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(air whooshing)

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- In this video,

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we will study together
'the Unigram Language Model

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subword tokenization algorithm'.

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The overall training strategy

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of a Unigram Language Model tokenizer

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is to start with a very large vocabulary

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and then to remove
tokens at each iteration

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until we reach the desired size.

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At each iteration,

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we will calculate a loss
on our training corpus

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thanks to the Unigram model.

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As the loss calculation depends
on the available vocabulary,

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we can use it to choose how
to reduce the vocabulary.

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So we look at the evolution of the loss

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by removing in turn each
token from the vocabulary.

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We will choose to remove the p-percents

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which increase the loss the less.

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Before going further

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in the explanation of
the training algorithm,

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I need to explain what
is an Unigram model.

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The Unigram Language Model

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is a type of Statistical Language Modem.

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A Statistical Language Model

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will assign a probability to a text

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considering that the text is
in fact a sequence of tokens.

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The simplest sequences
of tokens to imagine

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are the words that compose the
sentence or the characters.

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The particularity of
Unigram Language Model

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is that it assumes that
the occurrence of each word

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is independent of its previous word.

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This assumption allows us to write

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that the probability of a text

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is equal to the product
of the probabilities

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of the tokens that compose it.

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It should be noted here that
it is a very simple model

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which would not be adapted
to the generation of text

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since this model would always
generate the same token,

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the one which has the
greatest probability.

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Nevertheless, to do tokenization,

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this model is very useful to us

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because it can be used

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to estimate the relative
likelihood of different phrases.

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We are now ready

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to return to our explanation
of the training algorithm.

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Let's say that we have
as a training corpus

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with 10 times the word hug,

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12 times the word pug,

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5 times the word lug,

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4 times bug

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and 5 times dug.

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As said earlier,

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the training starts with a big vocabulary.

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Obviously, as we are using a toy corpus,

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this vocabulary will not be that big

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but it should show you the principle.

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A first method is to list all
the possible strict substrings

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and that's what we'll do here.

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We could also have used the BPE algorithm

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with a very large vocabulary size

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but for now, the strict
substrings are enough.

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The training of the Unigram tokenizer

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is based on the
Expectation-Maximization method.

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At each iteration,

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we estimate the
probabilities of the tokens

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of the vocabulary

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and then we remove the p-percent of tokens

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that minimize the loss on the corpus

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and which do not belong
to the basic character

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as we want to keep in our final vocabulary

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the basic characters to be
able to tokenize any word.

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Let's go for it!

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The probability of a
token simply estimated

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by the number of appearance of this token

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in our training corpus

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divided by the total number of
appearance of all the tokens.

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We could use this vocabulary
to tokenize our words

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according to the Unigram model.

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We will do it together
to understand two things:

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how we tokenize a word
with a Unigram model

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and how the loss is
calculated on our corpus.

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The Unigram LM tokenization
of our text 'Hug'

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will be the one with the highest
probability of occurrence

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according to our Unigram model.

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To find it, the simplest way to proceed

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would be to list all the
possible segmentations

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of our text 'Hug',

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calculate the probability of
each of these segmentations

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and then choose the one with
the highest probability.

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With the current vocabulary,

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two tokenizations get
exactly the same probability.

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So we choose one of them

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and keep in memory the
associated probability.

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To compute the loss on
our training corpus,

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we need to tokenize as we just did

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all the remaining words in the corpus.

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The loss is then the sum over
all the words in the corpus

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of the frequency of occurrence of the word

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multiplied by the opposite
of the log of the probability

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associated with the
tokenization of the word.

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We obtain here a loss of 170.

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Remember, our initial goal
was to reduce the vocabulary.

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To do this, we will remove
a token from the vocabulary

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and calculate the associated loss.

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Let's remove for example, the token 'ug'.

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We notice that the tokenization for 'hug'

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with the letter 'h' and the
tuple 'ug' is now impossible.

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Nevertheless, as we saw earlier

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that two tokenizations
had the same probability,

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we can still choose the
remaining tokenization

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with a probability of 1.10e-2.

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The tokenizations of the
other words of the vocabulary

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also remain unchanged.

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And finally, even if we
remove the token 'ug'

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from our vocabulary the
loss remains equal to 170.

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For this first iteration,

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if we continue the calculation,

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we would notice that we
could remove any token

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without it impacting the loss.

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We will therefore choose at
random to remove the token 'ug'

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before starting a second iteration.

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So we estimate again the
probability of each token

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before calculating the impact
of each token on the loss.

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For example, if we remove now

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the token composed of
the letters 'h' and 'u',

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there is only one possible
tokenization left for hug.

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The tokenization of the
other words of the vocabulary

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is not changed.

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In the end,

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we obtain by removing the token

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composed of the letters 'h'
and 'u' from the vocabulary,

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a loss of 168.

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Finally, to choose which token to remove,

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we will for each remaining
token of the vocabulary,

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which is not an elementary token,

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calculate the associated loss.

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Then, compare these losses between them.

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The token which we will remove

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is the token which impacts
the least the loss,

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here the token 'bu'.

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We had mentioned at the
beginning of the video

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that at each iteration we could remove

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p-percent of the tokens by iteration.

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The second token that could
be removed at this iteration

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is the token 'du'.

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And that's it.

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We just have to repeat these steps

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until we get the vocabulary
of the desired size.

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One last thing.

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In practice, when we tokenize
a word with a Unigram model,

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we don't compute the
set of probabilities of

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all the possible splits of a word

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before comparing them to keep the best one

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but we use the Viterbi algorithm

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which is much more efficient way to do it.

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And that's it!

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I hope that this example

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has allowed you to better understand

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the Unigram tokenization algorithm.

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(air whooshing)

