Intuition Behind the Attention Mechanism from Transformers using Spreadsheets

Fernando Marcos Wittmann
3 Nov 202317:05

Summary

TLDRThe video script offers an insightful explanation of the attention mechanism within the Transformer architecture, focusing on cross-attention. It illustrates how embeddings from inputs and outputs are utilized, using a simple English to Portuguese translation example. The process involves calculating query, key, and value matrices, applying a scaled dot-product attention equation, and transforming the target sequence based on input sequence similarity. The use of spreadsheets for visualizing mathematical operations is highlighted, providing a clear step-by-step guide to implementing cross-attention.

Takeaways

  • 🧠 The video discusses the attention mechanism in Transformers, focusing on cross-attention.
  • 🔄 Cross-attention involves comparing embeddings from the input and output, such as comparing sentences in different languages.
  • 📄 The script references the original Transformer paper and the specific architecture being implemented.
  • 🔢 The input and output sentences are transformed into embeddings through linear transformations.
  • 📊 The video uses a TOD chart to illustrate the similarity between words, showing how embeddings can visually represent relationships.
  • 🤖 The embeddings are learned weights, not random numbers, and are used to represent words in the model.
  • 📈 The attention equation is derived from information retrieval concepts, using query, key, and value terms.
  • 🔍 The video aims to provide intuition on how the attention mechanism works in practice, using spreadsheets for visualization.
  • 🔢 The script explains the process of matrix multiplication and normalization to prevent gradient explosion.
  • 📊 The soft Max function is applied to convert values into a proportion that adds up to one, representing percentage contributions.
  • 🔄 The final step is to multiply the soft Max output by the value matrix to create a transformed output or target embedding.

Q & A

  • What is the main topic of the video?

    -The main topic of the video is the attention mechanism in Transformers, specifically focusing on the cross-attention aspect of the Transformer architecture.

  • What is the significance of cross-attention in the Transformer architecture?

    -Cross-attention is significant because it involves comparing embeddings from different sequences, such as input and output, which is crucial for tasks like language translation models.

  • How does the video illustrate the concept of embeddings?

    -The video illustrates embeddings by showing how a sentence is transformed into a matrix of words, with each word represented as an embedding. These embeddings are learned weights that help the model understand the relationships between words.

  • What are the three key terms involved in the attention equation?

    -The three key terms involved in the attention equation are query, key, and value. These terms are borrowed from information retrieval and play a crucial role in how attention works in practice.

  • How does the video demonstrate the concept of similarity between words?

    -The video demonstrates the concept of similarity by showing how certain words are more similar to each other based on their embeddings. For example, 'I am' is shown to be more similar to 'so' than to 'happy' due to their relative positions in the embedding space.

  • What is the purpose of the softmax function in the attention mechanism?

    -The softmax function is used to convert the values obtained from the attention equation into a proportion that adds up to one. This helps in representing the contribution of each word in the attention transformation as a percentage.

  • How does the video explain the transformation of the target sequence?

    -The video explains that the target sequence is transformed by multiplying the softmax output (which represents the percentage contribution of each word) with the original vectors (embeddings) of the words in the input sequence.

  • What is the role of normalization in the attention mechanism?

    -Normalization is important in the attention mechanism to prevent large values from causing gradient explosions in neural networks. The video shows that by dividing the matrix multiplication result by the square root of the embedding dimension, the values are scaled appropriately.

  • How does the video utilize spreadsheets for the explanation?

    -The video uses spreadsheets to visually demonstrate the mathematical operations involved in the attention mechanism. This helps viewers understand how the equations are applied and how the numbers interact with each other.

  • What is the difference between the scaled dot-product attention explained in the video and the multi-head attention?

    -The main difference is that the scaled dot-product attention, which is implemented in the video, uses learned weights for the input and output sequences, while multi-head attention involves multiple attention heads that can focus on different aspects of the input and output sequences.

  • What is the significance of the example used in the video (English to Portuguese translation)?

    -The example of English to Portuguese translation is used to illustrate how cross-attention works in practice, showing how words from one language can be related to words in another language and how the model can learn these relationships to perform translation tasks.

Outlines

00:00

🤖 Introduction to Attention Mechanism in Transformers

This paragraph introduces the concept of the attention mechanism within the Transformer architecture, focusing on the cross-attention component. The speaker aims to provide an intuitive understanding of how cross-attention works by using an example of language translation. The explanation includes the transformation of input sentences into embeddings and how these embeddings are used to compare different languages, specifically English and Portuguese in this case. The speaker also touches on the concept of learned weights from embeddings and illustrates the process using a TOS chart to show similarities between words.

05:00

🔍 Clarifying Query, Key, and Value in Cross-Attention

In this section, the speaker clarifies the roles of query, key, and value in the cross-attention mechanism. It is explained that the target sequence acts as the query, while the context sequence serves as the key and value. The speaker references a TensorFlow tutorial to provide a clear example of this relationship. The use of spreadsheets for visualizing mathematical operations and the step-by-step implementation of the cross-attention layer is also discussed, emphasizing the importance of understanding matrix multiplication and its application in this context.

10:02

📊 Normalization and Softmax in Attention Mechanism

This paragraph delves into the normalization and application of the softmax function within the attention mechanism. The speaker explains the need to convert values into a proportion that adds up to one, representing a percentage contribution. The process of dividing the matrix multiplication by the square root of the embedding dimensions is described to normalize the values. The softmax function is then applied to convert all values into positive numbers, which are used to create a weighted contribution to the final output. The speaker provides a detailed walkthrough of these calculations and their significance in transforming the target embedding.

15:05

🎯 Implementing Scaled Dot-Product Attention

The speaker concludes the explanation by demonstrating the implementation of scaled dot-product attention, specifically in the context of cross-attention. The process of combining the softmax output with the value vectors to create a transformed output or target embedding is detailed. The speaker illustrates how the final vector position is influenced by the percentage contributions from the input sequence. The example given shows how the new vector position is calculated based on these contributions, resulting in a vector that better represents the context of the sentence. The speaker emphasizes the learned nature of the embeddings and the transformative power of the attention mechanism in understanding and utilizing sentence context.

Mindmap

Keywords

💡Transformers

Transformers is a type of deep learning model introduced in the paper 'Attention Is All You Need'. It is primarily used for natural language processing tasks. The model gets its name from the 'transformer' architecture which uses self-attention mechanisms to process sequences of data. In the context of the video, the speaker is discussing the attention mechanism within the Transformer architecture, which allows the model to weigh the importance of different parts of the input data when generating an output, such as in language translation tasks.

💡Attention Mechanism

The attention mechanism in neural networks, particularly in the context of Transformers, is a technique that allows the model to dynamically focus on different parts of the input sequence when generating each element of the output sequence. It is inspired by the way humans pay attention to certain parts of the information when processing it. In the video, the speaker is aiming to provide intuition about the cross-attention mechanism, which is a specific type of attention used when the input and output sequences are different, such as in language translation.

💡Cross-Attention

Cross-attention is a specific type of attention mechanism used in the Transformer model where the input and output sequences are different. It involves calculating attention scores by comparing the embeddings from the input sequence (the context sequence) with the embeddings from the output sequence (the target sequence). The video script provides an example of using cross-attention in a language translation task, where the input is an English sentence and the output is its translation in Portuguese.

💡Embeddings

Embeddings in the context of natural language processing are dense vector representations of words or phrases that capture their semantic meaning in a numerical form. These vectors are learned during the training of the neural network and are used as inputs to the model. In the video, the speaker discusses how the input sentence is transformed into a matrix of word embeddings, and similarly, the output embeddings are used in the cross-attention mechanism to weigh the importance of different words in the input when generating the output.

💡Query, Key, and Value

In the attention mechanism of Transformers, the terms query, key, and value are used to describe the components involved in the attention calculation. The query is a vector that represents the current word being processed and is used to score the relevance of different keys. The keys are vectors that represent the embeddings of all the words in the input sequence. The values are the corresponding vectors to the keys and are outputted when a high attention score is assigned by the query to a key. In the video, the speaker explains that in cross-attention, the target sequence (output) acts as the query, and the context sequence (input) acts as the key and value.

💡Softmax Function

The softmax function is a mathematical function that takes in a vector of arbitrary real values and outputs a vector of values in the range [0, 1] that add up to 1. It is commonly used in the attention mechanism to convert the raw attention scores (which can be positive or negative) into probabilities that represent the importance of each element in the input sequence. In the video, the speaker applies the softmax function to the attention scores to create a probability distribution that will be used to weigh the values in the next step of the attention calculation.

💡Scaled Dot-Product Attention

Scaled dot-product attention is a specific implementation of the attention mechanism in the Transformer model. It calculates the attention score by taking the dot product of the query with all the keys, and then scales the result by dividing it by the square root of the dimension of the embeddings. This scaling factor prevents the scores from becoming too large, which could lead to gradient vanishing or exploding during training. In the video, the speaker implements scaled dot-product attention to calculate the attention scores and transform the target sequence based on the input sequence.

💡Matrix Multiplication

Matrix multiplication is a mathematical operation that takes a set of linear equations and transforms them into another set. In the context of the video, matrix multiplication is used to calculate the attention scores by multiplying the query vector with the transpose of the key matrix. The result is a matrix where each entry represents the compatibility score between the query and each key.

💡Normalization

Normalization in the context of neural networks often refers to the process of scaling data so that it has a mean of zero and a standard deviation of one. In the video, the speaker discusses normalizing the embeddings by dividing the dot product by the square root of the embedding dimension to prevent large values that could cause gradient issues during training. This helps in maintaining the stability of the learning process.

💡Language Translation

Language translation is the process of converting text from one language to another. In the context of the video, the speaker uses language translation as an example to illustrate how the cross-attention mechanism works in the Transformer model. The input is an English sentence, and the output is its translation in Portuguese. The attention mechanism helps the model understand the relationships between words in the source language and how they should be represented in the target language.

💡Spreadsheets

Spreadsheets are software applications used for organizing, storing, and analyzing data in a tabular format. In the video, the speaker uses spreadsheets to visualize and calculate the attention mechanism. The spreadsheets allow the speaker to manually perform the mathematical operations involved in the attention mechanism, which helps in understanding the intuition behind the calculations and the flow of data through the model.

Highlights

The video provides an in-depth explanation of the attention mechanism in Transformers, specifically focusing on cross-attention.

Cross-attention is implemented by comparing embeddings from the input to embeddings from the output.

The example given involves translating a small English sentence into Portuguese.

The input and output embeddings are representations of sentences transformed into a matrix of words.

Multiple linear transformations are applied to maintain the same shape for both input and output representations.

The video uses a TOC chart to illustrate the similarity between words in the input and their corresponding translations.

The attention equation is derived from information retrieval concepts, with query, key, and value terms.

Scaled dot attention and multi-head attention are two implementations provided in the original paper.

The video focuses on implementing scaled dot attention, with learned weights for both input and output.

A step-by-step implementation of the cross-attention mechanism is demonstrated using spreadsheets for visualization.

The target sequence acts as the query, and the context sequence serves as the key and value in cross-attention.

The multiplication of the query, key, and value matrices is explained, drawing parallels to similarity matrices.

Normalization is applied to the vectors to prevent large values that could cause gradient explosion.

The soft max function is used to convert the values into a proportion that adds up to one, representing percentage contributions.

The video demonstrates how to apply the soft max function and calculate the sum for normalization.

The final step involves multiplying the soft max output with the value matrix to create a transformed target embedding.

The transformed target embedding is a new position in the vector space, based on the contributions from the input sequence.

The video concludes by summarizing the implementation of scaled dot product and cross-attention in the context of Transformers.

Transcripts

play00:01

okay so in this video I want to give you

play00:04

guys some intuition about Transformers

play00:08

or actually to about the attention

play00:12

mechanism in Transformers in their

play00:15

Transformer

play00:17

architecture uh and uh actually being

play00:20

more specific if we check the the paper

play00:24

this is like the full Transformer

play00:26

architecture uh the portion that our be

play00:30

implemented implementing is this one

play00:33

which is called cross cross attention

play00:37

and the reason is because we are here

play00:41

Crossing embeddings from the inputs and

play00:45

embeddings from the output so for a

play00:48

language model for a

play00:51

translation example uh we would in this

play00:55

portion be

play00:57

comparing uh like one language with the

play01:00

order like sentences and in my example

play01:04

uh I'll be using as inputs like a very

play01:08

small sentence in

play01:11

English and as output like the embedding

play01:15

outputs that I have here that I'll be

play01:18

combining I'll be using the translation

play01:21

into Portuguese and here on purpose I'm

play01:26

using a translation in which we have

play01:29

three word Words which could be

play01:31

translated into two words here uh I am

play01:35

would be equivalent to so in Portuguese

play01:38

and happy would be equivalent to

play01:41

phiz and like to start uh here I won't

play01:45

be covering the rest the of the details

play01:49

here I can maybe cover in a different

play01:51

video uh but like just to summarize what

play01:55

we have here as both inputs and and for

play02:00

for this on this side and also inputs on

play02:02

this side are like

play02:04

embeddings and more specifically

play02:06

transform it

play02:08

embeddings uh our input like the

play02:10

sentence is going to be transformed into

play02:13

a matrix of Words which we call eddings

play02:16

and multiple linear Transformations are

play02:20

applied here uh but we still get the

play02:23

same shape so both here and here we'll

play02:27

get as inputs from this side and this

play02:30

side we'll get uh representations

play02:34

embedding transform it embedding

play02:37

representations of each sentence uh so

play02:41

in this example as you guys can see I'm

play02:44

using here random numbers but like in

play02:47

practice uh those numbers they are like

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since they come from embeddings they are

play02:53

actually weight they they they've been

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learned and for illustration I'm I'm

play02:59

plotting here in a in a TOD chart uh

play03:03

that this sentence like the words I

play03:07

am uh they are like more similar than

play03:11

the word happy uh because here both are

play03:14

more like related to first person uh and

play03:19

here the translation I'm also uh placing

play03:24

like in a similar position and also the

play03:27

happy I'm placing more similar

play03:30

like clor position to

play03:33

happy uh and here I'll be

play03:38

replicating uh like the the full like

play03:42

the the equations that are applied here

play03:46

in in the paper um there they they give

play03:49

the Taos on two implementations the

play03:52

scales do attention and the multi head

play03:55

attention here I'll be implementing the

play03:58

scal that

play04:00

attention uh and the main difference is

play04:02

that we have learned weights in like the

play04:07

input and output so like maybe also in a

play04:10

later moment in another video I can like

play04:14

transform this into a multi head

play04:16

attention but like in chart what I I'll

play04:20

be implementing here is pretty much this

play04:22

equation and this is actually the

play04:25

attention equation and we have three

play04:28

terms here here as input which is they

play04:32

call query key and

play04:34

values uh those terms comes like from

play04:40

from information

play04:43

retrieval um and uh here I I hope to

play04:47

give some intuition on how they work in

play04:51

practice uh so we we have the here that

play04:54

there is this soft Max of those two

play04:57

terms and then they will be m mped by

play05:00

this value but here we need to know what

play05:03

will be like the query key and what will

play05:06

be the value here and I notice this

play05:10

wasn't clear in in the paper uh we only

play05:13

see that the input two of the inputs

play05:17

come

play05:18

from uh two of the terms comes from the

play05:21

input and one of the term comes from the

play05:25

output uh and this I found in an order

play05:29

tutorial which I'll show in a minute so

play05:32

in this tutorial from tensor flow then

play05:36

we can see like in the cross attention

play05:38

layer which is the part we'll be

play05:41

implementing uh then we we can see that

play05:44

the target sequence which is what comes

play05:47

from this side uh is is going to be the

play05:51

query uh and uh the context sequence

play05:55

which comes from here are going to be

play05:57

the key and the value so I'll be

play06:00

implementing here step by step on

play06:02

spreadsheets and the reason I'm using

play06:05

spreadsheets is because it's a better

play06:08

way to visualize like the math and the

play06:11

numbers like how the multiplication so

play06:15

it's helping help to give some

play06:17

intuitions so let's start so the first

play06:20

thing I'm doing here is actually uh when

play06:24

I have like a give selection here I'm

play06:27

giving a name here and input and this is

play06:31

going to be my output so like just to

play06:33

give some context when I for example

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call input here and press command shift

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enter and this is a array formula uh

play06:45

which isn't very common on spreadsheets

play06:48

but here I use a lot because it's more

play06:50

similar to how we would see in nonp a

play06:54

operation it's an

play06:55

operation that uh is applied to the full

play06:59

Matrix and gives us output the full

play07:02

Matrix as you can see here uh I'm giving

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context on this because I'll be doing a

play07:07

lot so for example if I multiply this by

play07:10

two then notice notice that the full

play07:15

input here this full range that I name

play07:18

it here uh is this like multiply it by

play07:22

two uh so like as it was mentioned so

play07:26

the the query is going to be the the

play07:29

target sequence which is the output so

play07:33

in this case I'm just going to call the

play07:35

output here which is the selection and

play07:39

have it here and then as input if we see

play07:44

in the formula we have the transpose it

play07:47

of the key which is our input so in this

play07:50

case we can just call the

play07:52

transpose of the

play07:56

input and done

play07:59

and here we needed to multiply those two

play08:04

Matrix uh the mul the multiplication

play08:07

here is if you are not like not very

play08:10

familiar there is a like very good

play08:13

resource here that shows like how those

play08:17

uh multiplication step by step are

play08:20

applied uh here I'll be just using like

play08:23

the formula U of matrix multiplication

play08:27

for multiplying those two

play08:30

uh but pretty much what we have here is

play08:33

like those two numbers are going to be

play08:35

multiplied by those two numbers and then

play08:38

add it and then something analog is

play08:41

going to happen in the rest and what do

play08:44

we have here is something analog it's

play08:48

not exactly the cosign similarity but

play08:51

it's very analog to a similarity Matrix

play08:56

um in practice if those uh vector vors

play08:59

that we have here are like all of them

play09:02

if they have the same um uh Norm like

play09:07

the same distance from the the origin or

play09:12

like if they are normalized in practice

play09:15

what we have here is like a similarity

play09:18

of each one of those words and that we

play09:22

have as Target sequence and the words

play09:24

that we have as input sequence uh so as

play09:28

we you can see we have here like higher

play09:32

values for like uh numbers that are

play09:36

closer to each other like they they have

play09:38

the similarity and so we see like I am

play09:42

here it's SM similar with so and happy

play09:44

is SM similar with

play09:47

Phillies uh and actually in the paper if

play09:51

you apply this multiplication to like a

play09:55

embedding that is very big uh those

play09:58

values they tend to be very large and

play10:01

usually for neuron networks we want

play10:04

small

play10:05

values because large values makes the

play10:09

gradients to

play10:11

explode and in order like to do this

play10:14

normalization we can divide by the

play10:17

number of embed the dimension of

play10:19

embeddings that we have in this case our

play10:22

embeddings have two Dimensions so the

play10:25

actual value that we would have here

play10:28

would be this matrix multiplication

play10:30

divided by the square root of

play10:34

two and let

play10:36

me and let me finish here okay so then

play10:41

then here we have

play10:43

implemented uh what we have inside here

play10:46

and then the next step here is to apply

play10:49

this soft Max function which we have uh

play10:52

in this side and the idea of the soft

play10:55

Max function is to convert all of those

play10:58

values

play11:00

into a proportion that would add up to

play11:04

one so it's like a percentage

play11:07

contribution and we need to use this

play11:10

exponential function because sometimes

play11:12

we have negative values and sometimes

play11:15

positive values so the idea here is to

play11:18

use the exponential um equation in order

play11:22

to convert all of those values into

play11:24

positive values so this is what I'm

play11:27

going to do here so EXP exponential of

play11:30

all of those values so again when I do

play11:34

like this array formula then what we

play11:38

have here this is the exponential of

play11:41

this value this is going to be the

play11:43

exponential this and so on so it's just

play11:45

a shortcut cut so as you can see now we

play11:49

all of those values were converted to

play11:51

positive and we divided this by the sum

play11:54

in this case is actually the sum of each

play11:57

row which um I'm going to to calculate

play11:59

here so I just need to calculate this

play12:03

sum and then do the same for the bottom

play12:07

and then finally the soft Max of uh of

play12:11

this amount of this Matrix is going to

play12:14

be the this

play12:16

Matrix divided by those values so I'm

play12:20

pretty much like dividing all of those

play12:22

numbers like 1.2 by 3.9 and then two and

play12:26

then so on this is what I'm doing here

play12:30

and uh what do we have here uh if you

play12:34

notice all of those numbers here they

play12:37

will add to one so it's like a

play12:39

percentage

play12:41

contribution uh of uh each one of uh

play12:45

those uh words here in Bings that you

play12:49

want to be propagated in this attention

play12:53

transformation so after we get this soft

play12:58

Max uh we need now uh to get the the

play13:02

value like uh which in in which is also

play13:07

this input sequence so I'll get

play13:10

here and what will happen now is we'll

play13:15

be multiplying both in order to create

play13:18

this

play13:20

transformed uh output or transformed

play13:23

Target um embedding and this is it's

play13:27

like you're are telling

play13:29

that you you want to create a

play13:32

transformat uh targeting Bing as like a

play13:37

based on how similar like giving like

play13:40

some percentage of contributions from

play13:43

the memory from the input that we have

play13:46

uh so pretty much like for example for

play13:48

the word so we have that we want 30% of

play13:53

contribution from the the word I and 64%

play13:58

of cont contribution from the word m so

play14:00

what we have here I'll do like step by

play14:03

step just to show how exactly those

play14:05

numbers are coming up so it's this

play14:08

number times like this original Vector

play14:12

plus this number times this original

play14:15

Vector plus this number times this

play14:18

original Vector so here we have

play14:21

0.7 and then and then here I have the

play14:25

same thing but now for this second

play14:29

Vector so here and then plus this term

play14:34

times this second Vector plus this term

play14:39

times this third Vector uh so what we

play14:43

have here is like a new

play14:46

position of this Vector

play14:49

so which is going to be based on like

play14:52

those contributions so since uh like the

play14:55

word I and the word m they are more s

play14:58

similar than the word happy is like you

play15:01

are like sending um the vector like to a

play15:05

new position which is like closer to

play15:09

both of them uh but again like all of

play15:12

those values those embeddings they are

play15:13

learned and then this transformation is

play15:17

applied in a way like to uh to to use

play15:22

the context of of the S sentence in

play15:25

order to give a new position to to that

play15:28

uh vector and here I can do the same

play15:31

calculation here or I can just do M both

play15:34

here and multiply both of those

play15:39

vectors and oops and then I need to

play15:42

delete here so here we have this new

play15:45

word so and phis we we have here that

play15:49

the new Vector is going to have 70% of

play15:53

the original Vector uh uh of of Happy

play15:59

but also it's going to have like about

play16:02

30% of those two vectors uh so that's

play16:06

the new position of the word

play16:09

phis and that's it so here we

play16:12

implemented uh this scaled do product

play16:16

and more specifically this cross

play16:18

attention since we are um like Crossing

play16:22

this input the and the

play16:25

Target and uh

play16:29

and like this the only like difference

play16:33

with the original like what's

play16:35

implemented in the paper is that there

play16:37

will be those linear multiplications and

play16:41

also like for this case we we don't have

play16:43

masks uh but there will be like some

play16:46

attentions that they will have masks or

play16:49

there will be like attention components

play16:51

that they will be like comparing the

play16:53

words with themselves uh but yeah that's

play16:56

it I hope it was helpful to give some

play17:00

intuitions and uh and yeah that's it

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Related Tags
TransformersAttentionMechanismCrossAttentionLanguageModelMachineTranslationEmbeddingsMathIntuitionScaledDotProductSequenceProcessingTensorFlow