> 00:12:00,959
probability of x

286
00:12:02,120 --> 00:12:05,399
directly any

287
00:12:07,680 --> 00:12:12,760
ideas uh of big X sorry uh why don't we

288
00:12:11,079 --> 00:12:17,560
try to calculate the probability of this

289
00:12:12,760 --> 00:12:21,360
is great directly without deated the

290
00:12:17,560 --> 00:12:21,360
IND that

291
00:12:25,519 --> 00:12:31,560
possibility it could be word salid if

292
00:12:27,760 --> 00:12:35,279
you did it in a in a particular way yes

293
00:12:31,560 --> 00:12:35,279
um so that that's a good point

294
00:12:39,519 --> 00:12:47,000
yeah yeah so for example we talked about

295
00:12:43,760 --> 00:12:50,120
um uh we'll talk about

296
00:12:47,000 --> 00:12:51,920
models um or I I mentioned this briefly

297
00:12:50,120 --> 00:12:54,000
last time you can mention it in more

298
00:12:51,920 --> 00:12:55,639
detail this time but this is great we

299
00:12:54,000 --> 00:12:59,880
probably have never seen this before

300
00:12:55,639 --> 00:13:01,399
right so if we predict only things that

301
00:12:59,880 --> 00:13:03,199
we've seen before if we only assign a

302
00:13:01,399 --> 00:13:04,600
non-zero probability to the things we've

303
00:13:03,199 --> 00:13:06,000
seen before there's going to be lots of

304
00:13:04,600 --> 00:13:07,079
sentences that we've never seen before

305
00:13:06,000 --> 00:13:10,000
it makes it

306
00:13:07,079 --> 00:13:13,760
supercars um that that's basically close

307
00:13:10,000 --> 00:13:16,399
to what I wanted to say so um the reason

308
00:13:13,760 --> 00:13:18,040
why we don't typically do it with um

309
00:13:16,399 --> 00:13:21,240
predicting the whole sentence directly

310
00:13:18,040 --> 00:13:22,800
is because if we think about the size of

311
00:13:21,240 --> 00:13:24,959
the classification problem we need to

312
00:13:22,800 --> 00:13:27,880
solve in order to predict the next word

313
00:13:24,959 --> 00:13:30,320
it's a v uh where V is the size of the

314
00:13:27,880 --> 00:13:33,120
vocabulary but the size of the

315
00:13:30,320 --> 00:13:35,399
classification problem that we need to

316
00:13:33,120 --> 00:13:38,040
um we need to solve if we predict

317
00:13:35,399 --> 00:13:40,079
everything directly is V to the N where

318
00:13:38,040 --> 00:13:42,240
n is the length of the sequence and

319
00:13:40,079 --> 00:13:45,240
that's just huge the vocabulary is so

320
00:13:42,240 --> 00:13:48,440
big that it's hard to kind of uh know

321
00:13:45,240 --> 00:13:51,000
how we handle that so basically by doing

322
00:13:48,440 --> 00:13:53,160
this sort of decomposition we decompose

323
00:13:51,000 --> 00:13:56,440
this into uh

324
00:13:53,160 --> 00:13:58,120
n um prediction problems of size V and

325
00:13:56,440 --> 00:13:59,519
that's kind of just a lot more

326
00:13:58,120 --> 00:14:03,079
manageable for from the point of view of

327
00:13:59,519 --> 00:14:06,000
how we train uh know how we train

328
00:14:03,079 --> 00:14:09,399
models um that being said there are

329
00:14:06,000 --> 00:14:11,360
other Alternatives um something very

330
00:14:09,399 --> 00:14:13,920
widely known uh very widely used is

331
00:14:11,360 --> 00:14:16,440
called a MK language model um a mast

332
00:14:13,920 --> 00:14:19,480
language model is something like Bert or

333
00:14:16,440 --> 00:14:21,680
debera or Roberta or all of these models

334
00:14:19,480 --> 00:14:25,000
that you might have heard if you've been

335
00:14:21,680 --> 00:14:28,279
in MLP for more than two years I guess

336
00:14:25,000 --> 00:14:30,680
um and basically what they do is they

337
00:14:28,279 --> 00:14:30,680
predict

338
00:14:32,199 --> 00:14:37,480
uh they like mask out this word and they

339
00:14:34,839 --> 00:14:39,480
predict the middle word so they mask out

340
00:14:37,480 --> 00:14:41,440
is and then try to predict that given

341
00:14:39,480 --> 00:14:45,320
all the other words the problem with

342
00:14:41,440 --> 00:14:48,959
these models is uh twofold number one

343
00:14:45,320 --> 00:14:51,880
they don't actually give you a uh good

344
00:14:48,959 --> 00:14:55,399
probability here uh like a a properly

345
00:14:51,880 --> 00:14:57,800
formed probability here

346
00:14:55,399 --> 00:14:59,160
because this is true only as long as

347
00:14:57,800 --> 00:15:01,920
you're only conditioning on things that

348
00:14:59,160 --> 00:15:03,480
you've previously generated so that

349
00:15:01,920 --> 00:15:04,839
they're not actually true language

350
00:15:03,480 --> 00:15:06,920
models from the point of view of being

351
00:15:04,839 --> 00:15:10,040
able to easily predict the probability

352
00:15:06,920 --> 00:15:11,399
of a sequence um and also it's hard to

353
00:15:10,040 --> 00:15:13,399
generate from them because you need to

354
00:15:11,399 --> 00:15:15,440
generate in some order and mass language

355
00:15:13,399 --> 00:15:17,600
models don't specify economical orders

356
00:15:15,440 --> 00:15:19,120
so they're good for some things like

357
00:15:17,600 --> 00:15:21,720
calculating representations of the

358
00:15:19,120 --> 00:15:22,920
output but they're not useful uh they're

359
00:15:21,720 --> 00:15:25,240
not as useful for

360
00:15:22,920 --> 00:15:26,880
Generation Um there's also energy based

361
00:15:25,240 --> 00:15:28,759
language models which basically create a

362
00:15:26,880 --> 00:15:30,000
scoring function that's not necessarily

363
00:15:28,759 --> 00:15:31,279
left to right or right to left or

364
00:15:30,000 --> 00:15:33,120
anything like that but that's very

365
00:15:31,279 --> 00:15:34,639
Advanced um if you're interested in them

366
00:15:33,120 --> 00:15:36,319
I can talk more about them that we'll

367
00:15:34,639 --> 00:15:38,920
skip

368
00:15:36,319 --> 00:15:41,600
them and um also all of the language

369
00:15:38,920 --> 00:15:45,639
models that you hear about nowadays GPT

370
00:15:41,600 --> 00:15:48,800
uh llama whatever else are all other

371
00:15:45,639 --> 00:15:52,880
models cool so I'm going to go into the

372
00:15:48,800 --> 00:15:52,880
very um any questions about that

373
00:15:57,600 --> 00:16:00,600
yeah

374
00:16:00,680 --> 00:16:04,160
yeah so in Mass language models the

375
00:16:02,680 --> 00:16:06,000
question was in Mass language models

376
00:16:04,160 --> 00:16:08,360
couldn't you just mask out the last

377
00:16:06,000 --> 00:16:10,759
token and predict that sure you could do

378
00:16:08,360 --> 00:16:13,079
that but there it's just not trained

379
00:16:10,759 --> 00:16:14,720
that way so it won't do a very good job

380
00:16:13,079 --> 00:16:16,880
if you always trained it that way it's

381
00:16:14,720 --> 00:16:18,160
an autor regressive language model so

382
00:16:16,880 --> 00:16:22,240
you're you're back to where you were in

383
00:16:18,160 --> 00:16:24,800
the first place um cool so now we I'll

384
00:16:22,240 --> 00:16:26,399
talk about unigram language models and

385
00:16:24,800 --> 00:16:29,319
so the simplest language models are

386
00:16:26,399 --> 00:16:33,560
count-based unigram language models and

387
00:16:29,319 --> 00:16:35,319
the way they work is um basically we

388
00:16:33,560 --> 00:16:38,519
want to calculate this probability

389
00:16:35,319 --> 00:16:41,240
conditioned on all the previous ones and

390
00:16:38,519 --> 00:16:42,360
the way we do this is we just say

391
00:16:41,240 --> 00:16:45,680
actually we're not going to worry about

392
00:16:42,360 --> 00:16:48,759
the order at all and we're just going to

393
00:16:45,680 --> 00:16:52,240
uh predict the probability of the next

394
00:16:48,759 --> 00:16:55,279
word uh independently of all the other

395
00:16:52,240 --> 00:16:57,519
words so if you have something like this

396
00:16:55,279 --> 00:16:59,720
it's actually extremely easy to predict

397
00:16:57,519 --> 00:17:02,480
the probability of this word and the way

398
00:16:59,720 --> 00:17:04,280
you do this is you just count up the

399
00:17:02,480 --> 00:17:08,360
number of times this word appeared in

400
00:17:04,280 --> 00:17:10,480
the training data set and divide by the

401
00:17:08,360 --> 00:17:12,559
uh divide by the total number of words

402
00:17:10,480 --> 00:17:14,240
in the pring data set and now you have a

403
00:17:12,559 --> 00:17:15,959
language model this is like language

404
00:17:14,240 --> 00:17:17,760
model 101 it's the easiest possible

405
00:17:15,959 --> 00:17:19,520
language model you can write in you know

406
00:17:17,760 --> 00:17:21,120
three lines of python

407
00:17:19,520 --> 00:17:25,039
basically

408
00:17:21,120 --> 00:17:28,480
um so it has a few problems uh the first

409
00:17:25,039 --> 00:17:31,120
problem with this language model is um

410
00:17:28,480 --> 00:17:32,960
handling unknown words so what happens

411
00:17:31,120 --> 00:17:38,679
if you have a word that you've never

412
00:17:32,960 --> 00:17:41,000
seen before um in this language model

413
00:17:38,679 --> 00:17:42,240
here what is the probability of any

414
00:17:41,000 --> 00:17:44,720
sequence that has a word that you've

415
00:17:42,240 --> 00:17:47,440
never seen before yeah the probability

416
00:17:44,720 --> 00:17:49,240
of the sequence gets zero so there might

417
00:17:47,440 --> 00:17:51,120
not be such a big problem for generating

418
00:17:49,240 --> 00:17:52,480
things from the language model because

419
00:17:51,120 --> 00:17:54,520
you know maybe it's fine if you only

420
00:17:52,480 --> 00:17:55,960
generate words that you've seen before

421
00:17:54,520 --> 00:17:57,679
uh but it is definitely a problem of

422
00:17:55,960 --> 00:17:59,720
scoring things with the language model

423
00:17:57,679 --> 00:18:02,039
and it's also a problem of uh for

424
00:17:59,720 --> 00:18:04,440
something like translation if you get an

425
00:18:02,039 --> 00:18:05,840
unknown word uh when you're translating

426
00:18:04,440 --> 00:18:07,799
something then you would like to be able

427
00:18:05,840 --> 00:18:11,320
to translate it reasonably but you can't

428
00:18:07,799 --> 00:18:13,799
do that so um that's an issue so how do

429
00:18:11,320 --> 00:18:15,840
we how do we fix this um there's a

430
00:18:13,799 --> 00:18:17,640
couple options the first option is to

431
00:18:15,840 --> 00:18:19,440
segment to characters and subwords and

432
00:18:17,640 --> 00:18:21,720
this is now the preferred option that

433
00:18:19,440 --> 00:18:24,360
most people use nowadays uh just run

434
00:18:21,720 --> 00:18:26,840
sentence piece segment your vocabulary

435
00:18:24,360 --> 00:18:28,400
and you're all set you're you'll now no

436
00:18:26,840 --> 00:18:29,679
longer have any unknown words because

437
00:18:28,400 --> 00:18:30,840
all the unknown words get split into

438
00:18:29,679 --> 00:18:33,559
shorter

439
00:18:30,840 --> 00:18:36,240
units there's also other options that

440
00:18:33,559 --> 00:18:37,919
you can use if you're uh very interested

441
00:18:36,240 --> 00:18:41,280
in or serious about this and want to

442
00:18:37,919 --> 00:18:43,720
handle this like uh as part of a

443
00:18:41,280 --> 00:18:45,960
research project or something like this

444
00:18:43,720 --> 00:18:48,520
and uh the way you can do this is you

445
00:18:45,960 --> 00:18:50,120
can build an unknown word model and an

446
00:18:48,520 --> 00:18:52,200
unknown word model basically what it

447
00:18:50,120 --> 00:18:54,520
does is it uh predicts the probability

448
00:18:52,200 --> 00:18:56,200
of unknown words using characters and

449
00:18:54,520 --> 00:18:59,559
then it models the probability of words

450
00:18:56,200 --> 00:19:01,159
using words and so now you can you have

451
00:18:59,559 --> 00:19:02,559
kind of like a hierarchical model where

452
00:19:01,159 --> 00:19:03,919
you first try to predict words and then

453
00:19:02,559 --> 00:19:06,720
if you can't predict words you predict

454
00:19:03,919 --> 00:19:08,960
unknown words so this isn't us as widely

455
00:19:06,720 --> 00:19:11,520
anymore but it's worth thinking about uh

456
00:19:08,960 --> 00:19:11,520
or knowing

457
00:19:11,840 --> 00:19:20,880
about okay uh so a second detail um a

458
00:19:17,200 --> 00:19:22,799
parameter uh so parameterizing in log

459
00:19:20,880 --> 00:19:25,880
space

460
00:19:22,799 --> 00:19:28,400
so the um multiplication of

461
00:19:25,880 --> 00:19:29,840
probabilities can be reexpressed is the

462
00:19:28,400 --> 00:19:31,840
addition of log

463
00:19:29,840 --> 00:19:34,159
probabilities uh so this is really

464
00:19:31,840 --> 00:19:35,720
important and this is widely used in all

465
00:19:34,159 --> 00:19:37,520
language models whether they're unigram

466
00:19:35,720 --> 00:19:39,640
language models or or neural language

467
00:19:37,520 --> 00:19:41,799
models there's actually a very simple

468
00:19:39,640 --> 00:19:45,440
reason why we why we do it this way does

469
00:19:41,799 --> 00:19:45,440
anybody uh know the

470
00:19:46,440 --> 00:19:52,679
answer what would happen if we

471
00:19:48,280 --> 00:19:56,720
multiplied uh let's say uh 30 30 tokens

472
00:19:52,679 --> 00:20:00,360
worth of probabilities together um

473
00:19:56,720 --> 00:20:02,120
yeah uh yeah too too small um so

474
00:20:00,360 --> 00:20:06,120
basically the problem is numerical

475
00:20:02,120 --> 00:20:07,520
underflow um so modern computers if if

476
00:20:06,120 --> 00:20:08,840
we weren't doing this on a computer and

477
00:20:07,520 --> 00:20:11,240
we were just doing math it wouldn't

478
00:20:08,840 --> 00:20:14,280
matter at all um but because we're doing

479
00:20:11,240 --> 00:20:17,280
it on a computer uh we

480
00:20:14,280 --> 00:20:17,280
have

481
00:20:20,880 --> 00:20:26,000
ours we have our

482
00:20:23,000 --> 00:20:26,000
32bit

483
00:20:27,159 --> 00:20:30,159
float

484
00:20:32,320 --> 00:20:37,720
where we have uh the exponent in the the

485
00:20:35,799 --> 00:20:40,159
fraction over here so the largest the

486
00:20:37,720 --> 00:20:41,960
exponent can get is limited by the

487
00:20:40,159 --> 00:20:45,880
number of exponent bits that we have in

488
00:20:41,960 --> 00:20:48,039
a 32-bit float and um if that's the case

489
00:20:45,880 --> 00:20:52,480
I forget exactly how large it is it's

490
00:20:48,039 --> 00:20:53,440
like yeah something like 30 minus 38 is

491
00:20:52,480 --> 00:20:56,640
that

492
00:20:53,440 --> 00:20:58,520
right yeah but anyway like if the number

493
00:20:56,640 --> 00:21:00,640
gets too small you'll underflow it goes

494
00:20:58,520 --> 00:21:02,400
to zero and you'll get a zero

495
00:21:00,640 --> 00:21:05,720
probability despite the fact that it's

496
00:21:02,400 --> 00:21:07,640
not actually zero so um that's usually

497
00:21:05,720 --> 00:21:09,440
why we do this it's also a little bit

498
00:21:07,640 --> 00:21:12,960
easier for people just to look at like

499
00:21:09,440 --> 00:21:15,200
minus 30 instead of looking to something

500
00:21:12,960 --> 00:21:19,960
something time 10 to the minus 30 or

501
00:21:15,200 --> 00:21:24,520
something so uh that is why we normally

502
00:21:19,960 --> 00:21:27,159
go um another thing that you can note is

503
00:21:24,520 --> 00:21:28,760
uh you can treat each of these in a

504
00:21:27,159 --> 00:21:31,360
unigram model you can treat each of

505
00:21:28,760 --> 00:21:37,039
these as parameters so we talked about

506
00:21:31,360 --> 00:21:39,640
parameters of a model uh like a um like

507
00:21:37,039 --> 00:21:41,120
a bag of words model and we can

508
00:21:39,640 --> 00:21:44,080
similarly treat these unigram

509
00:21:41,120 --> 00:21:47,760
probabilities as parameters so um how

510
00:21:44,080 --> 00:21:47,760
many parameters does a unigram model

511
00:21:48,080 --> 00:21:51,320
have any

512
00:21:57,039 --> 00:22:02,400
ideas

513
00:21:59,600 --> 00:22:04,440
yeah yeah exactly parameters equal to

514
00:22:02,400 --> 00:22:08,120
the size of the vocabulary so this one's

515
00:22:04,440 --> 00:22:10,880
easy and then we can go um we can go to

516
00:22:08,120 --> 00:22:13,880
the slightly less easy ones

517
00:22:10,880 --> 00:22:16,039
there so anyway this is a unigram model

518
00:22:13,880 --> 00:22:17,960
uh it's it's not too hard um you

519
00:22:16,039 --> 00:22:20,480
basically count up and divide and then

520
00:22:17,960 --> 00:22:22,720
you add the the probabilities here you

521
00:22:20,480 --> 00:22:25,440
could easily do it in a short Python

522
00:22:22,720 --> 00:22:28,400
program higher order engram models so

523
00:22:25,440 --> 00:22:31,600
higher order engram models um what these

524
00:22:28,400 --> 00:22:35,520
do is they essentially limit the context

525
00:22:31,600 --> 00:22:40,240
length to a length of N and then they

526
00:22:35,520 --> 00:22:42,600
count and divide so the way it works

527
00:22:40,240 --> 00:22:45,559
here maybe this is a little bit uh

528
00:22:42,600 --> 00:22:47,320
tricky but I can show an example so what

529
00:22:45,559 --> 00:22:49,840
we do is we count up the number of times

530
00:22:47,320 --> 00:22:51,320
we've seen this is an example and then

531
00:22:49,840 --> 00:22:53,480
we divide by the number of times we've

532
00:22:51,320 --> 00:22:55,960
seen this is n and that's the

533
00:22:53,480 --> 00:22:56,960
probability of example given the the

534
00:22:55,960 --> 00:22:58,720
previous

535
00:22:56,960 --> 00:23:00,559
coms

536
00:22:58,720 --> 00:23:02,039
so the problem with this is anytime we

537
00:23:00,559 --> 00:23:03,400
get a sequence that we've never seen

538
00:23:02,039 --> 00:23:04,960
before like we would like to model

539
00:23:03,400 --> 00:23:07,200
longer sequences to make this more

540
00:23:04,960 --> 00:23:08,600
accurate but anytime we've get a uh we

541
00:23:07,200 --> 00:23:10,720
get a sequence that we've never seen

542
00:23:08,600 --> 00:23:12,919
before um it will get a probability of

543
00:23:10,720 --> 00:23:15,919
zero similarly because this count on top

544
00:23:12,919 --> 00:23:19,919
of here will be zero so the way that uh

545
00:23:15,919 --> 00:23:22,640
engram language models work with this uh

546
00:23:19,919 --> 00:23:27,320
handle this is they have fall back to

547
00:23:22,640 --> 00:23:31,840
Shorter uh engram models so um this

548
00:23:27,320 --> 00:23:33,480
model sorry when I say NR uh n is the

549
00:23:31,840 --> 00:23:35,520
length of the context so this is a four

550
00:23:33,480 --> 00:23:37,679
gr model here because the top context is

551
00:23:35,520 --> 00:23:40,520
four so the photogram model would

552
00:23:37,679 --> 00:23:46,640
calculate this and then interpolate it

553
00:23:40,520 --> 00:23:48,640
like this with a um with a trigram model

554
00:23:46,640 --> 00:23:50,400
uh and then the trigram model itself

555
00:23:48,640 --> 00:23:51,720
would interpolate with the Byram model

556
00:23:50,400 --> 00:23:53,440
the Byram model would interpolate with

557
00:23:51,720 --> 00:23:56,880
the unram

558
00:23:53,440 --> 00:23:59,880
model oh this one oh

559
00:23:56,880 --> 00:23:59,880
okay

560
00:24:02,159 --> 00:24:05,440
um one

561
00:24:07,039 --> 00:24:12,320
second could you uh help get it from the

562
00:24:10,000 --> 00:24:12,320
lock

563
00:24:26,799 --> 00:24:29,799
box

564
00:24:43,640 --> 00:24:50,200
um okay sorry

565
00:24:46,880 --> 00:24:53,640
so getting bad

566
00:24:50,200 --> 00:24:56,640
here just

567
00:24:53,640 --> 00:24:56,640
actually

568
00:24:56,760 --> 00:25:02,559
okay uh oh wow that's a lot

569
00:25:02,960 --> 00:25:12,080
better cool okay so

570
00:25:08,279 --> 00:25:14,159
um so this is uh how we deal with the

571
00:25:12,080 --> 00:25:18,799
fact that models can

572
00:25:14,159 --> 00:25:23,919
be um models can be more precise but

573
00:25:18,799 --> 00:25:26,679
more sparse and less precise but less

574
00:25:23,919 --> 00:25:28,720
sparse this is also another concept that

575
00:25:26,679 --> 00:25:31,039
we're going to talk about more later uh

576
00:25:28,720 --> 00:25:33,240
in another class but this is a variety

577
00:25:31,039 --> 00:25:33,240
of

578
00:25:33,679 --> 00:25:38,440
ensembling where we have different

579
00:25:35,960 --> 00:25:40,360
models that are good at different things

580
00:25:38,440 --> 00:25:42,279
and we combine them together so this is

581
00:25:40,360 --> 00:25:44,760
the first instance that you would see of

582
00:25:42,279 --> 00:25:46,159
this there are other instances of this

583
00:25:44,760 --> 00:25:50,320
but the reason why I mentioned that this

584
00:25:46,159 --> 00:25:51,840
is a a variety of ensembling is actually

585
00:25:50,320 --> 00:25:55,520
you're probably not going to be using

586
00:25:51,840 --> 00:25:57,840
engram models super widely unless you

587
00:25:55,520 --> 00:26:00,520
really want to process huge data sets

588
00:25:57,840 --> 00:26:02,399
because that is one advantage of them

589
00:26:00,520 --> 00:26:03,960
but some of these smoothing methods

590
00:26:02,399 --> 00:26:05,720
actually might be interesting even if

591
00:26:03,960 --> 00:26:10,520
you're using other models and ensembling

592
00:26:05,720 --> 00:26:10,520
them together so

593
00:26:10,600 --> 00:26:15,679
the in order to decide this

594
00:26:13,679 --> 00:26:19,559
interpolation coefficient one way we can

595
00:26:15,679 --> 00:26:23,440
do it is just set a fixed um set a fixed

596
00:26:19,559 --> 00:26:26,039
amount of probability that we use for

597
00:26:23,440 --> 00:26:29,000
every um every time so we could say that

598
00:26:26,039 --> 00:26:32,000
we always set this Lambda to 0.8 and

599
00:26:29,000 --> 00:26:34,320
some always set this Lambda 1us Lambda

600
00:26:32,000 --> 00:26:36,559
to 0.2 and interpolate those two

601
00:26:34,320 --> 00:26:39,120
together but actually there's more

602
00:26:36,559 --> 00:26:42,240
sophisticated methods of doing this and

603
00:26:39,120 --> 00:26:44,080
so one way of doing this is uh called

604
00:26:42,240 --> 00:26:47,240
additive

605
00:26:44,080 --> 00:26:50,600
smoothing excuse me and the the way that

606
00:26:47,240 --> 00:26:54,039
additive smoothing works is um basically

607
00:26:50,600 --> 00:26:54,919
we add Alpha to the uh to the top and

608
00:26:54,039 --> 00:26:58,000
the

609
00:26:54,919 --> 00:27:02,159
bottom and the reason why this is slight

610
00:26:58,000 --> 00:27:06,279
different as is as our accounts get

611
00:27:02,159 --> 00:27:10,799
larger we start to approach the true

612
00:27:06,279 --> 00:27:10,799
distribution so just to give an

613
00:27:12,080 --> 00:27:19,480
example let's say we have uh the

614
00:27:17,640 --> 00:27:21,640
box

615
00:27:19,480 --> 00:27:26,279
is

616
00:27:21,640 --> 00:27:26,279
um let's say initially we

617
00:27:26,520 --> 00:27:29,520
have

618
00:27:31,159 --> 00:27:37,600
uh let let's say our Alpha is

619
00:27:33,840 --> 00:27:43,559
one so initially if we have

620
00:27:37,600 --> 00:27:47,320
nothing um if we have no no evidence for

621
00:27:43,559 --> 00:27:47,320
our sorry I I

622
00:27:49,720 --> 00:27:54,960
realize let's say this is

623
00:27:52,640 --> 00:27:56,840
our fallback

624
00:27:54,960 --> 00:27:59,240
distribution um where this is a

625
00:27:56,840 --> 00:28:01,880
probability of Z 0.5 this is a

626
00:27:59,240 --> 00:28:03,360
probability of 0.3 and this is a

627
00:28:01,880 --> 00:28:06,559
probability of

628
00:28:03,360 --> 00:28:09,919
0.2 so now let's talk about our byr

629
00:28:06,559 --> 00:28:13,399
model um and our byr

630
00:28:09,919 --> 00:28:18,000
model has counts which is the

631
00:28:13,399 --> 00:28:18,000
the the box and the

632
00:28:19,039 --> 00:28:24,480
is so if we do something like this then

633
00:28:22,720 --> 00:28:26,720
um initially we have no counts like

634
00:28:24,480 --> 00:28:28,159
let's say we we have no data uh about

635
00:28:26,720 --> 00:28:30,760
this distribution

636
00:28:28,159 --> 00:28:33,200
um our counts would be zero and our

637
00:28:30,760 --> 00:28:35,919
Alpha would be

638
00:28:33,200 --> 00:28:37,840
one and so we would just fall back to

639
00:28:35,919 --> 00:28:40,960
this distribution we just have like one

640
00:28:37,840 --> 00:28:43,320
times uh one times this distribution

641
00:28:40,960 --> 00:28:45,679
let's say we then we have one piece of

642
00:28:43,320 --> 00:28:48,640
evidence and once we have one piece of

643
00:28:45,679 --> 00:28:52,279
evidence now this would be

644
00:28:48,640 --> 00:28:53,960
0.33 um and this would uh be Alpha equal

645
00:28:52,279 --> 00:28:56,399
to 1 so we'd have

646
00:28:53,960 --> 00:28:58,679
0.5 *

647
00:28:56,399 --> 00:29:00,399
0.33

648
00:28:58,679 --> 00:29:04,039
uh and

649
00:29:00,399 --> 00:29:07,720
0.5 time

650
00:29:04,039 --> 00:29:10,840
0.3 uh is the probability of the Box

651
00:29:07,720 --> 00:29:12,840
because um basically we we have one

652
00:29:10,840 --> 00:29:14,720
piece of evidence and we are adding a

653
00:29:12,840 --> 00:29:17,080
count of one to the lower order

654
00:29:14,720 --> 00:29:18,320
distribution then if we increase our

655
00:29:17,080 --> 00:29:24,159
count

656
00:29:18,320 --> 00:29:24,159
here um now we rely more

657
00:29:24,880 --> 00:29:30,960
strongly sorry that that would be wrong

658
00:29:27,720 --> 00:29:32,399
so so now we rely more strongly on the

659
00:29:30,960 --> 00:29:33,880
higher order distribution because we

660
00:29:32,399 --> 00:29:37,039
have more evidence for the higher order

661
00:29:33,880 --> 00:29:39,610
distribution so basically in this case

662
00:29:37,039 --> 00:29:41,240
um the probability

663
00:29:39,610 --> 00:29:44,559
[Music]

664
00:29:41,240 --> 00:29:48,200
of Lambda which I showed

665
00:29:44,559 --> 00:29:52,000
before is equal to the the sum of the

666
00:29:48,200 --> 00:29:54,200
counts plus um the sum of the counts

667
00:29:52,000 --> 00:29:56,480
over the sum of the counts plus

668
00:29:54,200 --> 00:29:58,159
Ali so as the sum of the counts gets

669
00:29:56,480 --> 00:30:00,240
larger you rely on the higher order

670
00:29:58,159 --> 00:30:01,640
distribution is the sum of the counts is

671
00:30:00,240 --> 00:30:02,760
if the sum of the counts is smaller you

672
00:30:01,640 --> 00:30:04,320
rely more on the lower order

673
00:30:02,760 --> 00:30:06,720
distribution so the more evidence you

674
00:30:04,320 --> 00:30:11,640
have the more you rely on so that's the

675
00:30:06,720 --> 00:30:11,640
basic idea behind these smoothing things

676
00:30:11,679 --> 00:30:16,679
um there's also a number of other

677
00:30:14,519 --> 00:30:18,760
varieties called uh

678
00:30:16,679 --> 00:30:20,799
discounting so uh the discount

679
00:30:18,760 --> 00:30:23,679
hyperparameter basically you subtract

680
00:30:20,799 --> 00:30:26,080
this off um uh you subtract this from

681
00:30:23,679 --> 00:30:27,840
the count so you would subtract like 0.5

682
00:30:26,080 --> 00:30:32,679
from each of the counts that you it's

683
00:30:27,840 --> 00:30:36,279
just empirically this is a better match

684
00:30:32,679 --> 00:30:38,600
for the fact that um natural language

685
00:30:36,279 --> 00:30:40,039
has a very longtailed distribution um

686
00:30:38,600 --> 00:30:41,600
you can kind of do the math and show

687
00:30:40,039 --> 00:30:43,720
that that works and that's actually in

688
00:30:41,600 --> 00:30:46,080
this um in this paper if you're

689
00:30:43,720 --> 00:30:49,880
interested in looking at more details of

690
00:30:46,080 --> 00:30:51,519
that um and then kind of the

691
00:30:49,880 --> 00:30:53,440
stateoftheart in language modeling

692
00:30:51,519 --> 00:30:56,600
before neural language models came out

693
00:30:53,440 --> 00:30:59,919
was this kesser smoothing and what it

694
00:30:56,600 --> 00:31:02,440
does is it discounts but it also

695
00:30:59,919 --> 00:31:04,480
modifies the lower order distribution so

696
00:31:02,440 --> 00:31:07,200
in the lower order distribution you

697
00:31:04,480 --> 00:31:09,039
basically um modify the counts with

698
00:31:07,200 --> 00:31:11,919
respect to how many times that word has

699
00:31:09,039 --> 00:31:13,519
appeared in new contexts with the IDE

700
00:31:11,919 --> 00:31:16,360
idea being that you only use the lower

701
00:31:13,519 --> 00:31:18,880
order distribution when you have uh new

702
00:31:16,360 --> 00:31:21,200
contexts um and so you can kind of Be

703
00:31:18,880 --> 00:31:23,600
Clever

704
00:31:21,200 --> 00:31:25,399
About You Can Be Clever about how you

705
00:31:23,600 --> 00:31:27,639
build this distribution based on the

706
00:31:25,399 --> 00:31:29,360
fact that you're only using it in the

707
00:31:27,639 --> 00:31:31,320
case when this distribution is not very

708
00:31:29,360 --> 00:31:33,960
Rel

709
00:31:31,320 --> 00:31:36,080
so I I would spend a lot more time

710
00:31:33,960 --> 00:31:37,960
teaching this when uh engram models were

711
00:31:36,080 --> 00:31:39,840
kind of the thing uh that people were

712
00:31:37,960 --> 00:31:41,960
using but now I'm going to go over them

713
00:31:39,840 --> 00:31:43,600
very quickly so you know don't worry if

714
00:31:41,960 --> 00:31:46,559
you weren't able to follow all the

715
00:31:43,600 --> 00:31:47,960
details but the basic um the basic thing

716
00:31:46,559 --> 00:31:49,279
take away from this is number one these

717
00:31:47,960 --> 00:31:51,639
are the methods that people use for

718
00:31:49,279 --> 00:31:53,440
engram language models number two if

719
00:31:51,639 --> 00:31:55,720
you're thinking about combining language

720
00:31:53,440 --> 00:31:57,519
models together in some way through you

721
00:31:55,720 --> 00:31:59,279
know ensembling their probability or

722
00:31:57,519 --> 00:32:00,480
something like this this is something

723
00:31:59,279 --> 00:32:02,279
that you should think about a little bit

724
00:32:00,480 --> 00:32:03,679
more carefully because like some

725
00:32:02,279 --> 00:32:05,240
language models might be good in some

726
00:32:03,679 --> 00:32:07,440
context other language models might be

727
00:32:05,240 --> 00:32:09,440
good in other contexts so you would need

728
00:32:07,440 --> 00:32:11,799
to think about that when you're doing um

729
00:32:09,440 --> 00:32:18,200
when you're combining the model

730
00:32:11,799 --> 00:32:18,200
that cool um any any questions about

731
00:32:19,080 --> 00:32:24,840
this Okay

732
00:32:21,159 --> 00:32:27,840
cool so there's a lot of problems that

733
00:32:24,840 --> 00:32:30,760
we have to deal with um when were

734
00:32:27,840 --> 00:32:32,600
creating engram models and that actually

735
00:32:30,760 --> 00:32:35,279
kind of motivated the reason why we

736
00:32:32,600 --> 00:32:36,639
moved to neural language models the

737
00:32:35,279 --> 00:32:38,720
first one is similar to what I talked

738
00:32:36,639 --> 00:32:40,519
about last time with text classification

739
00:32:38,720 --> 00:32:42,600
um that they can't share strength among

740
00:32:40,519 --> 00:32:45,159
similar words like bought and

741
00:32:42,600 --> 00:32:46,919
purchase um another thing is that they

742
00:32:45,159 --> 00:32:49,440
can't easily condition on context with

743
00:32:46,919 --> 00:32:51,240
intervening words so engram models if

744
00:32:49,440 --> 00:32:52,799
you have a rare word in your context

745
00:32:51,240 --> 00:32:54,320
immediately start falling back to the

746
00:32:52,799 --> 00:32:56,799
unigram distribution and they end up

747
00:32:54,320 --> 00:32:58,720
being very bad so uh that was another

748
00:32:56,799 --> 00:33:01,000
issue

749
00:32:58,720 --> 00:33:04,760
and they couldn't handle long distance

750
00:33:01,000 --> 00:33:09,080
um dependencies so if this was beyond

751
00:33:04,760 --> 00:33:10,559
the engram context that they would uh be

752
00:33:09,080 --> 00:33:14,320
handling then you wouldn't be able to

753
00:33:10,559 --> 00:33:15,840
manage this so actually before neural

754
00:33:14,320 --> 00:33:18,000
language models became a really big

755
00:33:15,840 --> 00:33:19,960
thing uh people came up with a bunch of

756
00:33:18,000 --> 00:33:22,760
individual solutions for this in order

757
00:33:19,960 --> 00:33:24,440
to solve the problems but actually it

758
00:33:22,760 --> 00:33:26,679
wasn't that these Solutions didn't work

759
00:33:24,440 --> 00:33:29,159
at all it was just that engineering all

760
00:33:26,679 --> 00:33:30,519
of them together was so hard that nobody

761
00:33:29,159 --> 00:33:32,120
actually ever did that and so they

762
00:33:30,519 --> 00:33:35,120
relied on just engram models out of the

763
00:33:32,120 --> 00:33:37,600
box and that wasn't scalable so it's

764
00:33:35,120 --> 00:33:39,279
kind of a funny example of how like

765
00:33:37,600 --> 00:33:42,000
actually neural networks despite all the

766
00:33:39,279 --> 00:33:43,559
pain that they cause in some areas are a

767
00:33:42,000 --> 00:33:47,120
much better engineering solution to

768
00:33:43,559 --> 00:33:51,279
solve all the issues that previous

769
00:33:47,120 --> 00:33:53,159
method cool um so when they use uh Eng

770
00:33:51,279 --> 00:33:54,799
grab models neural language models

771
00:33:53,159 --> 00:33:56,559
achieve better performance but Eng grab

772
00:33:54,799 --> 00:33:58,440
models are very very fast to estimate

773
00:33:56,559 --> 00:33:59,880
and apply you can even estimate them

774
00:33:58,440 --> 00:34:04,399
completely in

775
00:33:59,880 --> 00:34:07,720
parallel um engram models also I I don't

776
00:34:04,399 --> 00:34:10,399
know if this is necessarily

777
00:34:07,720 --> 00:34:13,200
A a thing that

778
00:34:10,399 --> 00:34:15,079
you a reason to use engram language

779
00:34:13,200 --> 00:34:17,720
models but it is a reason to think a

780
00:34:15,079 --> 00:34:20,320
little bit critically about uh neural

781
00:34:17,720 --> 00:34:22,720
language models which is neural language

782
00:34:20,320 --> 00:34:24,320
models actually can be worse than engram

783
00:34:22,720 --> 00:34:26,679
language models at modeling very low

784
00:34:24,320 --> 00:34:28,480
frequency phenomenas so engram language

785
00:34:26,679 --> 00:34:29,960
model can learn from a single example

786
00:34:28,480 --> 00:34:32,119
they only need a single example of

787
00:34:29,960 --> 00:34:36,879
anything before the probability of that

788
00:34:32,119 --> 00:34:38,639
continuation goes up very high um and uh

789
00:34:36,879 --> 00:34:41,359
but neural language models actually can

790
00:34:38,639 --> 00:34:43,599
forget or not memorize uh appropriately

791
00:34:41,359 --> 00:34:46,280
from single examples so they can be

792
00:34:43,599 --> 00:34:48,040
better at that um there's a toolkit the

793
00:34:46,280 --> 00:34:49,919
standard toolkit for estimating engram

794
00:34:48,040 --> 00:34:54,359
language models is called KLM it's kind

795
00:34:49,919 --> 00:34:57,599
of frighteningly fast um and so people

796
00:34:54,359 --> 00:35:00,400
have been uh saying like I've seen some

797
00:34:57,599 --> 00:35:01,599
jokes which are like job postings that

798
00:35:00,400 --> 00:35:04,040
say people who have been working on

799
00:35:01,599 --> 00:35:05,880
large language models uh for we want

800
00:35:04,040 --> 00:35:07,359
people who have been 10 years of

801
00:35:05,880 --> 00:35:09,240
experience working on large language

802
00:35:07,359 --> 00:35:11,960
models or something like that and a lot

803
00:35:09,240 --> 00:35:13,440
of people are saying wait nobody has 10

804
00:35:11,960 --> 00:35:16,400
years of experience working on large

805
00:35:13,440 --> 00:35:18,160
language models well Kenneth hfield who

806
00:35:16,400 --> 00:35:19,440
created KLM does have 10 years of

807
00:35:18,160 --> 00:35:22,800
experience working on large language

808
00:35:19,440 --> 00:35:24,599
models because he was estimating uh

809
00:35:22,800 --> 00:35:27,720
seven gr

810
00:35:24,599 --> 00:35:30,320
bottles um seven models with a

811
00:35:27,720 --> 00:35:35,040
vocabulary of let's say

812
00:35:30,320 --> 00:35:37,720
100,000 on um you know web text so how

813
00:35:35,040 --> 00:35:41,119
many parameters is at that's more than

814
00:35:37,720 --> 00:35:44,320
any you know large neural language model

815
00:35:41,119 --> 00:35:45,640
that we have nowadays so um they they

816
00:35:44,320 --> 00:35:47,520
have a lot of these parameters are

817
00:35:45,640 --> 00:35:49,400
sparse they're zero counts so obviously

818
00:35:47,520 --> 00:35:52,160
you don't uh you don't memorize all of

819
00:35:49,400 --> 00:35:55,040
them but uh

820
00:35:52,160 --> 00:35:57,800
yeah cool um another thing that maybe I

821
00:35:55,040 --> 00:35:59,359
should mention like so this doesn't

822
00:35:57,800 --> 00:36:01,960
sound completely outdated there was a

823
00:35:59,359 --> 00:36:05,400
really good paper

824
00:36:01,960 --> 00:36:08,400
recently that used the fact that engrams

825
00:36:05,400 --> 00:36:08,400
are

826
00:36:11,079 --> 00:36:17,319
so uses effect that engram models are so

827
00:36:14,280 --> 00:36:18,960
scalable it's this paper um it's called

828
00:36:17,319 --> 00:36:21,079
Data selection for language models via

829
00:36:18,960 --> 00:36:22,359
importance rese sampling and one

830
00:36:21,079 --> 00:36:24,359
interesting thing that they do in this

831
00:36:22,359 --> 00:36:28,920
paper is that they don't

832
00:36:24,359 --> 00:36:31,560
actually um they don't

833
00:36:28,920 --> 00:36:32,800
actually use neural models in any way

834
00:36:31,560 --> 00:36:34,920
despite the fact that they use the

835
00:36:32,800 --> 00:36:36,880
downstream data that they sample in

836
00:36:34,920 --> 00:36:41,319
order to calculate neural models but

837
00:36:36,880 --> 00:36:42,880
they run engram models over um over lots

838
00:36:41,319 --> 00:36:47,359
and lots of data and then they fit a

839
00:36:42,880 --> 00:36:50,000
gaussian distribution to the enr model

840
00:36:47,359 --> 00:36:51,520
counts basically uh in order to select

841
00:36:50,000 --> 00:36:53,040
the data in the reason why they do this

842
00:36:51,520 --> 00:36:55,280
is they want to do this over the entire

843
00:36:53,040 --> 00:36:56,760
web and running a neural model over the

844
00:36:55,280 --> 00:36:58,920
entire web would be too expensive so

845
00:36:56,760 --> 00:37:00,319
they use angr models instead so that's

846
00:36:58,920 --> 00:37:02,359
just an example of something in the

847
00:37:00,319 --> 00:37:04,920
modern context where keeping this in

848
00:37:02,359 --> 00:37:04,920
mind is a good

849
00:37:08,200 --> 00:37:14,000
idea okay I'd like to move to the next

850
00:37:10,960 --> 00:37:15,319
part so a language model evaluation uh

851
00:37:14,000 --> 00:37:17,200
this is important to know I'm not going

852
00:37:15,319 --> 00:37:19,079
to talk about language model evaluation

853
00:37:17,200 --> 00:37:20,599
on other tasks I'm only going to talk

854
00:37:19,079 --> 00:37:23,800
right now about language model

855
00:37:20,599 --> 00:37:26,280
evaluation on the task of language

856
00:37:23,800 --> 00:37:29,079
modeling and there's a number of metrics

857
00:37:26,280 --> 00:37:30,680
that we use for the task of language

858
00:37:29,079 --> 00:37:32,720
modeling evaluating language models on

859
00:37:30,680 --> 00:37:35,560
the task of language modeling the first

860
00:37:32,720 --> 00:37:38,480
one is log likelihood and basically uh

861
00:37:35,560 --> 00:37:40,160
the way we calculate log likelihood is

862
00:37:38,480 --> 00:37:41,640
uh sorry there's an extra parenthesis

863
00:37:40,160 --> 00:37:45,480
here but the way we calculate log

864
00:37:41,640 --> 00:37:47,160
likelihood is we get a test set that

865
00:37:45,480 --> 00:37:50,400
ideally has not been included in our

866
00:37:47,160 --> 00:37:52,520
training data and we take all of the

867
00:37:50,400 --> 00:37:54,200
documents or sentences in the test set

868
00:37:52,520 --> 00:37:57,040
we calculate the log probability of all

869
00:37:54,200 --> 00:37:59,520
of them uh we don't actually use this

870
00:37:57,040 --> 00:38:02,640
super broadly to evaluate models and the

871
00:37:59,520 --> 00:38:04,200
reason why is because this number is

872
00:38:02,640 --> 00:38:05,720
very dependent on the size of the data

873
00:38:04,200 --> 00:38:07,119
set so if you have a larger data set

874
00:38:05,720 --> 00:38:08,720
this number will be larger if you have a

875
00:38:07,119 --> 00:38:10,960
smaller data set this number will be

876
00:38:08,720 --> 00:38:14,040
smaller so the more common thing to do

877
00:38:10,960 --> 00:38:15,839
is per word uh log likelihood and per

878
00:38:14,040 --> 00:38:19,800
word log likelihood is basically

879
00:38:15,839 --> 00:38:22,760
dividing the um dividing the log

880
00:38:19,800 --> 00:38:25,520
probability of the entire corpus with uh

881
00:38:22,760 --> 00:38:28,359
the number of words that you have in the

882
00:38:25,520 --> 00:38:31,000
corpus

883
00:38:28,359 --> 00:38:34,599
um it's also common for papers to report

884
00:38:31,000 --> 00:38:36,359
negative log likelihood uh where because

885
00:38:34,599 --> 00:38:37,800
that's used as a loss and there lower is

886
00:38:36,359 --> 00:38:40,440
better so you just need to be careful

887
00:38:37,800 --> 00:38:42,560
about which one is being

888
00:38:40,440 --> 00:38:43,880
reported so this is pretty common I

889
00:38:42,560 --> 00:38:45,400
think most people are are somewhat

890
00:38:43,880 --> 00:38:49,040
familiar with

891
00:38:45,400 --> 00:38:49,800
this another thing that you might see is

892
00:38:49,040 --> 00:38:53,079
uh

893
00:38:49,800 --> 00:38:55,000
entropy and uh specifically this is

894
00:38:53,079 --> 00:38:57,319
often called cross entropy because

895
00:38:55,000 --> 00:38:59,880
you're calculating

896
00:38:57,319 --> 00:39:01,599
the you're estimating the model on a

897
00:38:59,880 --> 00:39:05,079
training data set and then evaluating it

898
00:39:01,599 --> 00:39:08,400
on a separate data set uh so uh on the

899
00:39:05,079 --> 00:39:12,200
test data set and this is calcul often

900
00:39:08,400 --> 00:39:14,640
or usually calculated as log 2 um of the

901
00:39:12,200 --> 00:39:17,119
probability divided by the number of

902
00:39:14,640 --> 00:39:18,760
words or units in the Corpus does anyone

903
00:39:17,119 --> 00:39:23,839
know why this is log

904
00:39:18,760 --> 00:39:23,839
two as opposed to a normal uh

905
00:39:25,440 --> 00:39:31,319
log

906
00:39:28,440 --> 00:39:31,319
anyone yeah

907
00:39:33,119 --> 00:39:38,720
so yeah so it's calculating as bits um

908
00:39:36,760 --> 00:39:43,160
and this is kind of

909
00:39:38,720 --> 00:39:45,240
a um this is kind of a historical thing

910
00:39:43,160 --> 00:39:47,119
and it's not super super important for

911
00:39:45,240 --> 00:39:51,800
language models but it's actually pretty

912
00:39:47,119 --> 00:39:54,599
interesting uh to to think about and so

913
00:39:51,800 --> 00:39:57,480
actually any probabilistic distribution

914
00:39:54,599 --> 00:40:00,040
can also be used for data compression

915
00:39:57,480 --> 00:40:03,319
um and so you know when you're running a

916
00:40:00,040 --> 00:40:05,000
zip file or you're running gzip or bz2

917
00:40:03,319 --> 00:40:07,359
or something like that uh you're

918
00:40:05,000 --> 00:40:09,240
compressing a file into a smaller file

919
00:40:07,359 --> 00:40:12,000
and any language model can also be used

920
00:40:09,240 --> 00:40:15,280
to compress a SM file into a smaller

921
00:40:12,000 --> 00:40:17,119
file um and so the way it does this is

922
00:40:15,280 --> 00:40:19,200
if you have more likely

923
00:40:17,119 --> 00:40:20,960
sequences uh for example more likely

924
00:40:19,200 --> 00:40:25,079
sentences or more likely documents you

925
00:40:20,960 --> 00:40:26,920
can press them into a a shorter uh

926
00:40:25,079 --> 00:40:29,440
output and

927
00:40:26,920 --> 00:40:29,440
kind of

928
00:40:29,640 --> 00:40:33,800
the

929
00:40:31,480 --> 00:40:35,720
ideal I I think it's pretty safe to say

930
00:40:33,800 --> 00:40:37,920
ideal because I think you can't get a

931
00:40:35,720 --> 00:40:42,920
better method for compression than this

932
00:40:37,920 --> 00:40:45,000
uh if I unless I'm uh you know not well

933
00:40:42,920 --> 00:40:46,800
versed enough in information Theory but

934
00:40:45,000 --> 00:40:49,240
I I think this is basically the ideal

935
00:40:46,800 --> 00:40:51,960
method for data compression and the way

936
00:40:49,240 --> 00:40:54,640
it works is um I have a figure up here

937
00:40:51,960 --> 00:40:58,800
but I'd like to recreate it here which

938
00:40:54,640 --> 00:41:02,640
is let's say we have a vocabulary of

939
00:40:58,800 --> 00:41:07,200
a um which has

940
00:41:02,640 --> 00:41:08,800
50% and then we have a vocabulary uh B

941
00:41:07,200 --> 00:41:11,560
which is

942
00:41:08,800 --> 00:41:14,040
33% and a vocabulary

943
00:41:11,560 --> 00:41:18,520
C

944
00:41:14,040 --> 00:41:18,520
uh yeah C which is about

945
00:41:18,640 --> 00:41:25,640
17% and so if you have a single token

946
00:41:22,960 --> 00:41:26,839
sequence um if you have a single token

947
00:41:25,640 --> 00:41:30,880
sequence

948
00:41:26,839 --> 00:41:30,880
what you do is you can

949
00:41:31,319 --> 00:41:38,800
see divide this into zero and one so if

950
00:41:36,400 --> 00:41:40,680
your single token sequence is a you can

951
00:41:38,800 --> 00:41:42,760
just put zero and you'll be done

952
00:41:40,680 --> 00:41:46,800
encoding it if your single token

953
00:41:42,760 --> 00:41:51,920
sequence is B

954
00:41:46,800 --> 00:41:56,520
then um one overlaps with b and c so now

955
00:41:51,920 --> 00:42:00,920
you need to further split this up into

956
00:41:56,520 --> 00:42:00,920
uh o and one and you can see

957
00:42:04,880 --> 00:42:11,440
that let make sure I did that right yeah

958
00:42:08,359 --> 00:42:11,440
you can you can see

959
00:42:15,599 --> 00:42:25,720
that one zero is entirely encompassed by

960
00:42:19,680 --> 00:42:29,200
uh by B so now B is one Z and C uh C is

961
00:42:25,720 --> 00:42:32,359
not L encompassed by that so you would

962
00:42:29,200 --> 00:42:39,240
need to further break this up and say

963
00:42:32,359 --> 00:42:41,880
it's Z one here and now one one

964
00:42:39,240 --> 00:42:45,520
one is encompassed by this so you would

965
00:42:41,880 --> 00:42:48,680
get uh you would get C if it was 111 and

966
00:42:45,520 --> 00:42:51,119
so every every sequence that started

967
00:42:48,680 --> 00:42:53,000
with zero would start out with a every

968
00:42:51,119 --> 00:42:54,960
sequence that started out with one zero

969
00:42:53,000 --> 00:42:57,200
would start with b and every sequence

970
00:42:54,960 --> 00:43:02,079
that started with 11 one1

971
00:42:57,200 --> 00:43:04,920
start um and so then you can look at the

972
00:43:02,079 --> 00:43:06,960
next word and let's say we're using a

973
00:43:04,920 --> 00:43:09,839
unigram model if we're using a unigram

974
00:43:06,960 --> 00:43:12,960
model for the next uh the next token

975
00:43:09,839 --> 00:43:18,200
let's say the next token is C

976
00:43:12,960 --> 00:43:23,640
so now the next token being C we already

977
00:43:18,200 --> 00:43:27,920
have B and now we take we subdivide

978
00:43:23,640 --> 00:43:33,040
B into

979
00:43:27,920 --> 00:43:35,720
a BC ba a BB and BC and then we find the

980
00:43:33,040 --> 00:43:40,720
next binary sequence that is entirely

981
00:43:35,720 --> 00:43:44,000
encompassed by uh BC by this like

982
00:43:40,720 --> 00:43:45,359
interval and so the moment we find a a

983
00:43:44,000 --> 00:43:48,520
binary sequence that's entirely

984
00:43:45,359 --> 00:43:50,599
encompassed by the interval uh then that

985
00:43:48,520 --> 00:43:53,400
is the the sequence that we can use to

986
00:43:50,599 --> 00:43:54,640
represent that SC and so um if you're

987
00:43:53,400 --> 00:43:56,520
interested in this you can look up the

988
00:43:54,640 --> 00:44:00,400
arithmetic coding on on wikip it's

989
00:43:56,520 --> 00:44:02,079
pretty fascinating but basically um here

990
00:44:00,400 --> 00:44:04,040
this is showing the example of the

991
00:44:02,079 --> 00:44:07,160
unigram model where the probabilities

992
00:44:04,040 --> 00:44:10,240
don't change based on the context but

993
00:44:07,160 --> 00:44:13,000
what if we knew that

994
00:44:10,240 --> 00:44:15,599
c had a really high probability of

995
00:44:13,000 --> 00:44:22,160
following B so if that's the case now we

996
00:44:15,599 --> 00:44:24,559
have like a a b c here um like based on

997
00:44:22,160 --> 00:44:25,880
our our byr model or neural language

998
00:44:24,559 --> 00:44:29,319
model or something like that so now this

999
00:44:25,880 --> 00:44:31,240
is interval is much much larger so it's

1000
00:44:29,319 --> 00:44:35,079
much more likely to entirely Encompass a

1001
00:44:31,240 --> 00:44:39,720
shorter string and because of that the

1002
00:44:35,079 --> 00:44:42,440
um the output can be much shorter and so

1003
00:44:39,720 --> 00:44:45,760
if you use this arithmetic encoding um

1004
00:44:42,440 --> 00:44:49,440
over a very long sequence of outputs

1005
00:44:45,760 --> 00:44:52,440
your the length of the sequence that is

1006
00:44:49,440 --> 00:44:56,000
needed to encode this uh this particular

1007
00:44:52,440 --> 00:45:00,359
output is going to be essentially um the

1008
00:44:56,000 --> 00:45:03,319
number of bits according to times the

1009
00:45:00,359 --> 00:45:06,480
times the sequence so this is very

1010
00:45:03,319 --> 00:45:10,000
directly connected to like compression

1011
00:45:06,480 --> 00:45:13,160
and information Theory and stuff like

1012
00:45:10,000 --> 00:45:15,359
that so that that's where entropy comes

1013
00:45:13,160 --> 00:45:17,680
from uh are are there any questions

1014
00:45:15,359 --> 00:45:17,680
about

1015
00:45:19,319 --> 00:45:22,319
this

1016
00:45:24,880 --> 00:45:28,119
yeah

1017
00:45:26,800 --> 00:45:31,880
uh for

1018
00:45:28,119 --> 00:45:34,319
c um so

1019
00:45:31,880 --> 00:45:36,599
111 is

1020
00:45:34,319 --> 00:45:37,920
because let me let me see if I can do

1021
00:45:36,599 --> 00:45:40,559
this

1022
00:45:37,920 --> 00:45:44,240
again

1023
00:45:40,559 --> 00:45:44,240
so I had one

1024
00:45:46,079 --> 00:45:54,520
one so here this interval is

1025
00:45:50,920 --> 00:45:56,839
one this interval is one one this

1026
00:45:54,520 --> 00:46:00,079
interval is 111

1027
00:45:56,839 --> 00:46:03,520
and 111 is the first interval that is

1028
00:46:00,079 --> 00:46:05,520
entirely overlapping with with c um and

1029
00:46:03,520 --> 00:46:08,760
it's not one Z because one one Z is

1030
00:46:05,520 --> 00:46:08,760
overlaping with b and

1031
00:46:09,960 --> 00:46:13,599
c so which

1032
00:46:14,280 --> 00:46:21,720
Cas so which case one

1033
00:46:20,160 --> 00:46:24,800
Z

1034
00:46:21,720 --> 00:46:26,319
one one one

1035
00:46:24,800 --> 00:46:30,800
Z

1036
00:46:26,319 --> 00:46:30,800
when would you use 110 to represent

1037
00:46:32,119 --> 00:46:38,839
something it's a good question I guess

1038
00:46:36,119 --> 00:46:40,599
maybe you wouldn't which seems a little

1039
00:46:38,839 --> 00:46:43,280
bit wasteful

1040
00:46:40,599 --> 00:46:46,160
so let me let me think about that I

1041
00:46:43,280 --> 00:46:49,920
think um it might be the case that you

1042
00:46:46,160 --> 00:46:52,319
just don't use it um

1043
00:46:49,920 --> 00:46:53,559
but yeah I'll try to think about that a

1044
00:46:52,319 --> 00:46:55,920
little bit more because it seems like

1045
00:46:53,559 --> 00:46:59,200
you should use every bet string right so

1046
00:46:55,920 --> 00:47:01,559
um yeah if anybody uh has has the answer

1047
00:46:59,200 --> 00:47:05,160
I'd be happy to hear it otherwise I take

1048
00:47:01,559 --> 00:47:07,079
you cool um so next thing is perplexity

1049
00:47:05,160 --> 00:47:10,640
so this is another one that you see

1050
00:47:07,079 --> 00:47:13,240
commonly and um so perplexity is

1051
00:47:10,640 --> 00:47:16,880
basically two to the ENT uh two to the

1052
00:47:13,240 --> 00:47:20,760
per word entropy or e to the uh negative

1053
00:47:16,880 --> 00:47:24,880
word level log likelihood in log space

1054
00:47:20,760 --> 00:47:28,240
um and so this uh T larger tends to be

1055
00:47:24,880 --> 00:47:32,559
better I'd like to do a little exercise

1056
00:47:28,240 --> 00:47:34,599
to see uh if this works so like let's

1057
00:47:32,559 --> 00:47:39,079
say we have one a dog sees a squirrel it

1058
00:47:34,599 --> 00:47:40,960
will usually um and can anyone guess the

1059
00:47:39,079 --> 00:47:43,480
next word just yell it

1060
00:47:40,960 --> 00:47:46,400
out bar

1061
00:47:43,480 --> 00:47:47,400
okay uh what about that what about

1062
00:47:46,400 --> 00:47:50,400
something

1063
00:47:47,400 --> 00:47:50,400
else

1064
00:47:52,640 --> 00:47:57,520
Chase Run

1065
00:47:54,720 --> 00:48:00,800
Run

1066
00:47:57,520 --> 00:48:00,800
okay John

1067
00:48:01,960 --> 00:48:05,280
John anything

1068
00:48:07,000 --> 00:48:10,400
else any other

1069
00:48:11,280 --> 00:48:16,960
ones so basically what this shows is

1070
00:48:13,640 --> 00:48:16,960
humans are really bad language

1071
00:48:17,160 --> 00:48:24,079
models so uh interestingly every single

1072
00:48:21,520 --> 00:48:26,559
one of the words you predicted here is a

1073
00:48:24,079 --> 00:48:32,240
uh a regular verb

1074
00:48:26,559 --> 00:48:35,200
um but in natural language model gpt2 uh

1075
00:48:32,240 --> 00:48:38,079
the first thing it predicts is B uh

1076
00:48:35,200 --> 00:48:40,440
which is kind of a like the Cula there's

1077
00:48:38,079 --> 00:48:43,400
also start and that will be like start

1078
00:48:40,440 --> 00:48:44,880
running start something um and humans

1079
00:48:43,400 --> 00:48:46,400
actually are really bad at doing this

1080
00:48:44,880 --> 00:48:49,079
are really bad at predicting next words

1081
00:48:46,400 --> 00:48:51,760
we're not trained that way um and so uh

1082
00:48:49,079 --> 00:48:54,319
we end up having these biases but anyway

1083
00:48:51,760 --> 00:48:55,799
um the reason why I did this quiz was

1084
00:48:54,319 --> 00:48:57,280
because that's essentially what

1085
00:48:55,799 --> 00:49:01,160
perplexity

1086
00:48:57,280 --> 00:49:02,680
means um and what what perplexity is is

1087
00:49:01,160 --> 00:49:04,559
it's the number of times you'd have to

1088
00:49:02,680 --> 00:49:07,000
sample from the probability distribution

1089
00:49:04,559 --> 00:49:09,200
before you get the answer right so you

1090
00:49:07,000 --> 00:49:11,160
were a little bit biased here because we

1091
00:49:09,200 --> 00:49:13,359
were doing sampling without replacement

1092
00:49:11,160 --> 00:49:15,480
so like nobody was actually picking a

1093
00:49:13,359 --> 00:49:17,000
word that had already been said but it's

1094
00:49:15,480 --> 00:49:18,319
essentially like if you guessed over and

1095
00:49:17,000 --> 00:49:20,839
over and over again how many times would

1096
00:49:18,319 --> 00:49:22,720
you need until you get it right and so

1097
00:49:20,839 --> 00:49:25,119
here like if the actual answer was start

1098
00:49:22,720 --> 00:49:27,480
the perplexity would be 4.66 so we'd

1099
00:49:25,119 --> 00:49:30,240
expect language model to get it in uh

1100
00:49:27,480 --> 00:49:34,400
four guesses uh between four and five

1101
00:49:30,240 --> 00:49:38,559
guesses and you guys all did six so you

1102
00:49:34,400 --> 00:49:41,599
lose um so uh another important thing to

1103
00:49:38,559 --> 00:49:42,799
mention is evaluation in vocabulary uh

1104
00:49:41,599 --> 00:49:44,880
so for fair

1105
00:49:42,799 --> 00:49:47,319
comparison um make sure that the

1106
00:49:44,880 --> 00:49:49,559
denominator is the same so uh if you're

1107
00:49:47,319 --> 00:49:51,559
calculating the perplexity make sure

1108
00:49:49,559 --> 00:49:53,359
that you're dividing by the same number

1109
00:49:51,559 --> 00:49:55,799
uh every time you're dividing by words

1110
00:49:53,359 --> 00:49:58,520
if it's uh the other paper or whatever

1111
00:49:55,799 --> 00:50:00,680
is dividing by words or like let's say

1112
00:49:58,520 --> 00:50:02,160
you're comparing llama to gp2 they have

1113
00:50:00,680 --> 00:50:04,880
different tokenizers so they'll have

1114
00:50:02,160 --> 00:50:07,040
different numbers of tokens so comparing

1115
00:50:04,880 --> 00:50:10,880
uh with different denominators is not uh

1116
00:50:07,040 --> 00:50:12,440
not fair um if you're allowing unknown

1117
00:50:10,880 --> 00:50:14,559
words or characters so if you allow the

1118
00:50:12,440 --> 00:50:17,640
model to not predict

1119
00:50:14,559 --> 00:50:19,119
any token then you need to be fair about

1120
00:50:17,640 --> 00:50:22,040
that

1121
00:50:19,119 --> 00:50:25,160
too um so I'd like to go into a few

1122
00:50:22,040 --> 00:50:27,960
Alternatives these are very similar to

1123
00:50:25,160 --> 00:50:29,400
the Network classifiers and bag of words

1124
00:50:27,960 --> 00:50:30,680
classifiers that I talked about before

1125
00:50:29,400 --> 00:50:32,480
so I'm going to go through them rather

1126
00:50:30,680 --> 00:50:35,480
quickly because I think you should get

1127
00:50:32,480 --> 00:50:38,119
the basic idea but basically the

1128
00:50:35,480 --> 00:50:40,000
alternative is uh featued models so we

1129
00:50:38,119 --> 00:50:42,559
calculate features of to account based

1130
00:50:40,000 --> 00:50:44,599
models as featued models so we calculate

1131
00:50:42,559 --> 00:50:46,880
features of the context and based on the

1132
00:50:44,599 --> 00:50:48,280
features calculate probabilities

1133
00:50:46,880 --> 00:50:50,480
optimize the feature weights using

1134
00:50:48,280 --> 00:50:53,839
gradient descent uh

1135
00:50:50,480 --> 00:50:56,119
Etc and so for example if we have uh

1136
00:50:53,839 --> 00:50:58,880
input giving a

1137
00:50:56,119 --> 00:51:02,960
uh we calculate features so um we might

1138
00:50:58,880 --> 00:51:05,400
look up uh the word identity of the two

1139
00:51:02,960 --> 00:51:08,240
previous words look up the word identity

1140
00:51:05,400 --> 00:51:11,000
of the word uh directly previous add a

1141
00:51:08,240 --> 00:51:13,480
bias add them all together get scores

1142
00:51:11,000 --> 00:51:14,960
and calculate probabilities where each

1143
00:51:13,480 --> 00:51:16,920
Vector is the size of the output

1144
00:51:14,960 --> 00:51:19,680
vocabulary and feature weights are

1145
00:51:16,920 --> 00:51:21,799
optimized using SGD so this is basically

1146
00:51:19,680 --> 00:51:24,240
a bag of words classifier but it's a

1147
00:51:21,799 --> 00:51:27,200
multiclass bag of words classifier over

1148
00:51:24,240 --> 00:51:28,960
the next token so it's very similar to

1149
00:51:27,200 --> 00:51:30,839
our classification task before except

1150
00:51:28,960 --> 00:51:33,160
now instead of having two classes we

1151
00:51:30,839 --> 00:51:36,280
have you know 10,000 classes or 100,000

1152
00:51:33,160 --> 00:51:38,480
classes oh yeah sorry very quick aside

1153
00:51:36,280 --> 00:51:40,280
um these were actually invented by Rony

1154
00:51:38,480 --> 00:51:41,440
Rosenfeld who's the head of the machine

1155
00:51:40,280 --> 00:51:45,119
learning department at the end the

1156
00:51:41,440 --> 00:51:47,799
machine learning Department uh so um 27

1157
00:51:45,119 --> 00:51:50,760
years ago I guess so he has even more

1158
00:51:47,799 --> 00:51:52,680
experience large language modeling than

1159
00:51:50,760 --> 00:51:55,880
um

1160
00:51:52,680 --> 00:51:58,599
cool so um the one difference with a bag

1161
00:51:55,880 --> 00:52:02,119
of words classifier is

1162
00:51:58,599 --> 00:52:05,480
um we we have

1163
00:52:02,119 --> 00:52:07,640
biases um and we have the probability

1164
00:52:05,480 --> 00:52:09,400
Vector given the previous word but

1165
00:52:07,640 --> 00:52:11,720
instead of using a bag of words this

1166
00:52:09,400 --> 00:52:15,440
actually is using uh How likely is it

1167
00:52:11,720 --> 00:52:16,960
giving given two words previous so uh

1168
00:52:15,440 --> 00:52:18,040
the feature design would be a little bit

1169
00:52:16,960 --> 00:52:19,119
different and that would give you a

1170
00:52:18,040 --> 00:52:22,920
total

1171
00:52:19,119 --> 00:52:24,359
score um as a reminder uh last time we

1172
00:52:22,920 --> 00:52:26,440
did a training algorithm where we

1173
00:52:24,359 --> 00:52:27,480
calculated gradients loss function with

1174
00:52:26,440 --> 00:52:29,960
respect to the

1175
00:52:27,480 --> 00:52:32,319
parameters and uh we can use the chain

1176
00:52:29,960 --> 00:52:33,839
Rule and back propagation and updates to

1177
00:52:32,319 --> 00:52:36,400
move in the direction that increases

1178
00:52:33,839 --> 00:52:39,040
enough so nothing extremely different

1179
00:52:36,400 --> 00:52:42,640
from what we had for our

1180
00:52:39,040 --> 00:52:44,240
B um similarly this solves some problems

1181
00:52:42,640 --> 00:52:47,240
so this didn't solve the problem of

1182
00:52:44,240 --> 00:52:49,119
sharing strength among similar words it

1183
00:52:47,240 --> 00:52:50,839
did solve the problem of conditioning on

1184
00:52:49,119 --> 00:52:52,839
context with intervening words because

1185
00:52:50,839 --> 00:52:56,920
now we can condition directly on Doctor

1186
00:52:52,839 --> 00:52:59,680
without having to um combine with

1187
00:52:56,920 --> 00:53:01,200
gitrid um and it doesn't necessarily

1188
00:52:59,680 --> 00:53:03,480
handle longdistance dependencies because

1189
00:53:01,200 --> 00:53:05,240
we're still limited in our context with

1190
00:53:03,480 --> 00:53:09,079
the model I just

1191
00:53:05,240 --> 00:53:11,920
described so um if we so sorry back to

1192
00:53:09,079 --> 00:53:13,480
neural networks is what I should say um

1193
00:53:11,920 --> 00:53:15,160
so if we have a feedforward neural

1194
00:53:13,480 --> 00:53:18,480
network language model the way this

1195
00:53:15,160 --> 00:53:20,400
could work is instead of looking up

1196
00:53:18,480 --> 00:53:23,079
discrete features uh like we had in a

1197
00:53:20,400 --> 00:53:25,960
bag of words model uh we would look up

1198
00:53:23,079 --> 00:53:27,400
dents embeddings and so we concatenate

1199
00:53:25,960 --> 00:53:29,359
together these dense

1200
00:53:27,400 --> 00:53:32,319
embeddings and based on the dense

1201
00:53:29,359 --> 00:53:34,599
embeddings uh we do some sort of uh

1202
00:53:32,319 --> 00:53:36,079
intermediate layer transforms to extract

1203
00:53:34,599 --> 00:53:37,200
features like we did for our neural

1204
00:53:36,079 --> 00:53:39,359
network based

1205
00:53:37,200 --> 00:53:41,520
classifier um we multiply this by

1206
00:53:39,359 --> 00:53:43,559
weights uh we have a bias and we

1207
00:53:41,520 --> 00:53:46,559
calculate

1208
00:53:43,559 --> 00:53:49,200
scores and uh then we take a soft Max to

1209
00:53:46,559 --> 00:53:49,200
do

1210
00:53:50,400 --> 00:53:55,799
classification so um this can calculate

1211
00:53:53,359 --> 00:53:58,000
combination features uh like we we also

1212
00:53:55,799 --> 00:54:02,280
used in our uh neural network based

1213
00:53:58,000 --> 00:54:04,119
classifiers so um this could uh give us

1214
00:54:02,280 --> 00:54:05,760
a positive number for example if the

1215
00:54:04,119 --> 00:54:07,760
previous word is a determiner and the

1216
00:54:05,760 --> 00:54:10,440
second previous word is a verb so that

1217
00:54:07,760 --> 00:54:14,520
would be like uh in giving and then that

1218
00:54:10,440 --> 00:54:14,520
would allow us upway to that particular

1219
00:54:15,000 --> 00:54:19,559
examples um so this allows us to share

1220
00:54:17,640 --> 00:54:21,640
strength in various places in our model

1221
00:54:19,559 --> 00:54:23,520
which was also You Know instrumental in

1222
00:54:21,640 --> 00:54:25,599
making our our neural network

1223
00:54:23,520 --> 00:54:28,000
classifiers work for similar work and

1224
00:54:25,599 --> 00:54:30,119
stuff and so these would be word

1225
00:54:28,000 --> 00:54:32,160
embeddings so similar words get similar

1226
00:54:30,119 --> 00:54:35,079
embeddings another really important

1227
00:54:32,160 --> 00:54:38,480
thing is uh similar output words also

1228
00:54:35,079 --> 00:54:41,839
get similar rows in The softmax Matrix

1229
00:54:38,480 --> 00:54:44,440
and so here remember if you remember

1230
00:54:41,839 --> 00:54:48,240
from last class this was a big Matrix

1231
00:54:44,440 --> 00:54:50,400
where the size of the Matrix was the

1232
00:54:48,240 --> 00:54:53,319
number of vocabulary items times the

1233
00:54:50,400 --> 00:54:55,920
size of a word embedding this is also a

1234
00:54:53,319 --> 00:54:58,319
matrix where this is

1235
00:54:55,920 --> 00:55:02,200
the number of vocabulary items times the

1236
00:54:58,319 --> 00:55:04,160
size of a context embedding gr and so

1237
00:55:02,200 --> 00:55:06,160
these will also be similar because words

1238
00:55:04,160 --> 00:55:08,280
that appear in similar contexts will

1239
00:55:06,160 --> 00:55:11,920
also you know want similar embeddings so

1240
00:55:08,280 --> 00:55:15,119
they get uploaded in at the same

1241
00:55:11,920 --> 00:55:17,119
time and similar hidden States will have

1242
00:55:15,119 --> 00:55:19,799
similar context so ideally like if you

1243
00:55:17,119 --> 00:55:20,920
have giving a or delivering a or

1244
00:55:19,799 --> 00:55:22,680
something like that those would be

1245
00:55:20,920 --> 00:55:27,000
similar contexts so they would get

1246
00:55:22,680 --> 00:55:27,000
similar purple embeddings out out of the

1247
00:55:28,440 --> 00:55:31,599
so one trick that's widely used in

1248
00:55:30,200 --> 00:55:34,960
language model that further takes

1249
00:55:31,599 --> 00:55:38,799
advantage of this is uh tying

1250
00:55:34,960 --> 00:55:44,160
embeddings so here what this does is

1251
00:55:38,799 --> 00:55:48,280
sharing parameters between this um

1252
00:55:44,160 --> 00:55:49,920
lookup Matrix here and this uh Matrix

1253
00:55:48,280 --> 00:55:51,119
over here that we use for calculating

1254
00:55:49,920 --> 00:55:56,200
the

1255
00:55:51,119 --> 00:55:58,839
softmax and um the reason why this is

1256
00:55:56,200 --> 00:56:00,559
useful is twofold number one it gives

1257
00:55:58,839 --> 00:56:02,079
you essentially more training data to

1258
00:56:00,559 --> 00:56:04,440
learn these embeddings because instead

1259
00:56:02,079 --> 00:56:05,799
of learning the embeddings whenever a

1260
00:56:04,440 --> 00:56:08,520
word is in

1261
00:56:05,799 --> 00:56:10,599
context separately from learning the

1262
00:56:08,520 --> 00:56:13,520
embeddings whenever a word is predicted

1263
00:56:10,599 --> 00:56:15,480
you learn the the same embedding Matrix

1264
00:56:13,520 --> 00:56:19,319
whenever the word is in the context or

1265
00:56:15,480 --> 00:56:21,520
whatever it's predicted and so um that

1266
00:56:19,319 --> 00:56:24,119
makes it more accurate to learn these uh

1267
00:56:21,520 --> 00:56:26,960
embeddings well another thing is the

1268
00:56:24,119 --> 00:56:31,119
embedding mat can actually be very large

1269
00:56:26,960 --> 00:56:34,920
so like let's say we have aab of

1270
00:56:31,119 --> 00:56:37,520
10 100,000 and we have an embedding a

1271
00:56:34,920 --> 00:56:40,799
word embedding size of like 512 or

1272
00:56:37,520 --> 00:56:45,319
something like that

1273
00:56:40,799 --> 00:56:45,319
that's um 51 million

1274
00:56:46,839 --> 00:56:52,440
parameters um and this doesn't sound

1275
00:56:49,559 --> 00:56:55,520
like a lot of parameters at first but it

1276
00:56:52,440 --> 00:56:57,880
actually is a lot to learn when um

1277
00:56:55,520 --> 00:57:01,000
these get updated relatively

1278
00:56:57,880 --> 00:57:03,400
infrequently uh because

1279
00:57:01,000 --> 00:57:06,079
um these get updated relatively

1280
00:57:03,400 --> 00:57:07,960
infrequently because they only are

1281
00:57:06,079 --> 00:57:09,559
updated whenever that word or token

1282
00:57:07,960 --> 00:57:12,319
actually appears in your training data

1283
00:57:09,559 --> 00:57:14,119
so um this can be a good thing for

1284
00:57:12,319 --> 00:57:16,319
parameter savings parameter efficiency

1285
00:57:14,119 --> 00:57:16,319
as

1286
00:57:16,440 --> 00:57:22,520
well um so this uh solves most of the

1287
00:57:19,599 --> 00:57:24,319
problems here um but it doesn't solve

1288
00:57:22,520 --> 00:57:26,839
the problem of longdistance dependencies

1289
00:57:24,319 --> 00:57:29,839
because still limited by the overall

1290
00:57:26,839 --> 00:57:31,359
length of uh the context that we're

1291
00:57:29,839 --> 00:57:32,520
concatenating together here sure we

1292
00:57:31,359 --> 00:57:35,760
could make that longer but that would

1293
00:57:32,520 --> 00:57:37,200
make our model larger and um and bring

1294
00:57:35,760 --> 00:57:39,720
various

1295
00:57:37,200 --> 00:57:42,520
issues and so what I'm going to talk

1296
00:57:39,720 --> 00:57:44,599
about in on thur day is how we solve

1297
00:57:42,520 --> 00:57:47,559
this problem of modeling long contexts

1298
00:57:44,599 --> 00:57:49,720
so how do we um build recurrent neural

1299
00:57:47,559 --> 00:57:52,559
networks uh how do we build

1300
00:57:49,720 --> 00:57:54,960
convolutional uh convolutional networks

1301
00:57:52,559 --> 00:57:57,520
or how do we build attention based

1302
00:57:54,960 --> 00:58:00,720
Transformer models and these are all

1303
00:57:57,520 --> 00:58:02,119
options that are used um Transformers

1304
00:58:00,720 --> 00:58:04,359
are kind of

1305
00:58:02,119 --> 00:58:06,039
the the main thing that people use

1306
00:58:04,359 --> 00:58:08,400
nowadays but there's a lot of versions

1307
00:58:06,039 --> 00:58:11,880
of Transformers that borrow ideas from

1308
00:58:08,400 --> 00:58:14,960
recurrent uh and convolutional models

1309
00:58:11,880 --> 00:58:17,359
um recently a lot of long context models

1310
00:58:14,960 --> 00:58:19,440
us use ideas from recurrent networks and

1311
00:58:17,359 --> 00:58:22,160
a lot of for example speech models or

1312
00:58:19,440 --> 00:58:24,160
things like or image models use ideas

1313
00:58:22,160 --> 00:58:25,920
from convolutional networks so I think

1314
00:58:24,160 --> 00:58:28,760
learning all but at the same time is a

1315
00:58:25,920 --> 00:58:32,160
good idea in comparing

1316
00:58:28,760 --> 00:58:34,319
them cool uh any any questions about

1317
00:58:32,160 --> 00:58:35,799
this part I went through this kind of

1318
00:58:34,319 --> 00:58:37,319
quickly because it's pretty similar to

1319
00:58:35,799 --> 00:58:40,079
the the classification stuff that we

1320
00:58:37,319 --> 00:58:42,680
covered last time but uh any any things

1321
00:58:40,079 --> 00:58:42,680
that people want to

1322
00:58:43,880 --> 00:58:49,039
ask okay so next I'm going to talk about

1323
00:58:46,839 --> 00:58:51,559
a few other desiderata of language

1324
00:58:49,039 --> 00:58:53,039
models so the next one is really really

1325
00:58:51,559 --> 00:58:55,640
important it's a concept I want

1326
00:58:53,039 --> 00:58:57,640
everybody to know I actually

1327
00:58:55,640 --> 00:58:59,520
taught this informally up until this

1328
00:58:57,640 --> 00:59:02,039
class but now I I actually made slides

1329
00:58:59,520 --> 00:59:05,079
for it starting this time which is

1330
00:59:02,039 --> 00:59:07,240
calibration so the idea of calibration

1331
00:59:05,079 --> 00:59:10,200
is that the model quote unquote knows

1332
00:59:07,240 --> 00:59:14,559
when it knows or the the fact that it is

1333
00:59:10,200 --> 00:59:17,480
able to provide a a good answer um uh

1334
00:59:14,559 --> 00:59:21,640
provide a good confidence in its answer

1335
00:59:17,480 --> 00:59:23,640
and more formally this can be specified

1336
00:59:21,640 --> 00:59:25,240
as

1337
00:59:23,640 --> 00:59:27,799
the

1338
00:59:25,240 --> 00:59:29,200
feature that the model probability of

1339
00:59:27,799 --> 00:59:33,119
the answer matches the actual

1340
00:59:29,200 --> 00:59:37,319
probability of getting it right um and

1341
00:59:33,119 --> 00:59:37,319
so what this means

1342
00:59:41,960 --> 00:59:47,480
is the

1343
00:59:44,240 --> 00:59:51,839
probability of the

1344
00:59:47,480 --> 00:59:51,839
answer um is

1345
00:59:52,720 --> 00:59:59,880
correct given the fact that

1346
00:59:56,319 --> 00:59:59,880
the model

1347
01:00:00,160 --> 01:00:07,440
probability is equal to

1348
01:00:03,640 --> 01:00:07,440
P is equal to

1349
01:00:08,559 --> 01:00:12,760
ke

1350
01:00:10,480 --> 01:00:15,319
so I know this is a little bit hard to

1351
01:00:12,760 --> 01:00:18,240
parse I it always took me like a few

1352
01:00:15,319 --> 01:00:21,720
seconds to parse before I uh like when I

1353
01:00:18,240 --> 01:00:25,160
looked at it but basically if the model

1354
01:00:21,720 --> 01:00:26,920
if the model says the probability of it

1355
01:00:25,160 --> 01:00:29,440
being correct is

1356
01:00:26,920 --> 01:00:33,559
0.7 then the probability that the answer

1357
01:00:29,440 --> 01:00:35,960
is correct is actually 0.7 so um you

1358
01:00:33,559 --> 01:00:41,520
know if it says uh the probability is

1359
01:00:35,960 --> 01:00:41,520
0.7 100 times then it will be right 70

1360
01:00:43,640 --> 01:00:52,160
times and so the way we formalize this

1361
01:00:48,039 --> 01:00:55,200
um is is by this uh it was proposed by

1362
01:00:52,160 --> 01:00:57,760
this seminal paper by gu it all in

1363
01:00:55,200 --> 01:01:00,319
2017

1364
01:00:57,760 --> 01:01:03,319
and

1365
01:01:00,319 --> 01:01:05,520
unfortunately this data itself is hard

1366
01:01:03,319 --> 01:01:08,119
to collect

1367
01:01:05,520 --> 01:01:11,200
because the model probability is always

1368
01:01:08,119 --> 01:01:13,359
different right and so if the model

1369
01:01:11,200 --> 01:01:15,359
probability is like if the model

1370
01:01:13,359 --> 01:01:20,480
probability was actually 0.7 that'd be

1371
01:01:15,359 --> 01:01:22,000
nice but actually it's 0.793 to 6 8 5

1372
01:01:20,480 --> 01:01:24,599
and you never get another example where

1373
01:01:22,000 --> 01:01:26,319
the probability is exactly the same so

1374
01:01:24,599 --> 01:01:28,280
what we do instead is we divide the

1375
01:01:26,319 --> 01:01:30,240
model probabilities into buckets so we

1376
01:01:28,280 --> 01:01:32,880
say the model probability is between 0

1377
01:01:30,240 --> 01:01:36,599
and 0.1 we say the model probability is

1378
01:01:32,880 --> 01:01:40,319
between 0.1 and 0.2 0.2 and 0.3 so we

1379
01:01:36,599 --> 01:01:44,599
create buckets like this like these and

1380
01:01:40,319 --> 01:01:46,520
then we looked at the model confidence

1381
01:01:44,599 --> 01:01:52,839
the average model confidence within that

1382
01:01:46,520 --> 01:01:55,000
bucket so maybe uh between 0.1 and 0 uh

1383
01:01:52,839 --> 01:01:58,000
between 0 and 0.1 the model confidence

1384
01:01:55,000 --> 01:02:00,920
on average is 0 055 or something like

1385
01:01:58,000 --> 01:02:02,640
that so that would be this T here and

1386
01:02:00,920 --> 01:02:05,079
then the accuracy is how often did it

1387
01:02:02,640 --> 01:02:06,680
actually get a correct and this can be

1388
01:02:05,079 --> 01:02:09,720
plotted in this thing called a

1389
01:02:06,680 --> 01:02:15,039
reliability diagram and the reliability

1390
01:02:09,720 --> 01:02:17,599
diagram basically um the the

1391
01:02:15,039 --> 01:02:20,359
outputs uh

1392
01:02:17,599 --> 01:02:26,359
here so this is

1393
01:02:20,359 --> 01:02:26,359
um the this is the model

1394
01:02:27,520 --> 01:02:34,119
yeah I think the red is the model

1395
01:02:30,760 --> 01:02:36,400
um expected probability and then the

1396
01:02:34,119 --> 01:02:40,559
blue uh the blue is the actual

1397
01:02:36,400 --> 01:02:43,240
probability and then um

1398
01:02:40,559 --> 01:02:45,160
the difference between the expected and

1399
01:02:43,240 --> 01:02:47,160
the actual probability is kind of like

1400
01:02:45,160 --> 01:02:48,359
the penalty there is how how poorly

1401
01:02:47,160 --> 01:02:52,000
calibrated

1402
01:02:48,359 --> 01:02:55,880
the and one really important thing to

1403
01:02:52,000 --> 01:02:58,440
know is that calibration in accuracy are

1404
01:02:55,880 --> 01:03:00,599
not necessarily they don't go hand inand

1405
01:02:58,440 --> 01:03:02,359
uh they do to some extent but they don't

1406
01:03:00,599 --> 01:03:06,440
uh they don't necessarily go hand in

1407
01:03:02,359 --> 01:03:06,440
hand and

1408
01:03:07,200 --> 01:03:14,319
the example on the left is a a bad model

1409
01:03:11,200 --> 01:03:16,279
but a well calibrated so its accuracy is

1410
01:03:14,319 --> 01:03:18,720
uh its error is

1411
01:03:16,279 --> 01:03:20,000
44.9% um but it's well calibrated as you

1412
01:03:18,720 --> 01:03:21,440
can see like when it says it knows the

1413
01:03:20,000 --> 01:03:23,880
answer it knows the answer when it

1414
01:03:21,440 --> 01:03:27,799
doesn't answer does this model on the

1415
01:03:23,880 --> 01:03:30,000
other hand has better erir and um but

1416
01:03:27,799 --> 01:03:31,880
worse calibration so the reason why is

1417
01:03:30,000 --> 01:03:36,680
the model is very very confident all the

1418
01:03:31,880 --> 01:03:39,640
time and usually what happens is um

1419
01:03:36,680 --> 01:03:41,200
models that overfit to the data

1420
01:03:39,640 --> 01:03:43,359
especially when you do early stopping on

1421
01:03:41,200 --> 01:03:44,760
something like accuracy uh when you stop

1422
01:03:43,359 --> 01:03:47,279
the training on something like accuracy

1423
01:03:44,760 --> 01:03:49,960
will become very overconfident and uh

1424
01:03:47,279 --> 01:03:52,599
give confidence estimates um that are in

1425
01:03:49,960 --> 01:03:54,000
cor like this so this is important to

1426
01:03:52,599 --> 01:03:56,079
know and the reason why it's important

1427
01:03:54,000 --> 01:03:58,000
to know is actually because you know

1428
01:03:56,079 --> 01:04:00,960
models are very good at making up things

1429
01:03:58,000 --> 01:04:02,359
that aren't actually correct nowadays um

1430
01:04:00,960 --> 01:04:04,920
and but if you have a really well

1431
01:04:02,359 --> 01:04:07,760
calibrated model you could at least say

1432
01:04:04,920 --> 01:04:09,920
with what confidence you have this

1433
01:04:07,760 --> 01:04:12,760
working so how do you calculate the

1434
01:04:09,920 --> 01:04:14,160
probability of an answer so H yeah sorry

1435
01:04:12,760 --> 01:04:17,599
uh yes

1436
01:04:14,160 --> 01:04:17,599
yes yeah please

1437
01:04:17,799 --> 01:04:26,559
go the probability of percent or

1438
01:04:23,200 --> 01:04:28,039
percent um usually this would be for a

1439
01:04:26,559 --> 01:04:29,599
generated output because you want to

1440
01:04:28,039 --> 01:04:32,559
know the the probability that the

1441
01:04:29,599 --> 01:04:32,559
generated output is

1442
01:04:53,160 --> 01:04:56,160
cor

1443
01:05:01,079 --> 01:05:06,319
great that's what I'm about to talk

1444
01:05:03,000 --> 01:05:07,839
about so perfect perfect question um so

1445
01:05:06,319 --> 01:05:10,160
how do we calculate the answer

1446
01:05:07,839 --> 01:05:13,279
probability or um how do we calculate

1447
01:05:10,160 --> 01:05:15,039
the confidence in an answer um we're

1448
01:05:13,279 --> 01:05:18,319
actually going to go into more detail

1449
01:05:15,039 --> 01:05:20,760
about this um in a a later class but the

1450
01:05:18,319 --> 01:05:23,200
first thing is probability of the answer

1451
01:05:20,760 --> 01:05:25,799
and this is easy when there's a single

1452
01:05:23,200 --> 01:05:29,079
answer um like if there's only one

1453
01:05:25,799 --> 01:05:31,839
correct answer and you want your model

1454
01:05:29,079 --> 01:05:34,160
to be solving math problems and you want

1455
01:05:31,839 --> 01:05:38,319
it to return only the answer and nothing

1456
01:05:34,160 --> 01:05:40,760
else if it returns anything else like it

1457
01:05:38,319 --> 01:05:44,920
won't work then you can just use the

1458
01:05:40,760 --> 01:05:47,119
probability of the answer but what

1459
01:05:44,920 --> 01:05:49,559
if

1460
01:05:47,119 --> 01:05:52,000
um what if there are multiple acceptable

1461
01:05:49,559 --> 01:05:54,680
answers um and maybe a perfect example

1462
01:05:52,000 --> 01:06:02,240
of that is like where is CMU located

1463
01:05:54,680 --> 01:06:04,400
or um uh where where are we right now um

1464
01:06:02,240 --> 01:06:06,960
if the answer is where are we right

1465
01:06:04,400 --> 01:06:08,880
now um could be

1466
01:06:06,960 --> 01:06:12,880
Pittsburgh could be

1467
01:06:08,880 --> 01:06:12,880
CMU could be carnegy

1468
01:06:16,200 --> 01:06:24,440
melon could be other other things like

1469
01:06:18,760 --> 01:06:26,760
this right um and so another way that

1470
01:06:24,440 --> 01:06:28,319
you can calculate the confidence is

1471
01:06:26,760 --> 01:06:31,240
calculating the probability of the

1472
01:06:28,319 --> 01:06:33,680
answer plus uh you know paraphrases of

1473
01:06:31,240 --> 01:06:35,799
the answer or other uh other things like

1474
01:06:33,680 --> 01:06:37,680
this and so then you would just sum the

1475
01:06:35,799 --> 01:06:38,839
probability over all the qu like

1476
01:06:37,680 --> 01:06:41,680
acceptable

1477
01:06:38,839 --> 01:06:45,359
answers

1478
01:06:41,680 --> 01:06:47,680
um another thing that you can do is um

1479
01:06:45,359 --> 01:06:49,279
sample multiple outputs and count the

1480
01:06:47,680 --> 01:06:51,000
number of times you get a particular

1481
01:06:49,279 --> 01:06:54,440
answer this doesn't solve the problem of

1482
01:06:51,000 --> 01:06:58,119
paraphrasing ex paraphrases existing but

1483
01:06:54,440 --> 01:06:59,880
it does solve the problem of uh it does

1484
01:06:58,119 --> 01:07:01,480
solve two problems sometimes there are

1485
01:06:59,880 --> 01:07:05,240
language models where you can't get

1486
01:07:01,480 --> 01:07:06,640
probabilities out of them um this is not

1487
01:07:05,240 --> 01:07:08,680
so much of a problem anymore with the

1488
01:07:06,640 --> 01:07:11,240
GPT models because they're reintroducing

1489
01:07:08,680 --> 01:07:12,440
the ability to get probabilities but um

1490
01:07:11,240 --> 01:07:13,720
there are some models where you can just

1491
01:07:12,440 --> 01:07:16,279
sample from them and you can't get

1492
01:07:13,720 --> 01:07:18,680
probabilities out but also more

1493
01:07:16,279 --> 01:07:21,039
importantly um sometimes when you're

1494
01:07:18,680 --> 01:07:23,000
using things like uh Chain of Thought

1495
01:07:21,039 --> 01:07:26,520
reasoning which I'll talk about in more

1496
01:07:23,000 --> 01:07:29,839
detail but basically it's like um please

1497
01:07:26,520 --> 01:07:31,480
solve this math problem and explain

1498
01:07:29,839 --> 01:07:33,480
explain your solution and then if it

1499
01:07:31,480 --> 01:07:35,119
will do that it will generate you know a

1500
01:07:33,480 --> 01:07:36,279
really long explanation of how it got to

1501
01:07:35,119 --> 01:07:40,119
the solution and then it will give you

1502
01:07:36,279 --> 01:07:41,640
the answer at the very end and so then

1503
01:07:40,119 --> 01:07:44,960
you can't calculate the probability of

1504
01:07:41,640 --> 01:07:47,720
the actual like answer itself because

1505
01:07:44,960 --> 01:07:49,359
there's this long reasoning chain in

1506
01:07:47,720 --> 01:07:51,960
between and you have like all these

1507
01:07:49,359 --> 01:07:53,559
other all that other text there but what

1508
01:07:51,960 --> 01:07:55,480
you can do is you can sample those

1509
01:07:53,559 --> 01:07:56,920
reasoning chains 100 times and then see

1510
01:07:55,480 --> 01:07:59,599
how many times you got a particular

1511
01:07:56,920 --> 01:08:02,960
answer and that's actually a pretty um a

1512
01:07:59,599 --> 01:08:06,079
Prett pretty reasonable way of uh

1513
01:08:02,960 --> 01:08:09,000
getting a have

1514
01:08:06,079 --> 01:08:11,200
yet this is my favorite one I I love how

1515
01:08:09,000 --> 01:08:12,880
we can do this now it's just absolutely

1516
01:08:11,200 --> 01:08:16,480
ridiculous but you could ask the model

1517
01:08:12,880 --> 01:08:20,279
how confident it is and um it sometimes

1518
01:08:16,480 --> 01:08:22,359
gives you a reasonable uh a reasonable

1519
01:08:20,279 --> 01:08:24,600
answer um there's a really nice

1520
01:08:22,359 --> 01:08:26,400
comparison of different methods uh in

1521
01:08:24,600 --> 01:08:29,679
this paper which is also on on the

1522
01:08:26,400 --> 01:08:31,960
website and basically long story short

1523
01:08:29,679 --> 01:08:34,000
the conclusion from this paper is the

1524
01:08:31,960 --> 01:08:35,640
sampling multiple outputs one is the

1525
01:08:34,000 --> 01:08:36,839
best way to do it if you can't directly

1526
01:08:35,640 --> 01:08:39,520
calculate

1527
01:08:36,839 --> 01:08:41,359
probabilities um another thing that I'd

1528
01:08:39,520 --> 01:08:42,600
like people to pay very close attention

1529
01:08:41,359 --> 01:08:45,040
to is in the

1530
01:08:42,600 --> 01:08:46,480
Generation Um in the generation class

1531
01:08:45,040 --> 01:08:49,600
we're going to be talking about minimum

1532
01:08:46,480 --> 01:08:52,600
based risk which is a Criterion for

1533
01:08:49,600 --> 01:08:54,719
deciding how risky an output is and it's

1534
01:08:52,600 --> 01:08:56,199
actually a really good uh confidence

1535
01:08:54,719 --> 01:08:58,000
metric as well but I'm going to leave

1536
01:08:56,199 --> 01:08:59,440
that till when we discuss it more detail

1537
01:08:58,000 --> 01:09:02,759
with

1538
01:08:59,440 --> 01:09:05,359
it um any any questions

1539
01:09:02,759 --> 01:09:08,440
here okay

1540
01:09:05,359 --> 01:09:10,480
cool um so the other Criterion uh this

1541
01:09:08,440 --> 01:09:12,520
is just yet another Criterion that we

1542
01:09:10,480 --> 01:09:15,239
would like language models to be good at

1543
01:09:12,520 --> 01:09:17,600
um its efficiency and so basically the

1544
01:09:15,239 --> 01:09:21,920
model is easy to run on limited Hardware

1545
01:09:17,600 --> 01:09:25,400
by some you know uh metric of easy and

1546
01:09:21,920 --> 01:09:29,319
some metrics that we like to talk about

1547
01:09:25,400 --> 01:09:32,400
our parameter account so often you will

1548
01:09:29,319 --> 01:09:34,239
see oh this is the best model under

1549
01:09:32,400 --> 01:09:35,520
three billion parameters or this is the

1550
01:09:34,239 --> 01:09:37,960
best model under seven billion

1551
01:09:35,520 --> 01:09:39,600
parameters or um we trained a model with

1552
01:09:37,960 --> 01:09:42,159
one trillion parameters or something

1553
01:09:39,600 --> 01:09:44,719
like that you know

1554
01:09:42,159 --> 01:09:46,839
uh the thing is parameter count doesn't

1555
01:09:44,719 --> 01:09:49,640
really mean that much um from the point

1556
01:09:46,839 --> 01:09:52,839
of view of like ease of using the model

1557
01:09:49,640 --> 01:09:54,400
um unless you also think about other uh

1558
01:09:52,839 --> 01:09:56,480
you know deser

1559
01:09:54,400 --> 01:09:58,840
like just to give one example this is a

1560
01:09:56,480 --> 01:10:00,880
parameter count um let's say you have a

1561
01:09:58,840 --> 01:10:02,960
parameter count of 7 billion is that 7

1562
01:10:00,880 --> 01:10:05,719
billion parameters at 32-bit Precision

1563
01:10:02,960 --> 01:10:07,800
or is that 7 billion parameters at 4bit

1564
01:10:05,719 --> 01:10:09,400
Precision um will make a huge difference

1565
01:10:07,800 --> 01:10:12,960
in your memory footprint your speed

1566
01:10:09,400 --> 01:10:14,920
other things like that um so some of the

1567
01:10:12,960 --> 01:10:18,040
things that are more direct with respect

1568
01:10:14,920 --> 01:10:19,800
to efficiency are memory usage um and

1569
01:10:18,040 --> 01:10:22,440
there's two varieties of memory usage

1570
01:10:19,800 --> 01:10:24,280
one is model uh model only memory usage

1571
01:10:22,440 --> 01:10:27,120
so when you load loaded the model into

1572
01:10:24,280 --> 01:10:29,120
memory uh how much space does it take

1573
01:10:27,120 --> 01:10:31,159
and also Peak memory consumption when

1574
01:10:29,120 --> 01:10:33,159
you run have run the model over a

1575
01:10:31,159 --> 01:10:35,920
sequence of a certain length how much is

1576
01:10:33,159 --> 01:10:40,040
it going to P so that's another

1577
01:10:35,920 --> 01:10:43,000
thing another thing is latency um and

1578
01:10:40,040 --> 01:10:46,440
with respect to latency this can be

1579
01:10:43,000 --> 01:10:49,440
either how long does it take to start

1580
01:10:46,440 --> 01:10:52,080
outputting the first token um and how

1581
01:10:49,440 --> 01:10:54,840
long does it take to uh finish

1582
01:10:52,080 --> 01:10:59,480
outputting uh a generation of a certain

1583
01:10:54,840 --> 01:11:01,199
length and the first will have more to

1584
01:10:59,480 --> 01:11:04,960
do with how long does it take to encode

1585
01:11:01,199 --> 01:11:06,480
a sequence um which is usually faster

1586
01:11:04,960 --> 01:11:09,080
than how long does it take to generate a

1587
01:11:06,480 --> 01:11:11,360
sequence so this will have to do with

1588
01:11:09,080 --> 01:11:13,000
like encoding time this will require

1589
01:11:11,360 --> 01:11:15,880
encoding time of course but it will also

1590
01:11:13,000 --> 01:11:15,880
require generation

1591
01:11:16,280 --> 01:11:21,840
time also throughput so you know how

1592
01:11:19,239 --> 01:11:23,679
much um how many sentences can you

1593
01:11:21,840 --> 01:11:25,400
process in a certain amount of time so

1594
01:11:23,679 --> 01:11:26,480
of these are kind of desad that you you

1595
01:11:25,400 --> 01:11:29,000
would

1596
01:11:26,480 --> 01:11:30,280
say um we're going to be talking about

1597
01:11:29,000 --> 01:11:31,920
this more in the distillation and

1598
01:11:30,280 --> 01:11:33,199
compression and generation algorithms

1599
01:11:31,920 --> 01:11:35,640
classes so I won't go into a whole lot

1600
01:11:33,199 --> 01:11:36,840
of detail about this but um it's just

1601
01:11:35,640 --> 01:11:39,960
another thing that we want to be

1602
01:11:36,840 --> 01:11:43,560
thinking about in addition to

1603
01:11:39,960 --> 01:11:45,360
complexity um but since I'm I'm on the

1604
01:11:43,560 --> 01:11:47,800
topic of efficiency I would like to talk

1605
01:11:45,360 --> 01:11:49,480
just a little bit about it um in terms

1606
01:11:47,800 --> 01:11:51,000
of especially things that will be useful

1607
01:11:49,480 --> 01:11:53,600
for implementing your first

1608
01:11:51,000 --> 01:11:55,840
assignment and uh one thing that every

1609
01:11:53,600 --> 01:11:58,639
body should know about um if you've done

1610
01:11:55,840 --> 01:11:59,920
any like deep learning with pytorch or

1611
01:11:58,639 --> 01:12:02,639
something like this you already know

1612
01:11:59,920 --> 01:12:05,880
about this probably but uh I think it's

1613
01:12:02,639 --> 01:12:08,760
worth mentioning but basically mini

1614
01:12:05,880 --> 01:12:12,120
batching or batching uh is uh very

1615
01:12:08,760 --> 01:12:15,320
useful and the basic idea behind it is

1616
01:12:12,120 --> 01:12:17,560
that on Modern Hardware if you do many

1617
01:12:15,320 --> 01:12:20,520
of the same operations at once it's much

1618
01:12:17,560 --> 01:12:24,320
faster than doing um

1619
01:12:20,520 --> 01:12:25,480
like uh operations executively and

1620
01:12:24,320 --> 01:12:27,280
that's especially the case if you're

1621
01:12:25,480 --> 01:12:30,520
programming in an extremely slow

1622
01:12:27,280 --> 01:12:33,239
programming language like python um I

1623
01:12:30,520 --> 01:12:37,239
love python but it's slow I mean like

1624
01:12:33,239 --> 01:12:38,719
there's no argument about that um and so

1625
01:12:37,239 --> 01:12:40,520
what mini batching does is it combines

1626
01:12:38,719 --> 01:12:43,600
together smaller operations into one big

1627
01:12:40,520 --> 01:12:47,480
one and the basic idea uh for example if

1628
01:12:43,600 --> 01:12:51,679
we want to calculate our um our linear

1629
01:12:47,480 --> 01:12:56,560
layer with a t uh nonlinearity after it

1630
01:12:51,679 --> 01:12:59,760
we will take several inputs X1 X2 X3

1631
01:12:56,560 --> 01:13:02,040
concatenate them together and do a

1632
01:12:59,760 --> 01:13:04,600
Matrix Matrix multiply instead of doing

1633
01:13:02,040 --> 01:13:07,960
three Vector Matrix

1634
01:13:04,600 --> 01:13:09,239
multiplies and so what we do is we take

1635
01:13:07,960 --> 01:13:11,280
a whole bunch of examples we take like

1636
01:13:09,239 --> 01:13:13,840
64 examples or something like that and

1637
01:13:11,280 --> 01:13:18,000
we combine them together and calculate

1638
01:13:13,840 --> 01:13:21,280
out thingsit one thing to know is that

1639
01:13:18,000 --> 01:13:22,560
if you're working with sentences there's

1640
01:13:21,280 --> 01:13:24,719
different ways you can calculate the

1641
01:13:22,560 --> 01:13:27,360
size of your mini

1642
01:13:24,719 --> 01:13:28,880
normally nowadays the thing that people

1643
01:13:27,360 --> 01:13:30,400
do and the thing that I recommend is to

1644
01:13:28,880 --> 01:13:31,679
calculate the size of your mini batches

1645
01:13:30,400 --> 01:13:33,639
based on the number of tokens in the

1646
01:13:31,679 --> 01:13:35,840
mini batch it used to be that you would

1647
01:13:33,639 --> 01:13:39,719
do it based on the number of sequences

1648
01:13:35,840 --> 01:13:43,800
but the the problem is um one like 50

1649
01:13:39,719 --> 01:13:47,120
sequences of length like 100 is much

1650
01:13:43,800 --> 01:13:49,480
more memory intensive than uh 50

1651
01:13:47,120 --> 01:13:51,960
sequences of Link five and so you get

1652
01:13:49,480 --> 01:13:53,920
these vastly varying these mini batches

1653
01:13:51,960 --> 01:13:57,000
of vastly varying size and that's both

1654
01:13:53,920 --> 01:13:59,800
bad for you know memory overflows and

1655
01:13:57,000 --> 01:14:01,639
bad for um and bad for learning

1656
01:13:59,800 --> 01:14:04,280
stability so I I definitely recommend

1657
01:14:01,639 --> 01:14:06,880
doing it based on the number of

1658
01:14:04,280 --> 01:14:09,080
comps uh another thing is gpus versus

1659
01:14:06,880 --> 01:14:12,400
CPUs so

1660
01:14:09,080 --> 01:14:14,600
um uh CPUs one way you can think of it

1661
01:14:12,400 --> 01:14:17,320
is a CPUs kind of like a motorcycle it's

1662
01:14:14,600 --> 01:14:19,600
very fast at picking up and doing a

1663
01:14:17,320 --> 01:14:23,960
bunch of uh things very quickly

1664
01:14:19,600 --> 01:14:26,600
accelerating uh into starting new uh new

1665
01:14:23,960 --> 01:14:28,760
tasks a GPU is more like an airplane

1666
01:14:26,600 --> 01:14:30,719
which uh you wait forever in line in

1667
01:14:28,760 --> 01:14:33,360
security and

1668
01:14:30,719 --> 01:14:34,800
then and then uh it takes a long time to

1669
01:14:33,360 --> 01:14:40,400
get off the ground and start working but

1670
01:14:34,800 --> 01:14:43,679
once it does it's extremely fast um and

1671
01:14:40,400 --> 01:14:45,360
so if we do a simple example of how long

1672
01:14:43,679 --> 01:14:47,600
does it take to do a Matrix Matrix

1673
01:14:45,360 --> 01:14:49,040
multiply I calculated this a really long

1674
01:14:47,600 --> 01:14:51,280
time ago it's probably horribly out of

1675
01:14:49,040 --> 01:14:55,120
date now but the same general principle

1676
01:14:51,280 --> 01:14:56,560
stands which is if we have have um the

1677
01:14:55,120 --> 01:14:58,480
number of seconds that it takes to do a

1678
01:14:56,560 --> 01:15:02,080
Matrix Matrix multiply doing one of size

1679
01:14:58,480 --> 01:15:03,920
16 is actually faster on CPU because uh

1680
01:15:02,080 --> 01:15:07,760
the overhead it takes to get started is

1681
01:15:03,920 --> 01:15:10,880
very low but if you um once you start

1682
01:15:07,760 --> 01:15:13,360
getting up to size like 128 by 128

1683
01:15:10,880 --> 01:15:15,800
Matrix multiplies then doing it on GPU

1684
01:15:13,360 --> 01:15:17,320
is faster and then um it's you know a

1685
01:15:15,800 --> 01:15:19,679
100 times faster once you start getting

1686
01:15:17,320 --> 01:15:21,600
up to very large matrices so um if

1687
01:15:19,679 --> 01:15:24,000
you're dealing with very large networks

1688
01:15:21,600 --> 01:15:26,800
handling a GPU is good

1689
01:15:24,000 --> 01:15:30,159
um and this is the the speed up

1690
01:15:26,800 --> 01:15:31,440
percentage um one thing I should mention

1691
01:15:30,159 --> 01:15:34,239
is

1692
01:15:31,440 --> 01:15:36,440
um compute with respect to like doing

1693
01:15:34,239 --> 01:15:39,800
the assignments for this class if you

1694
01:15:36,440 --> 01:15:43,199
have a relatively recent Mac you're kind

1695
01:15:39,800 --> 01:15:44,760
of in luck because actually the gpus on

1696
01:15:43,199 --> 01:15:47,239
the Mac are pretty fast and they're well

1697
01:15:44,760 --> 01:15:48,960
integrated with um they're well

1698
01:15:47,239 --> 01:15:52,080
integrated with pipor and other things

1699
01:15:48,960 --> 01:15:53,440
like that so decently sized models maybe

1700
01:15:52,080 --> 01:15:54,840
up to the size that you would need to

1701
01:15:53,440 --> 01:15:57,840
run for assignment one or even

1702
01:15:54,840 --> 01:16:00,880
assignment two might uh just run on your

1703
01:15:57,840 --> 01:16:03,639
uh laptop computer um if you don't have

1704
01:16:00,880 --> 01:16:05,280
a GPU uh that you have immediately

1705
01:16:03,639 --> 01:16:06,760
accessible to you I we're going to

1706
01:16:05,280 --> 01:16:08,400
recommend that you use collab where you

1707
01:16:06,760 --> 01:16:10,120
can get a GPU uh for the first

1708
01:16:08,400 --> 01:16:12,440
assignments and then we'll have plug

1709
01:16:10,120 --> 01:16:15,159
reddits that you can use otherwise but

1710
01:16:12,440 --> 01:16:16,800
um GPU is usually like something that

1711
01:16:15,159 --> 01:16:18,440
you can get on the cloud or one that you

1712
01:16:16,800 --> 01:16:21,080
have on your Mac or one that you have on

1713
01:16:18,440 --> 01:16:24,600
your gaming computer or something like

1714
01:16:21,080 --> 01:16:26,040
that um there's a few speed tricks that

1715
01:16:24,600 --> 01:16:30,000
you should know for efficient GPU

1716
01:16:26,040 --> 01:16:32,480
operations so um one mistake that people

1717
01:16:30,000 --> 01:16:35,880
make when creating models is they repeat

1718
01:16:32,480 --> 01:16:38,080
operations over and over again and um

1719
01:16:35,880 --> 01:16:40,600
you don't want to be doing this so like

1720
01:16:38,080 --> 01:16:43,239
for example um this is multiplying a

1721
01:16:40,600 --> 01:16:45,320
matrix by a constant multiple times and

1722
01:16:43,239 --> 01:16:46,880
if you're just using out of thee box pie

1723
01:16:45,320 --> 01:16:49,280
torch this would be really bad because

1724
01:16:46,880 --> 01:16:50,400
you'd be repeating the operation uh when

1725
01:16:49,280 --> 01:16:52,679
it's not

1726
01:16:50,400 --> 01:16:54,480
necessary um you can also reduce the

1727
01:16:52,679 --> 01:16:57,360
number of operations that you need to

1728
01:16:54,480 --> 01:17:00,320
use so uh use Matrix Matrix multiplies

1729
01:16:57,360 --> 01:17:03,080
instead of Matrix Vector

1730
01:17:00,320 --> 01:17:07,920
multiplies and another thing is uh

1731
01:17:03,080 --> 01:17:10,719
reducing CPU GPU data movement and um so

1732
01:17:07,920 --> 01:17:12,360
when you do try to move memory um when

1733
01:17:10,719 --> 01:17:17,080
you do try to move memory try to do it

1734
01:17:12,360 --> 01:17:20,040
as early as possible and as uh and as

1735
01:17:17,080 --> 01:17:22,199
few times as possible and the reason why

1736
01:17:20,040 --> 01:17:24,199
you want to move things early or start

1737
01:17:22,199 --> 01:17:25,920
operations early is many GPU operations

1738
01:17:24,199 --> 01:17:27,159
are asynchronous so you can start the

1739
01:17:25,920 --> 01:17:28,800
operation and it will run in the

1740
01:17:27,159 --> 01:17:33,120
background while other things are

1741
01:17:28,800 --> 01:17:36,080
processing so um it's a good idea to try

1742
01:17:33,120 --> 01:17:39,840
to um to optimize and you can also use

1743
01:17:36,080 --> 01:17:42,360
your python profiler or um envidia GPU

1744
01:17:39,840 --> 01:17:43,679
profilers to try to optimize these

1745
01:17:42,360 --> 01:17:46,520
things as

1746
01:17:43,679 --> 01:17:49,840
well cool that's all I have uh we're

1747
01:17:46,520 --> 01:17:49,840
right at time