Intuition Behind the Attention Mechanism from Transformers using Spreadsheets

Summary

The 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.

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

okay so in this video I want to give you

guys some intuition about Transformers

or actually to about the attention

mechanism in Transformers in their

Transformer

architecture uh and uh actually being

more specific if we check the the paper

this is like the full Transformer

architecture uh the portion that our be

implemented implementing is this one

which is called cross cross attention

and the reason is because we are here

Crossing embeddings from the inputs and

embeddings from the output so for a

language model for a

translation example uh we would in this

portion be

comparing uh like one language with the

order like sentences and in my example

uh I'll be using as inputs like a very

small sentence in

English and as output like the embedding

outputs that I have here that I'll be

combining I'll be using the translation

into Portuguese and here on purpose I'm

using a translation in which we have

three word Words which could be

translated into two words here uh I am

would be equivalent to so in Portuguese

and happy would be equivalent to

phiz and like to start uh here I won't

be covering the rest the of the details

here I can maybe cover in a different

video uh but like just to summarize what

we have here as both inputs and and for

for this on this side and also inputs on

this side are like

embeddings and more specifically

transform it

embeddings uh our input like the

sentence is going to be transformed into

a matrix of Words which we call eddings

and multiple linear Transformations are

applied here uh but we still get the

same shape so both here and here we'll

get as inputs from this side and this

side we'll get uh representations

embedding transform it embedding

representations of each sentence uh so

in this example as you guys can see I'm

using here random numbers but like in

practice uh those numbers they are like

since they come from embeddings they are

actually weight they they they've been

learned and for illustration I'm I'm

plotting here in a in a TOD chart uh

that this sentence like the words I

am uh they are like more similar than

the word happy uh because here both are

more like related to first person uh and

here the translation I'm also uh placing

like in a similar position and also the

happy I'm placing more similar

like clor position to

happy uh and here I'll be

replicating uh like the the full like

the the equations that are applied here

in in the paper um there they they give

the Taos on two implementations the

scales do attention and the multi head

attention here I'll be implementing the

scal that

attention uh and the main difference is

that we have learned weights in like the

input and output so like maybe also in a

later moment in another video I can like

transform this into a multi head

attention but like in chart what I I'll

be implementing here is pretty much this

equation and this is actually the

attention equation and we have three

terms here here as input which is they

call query key and

values uh those terms comes like from

from information

retrieval um and uh here I I hope to

give some intuition on how they work in

practice uh so we we have the here that

there is this soft Max of those two

terms and then they will be m mped by

this value but here we need to know what

will be like the query key and what will

be the value here and I notice this

wasn't clear in in the paper uh we only

see that the input two of the inputs

come

from uh two of the terms comes from the

input and one of the term comes from the

output uh and this I found in an order

tutorial which I'll show in a minute so

in this tutorial from tensor flow then

we can see like in the cross attention

layer which is the part we'll be

implementing uh then we we can see that

the target sequence which is what comes

from this side uh is is going to be the

query uh and uh the context sequence

which comes from here are going to be

the key and the value so I'll be

implementing here step by step on

spreadsheets and the reason I'm using

spreadsheets is because it's a better

way to visualize like the math and the

numbers like how the multiplication so

it's helping help to give some

intuitions so let's start so the first

thing I'm doing here is actually uh when

I have like a give selection here I'm

giving a name here and input and this is

going to be my output so like just to

give some context when I for example

call input here and press command shift

enter and this is a array formula uh

which isn't very common on spreadsheets

but here I use a lot because it's more

similar to how we would see in nonp a

operation it's an

operation that uh is applied to the full

Matrix and gives us output the full

Matrix as you can see here uh I'm giving

context on this because I'll be doing a

lot so for example if I multiply this by

two then notice notice that the full

input here this full range that I name

it here uh is this like multiply it by

two uh so like as it was mentioned so

the the query is going to be the the

target sequence which is the output so

in this case I'm just going to call the

output here which is the selection and

have it here and then as input if we see

in the formula we have the transpose it

of the key which is our input so in this

case we can just call the

transpose of the

input and done

and here we needed to multiply those two

Matrix uh the mul the multiplication

here is if you are not like not very

familiar there is a like very good

resource here that shows like how those

uh multiplication step by step are

applied uh here I'll be just using like

the formula U of matrix multiplication

for multiplying those two

uh but pretty much what we have here is

like those two numbers are going to be

multiplied by those two numbers and then

add it and then something analog is

going to happen in the rest and what do

we have here is something analog it's

not exactly the cosign similarity but

it's very analog to a similarity Matrix

um in practice if those uh vector vors

that we have here are like all of them

if they have the same um uh Norm like

the same distance from the the origin or

like if they are normalized in practice

what we have here is like a similarity

of each one of those words and that we

have as Target sequence and the words

that we have as input sequence uh so as

we you can see we have here like higher

values for like uh numbers that are

closer to each other like they they have

the similarity and so we see like I am

here it's SM similar with so and happy

is SM similar with

Phillies uh and actually in the paper if

you apply this multiplication to like a

embedding that is very big uh those

values they tend to be very large and

usually for neuron networks we want

small

values because large values makes the

gradients to

explode and in order like to do this

normalization we can divide by the

number of embed the dimension of

embeddings that we have in this case our

embeddings have two Dimensions so the

actual value that we would have here

would be this matrix multiplication

divided by the square root of

two and let

me and let me finish here okay so then

then here we have

implemented uh what we have inside here

and then the next step here is to apply

this soft Max function which we have uh

in this side and the idea of the soft

Max function is to convert all of those

values

into a proportion that would add up to

one so it's like a percentage

contribution and we need to use this

exponential function because sometimes

we have negative values and sometimes

positive values so the idea here is to

use the exponential um equation in order

to convert all of those values into

positive values so this is what I'm

going to do here so EXP exponential of

all of those values so again when I do

like this array formula then what we

have here this is the exponential of

this value this is going to be the

exponential this and so on so it's just

a shortcut cut so as you can see now we

all of those values were converted to

positive and we divided this by the sum

in this case is actually the sum of each

row which um I'm going to to calculate

here so I just need to calculate this

sum and then do the same for the bottom

and then finally the soft Max of uh of

this amount of this Matrix is going to

be the this

Matrix divided by those values so I'm

pretty much like dividing all of those

numbers like 1.2 by 3.9 and then two and

then so on this is what I'm doing here

and uh what do we have here uh if you

notice all of those numbers here they

will add to one so it's like a

percentage

contribution uh of uh each one of uh

those uh words here in Bings that you

want to be propagated in this attention

transformation so after we get this soft

Max uh we need now uh to get the the

value like uh which in in which is also

this input sequence so I'll get

here and what will happen now is we'll

be multiplying both in order to create

this

transformed uh output or transformed

Target um embedding and this is it's

like you're are telling

that you you want to create a

transformat uh targeting Bing as like a

based on how similar like giving like

some percentage of contributions from

the memory from the input that we have

uh so pretty much like for example for

the word so we have that we want 30% of

contribution from the the word I and 64%

of cont contribution from the word m so

what we have here I'll do like step by

step just to show how exactly those

numbers are coming up so it's this

number times like this original Vector

plus this number times this original

Vector plus this number times this

original Vector so here we have

0.7 and then and then here I have the

same thing but now for this second

Vector so here and then plus this term

times this second Vector plus this term

times this third Vector uh so what we

have here is like a new

position of this Vector

so which is going to be based on like

those contributions so since uh like the

word I and the word m they are more s

similar than the word happy is like you

are like sending um the vector like to a

new position which is like closer to

both of them uh but again like all of

those values those embeddings they are

learned and then this transformation is

applied in a way like to uh to to use

the context of of the S sentence in

order to give a new position to to that

uh vector and here I can do the same

calculation here or I can just do M both

here and multiply both of those

vectors and oops and then I need to

delete here so here we have this new

word so and phis we we have here that

the new Vector is going to have 70% of

the original Vector uh uh of of Happy

but also it's going to have like about

30% of those two vectors uh so that's

the new position of the word

phis and that's it so here we

implemented uh this scaled do product

and more specifically this cross

attention since we are um like Crossing

this input the and the

Target and uh

and like this the only like difference

with the original like what's

implemented in the paper is that there

will be those linear multiplications and

also like for this case we we don't have

masks uh but there will be like some

attentions that they will have masks or

there will be like attention components

that they will be like comparing the

words with themselves uh but yeah that's

it I hope it was helpful to give some

intuitions and uh and yeah that's it