The math behind Attention: Keys, Queries, and Values matrices 

Hello all! In the video I made a comment about how the Key and Query matrices capture low and high level properties of the text. After reading some of your comments, I've realized that this is not true (or at least there's no clear reason for it to be true), and probably something I misunderstood while reading in different places in the literature and threads. Apologies for the error, and thank you to all who pointed it out! I've removed that part of the video.

This might be the best video on attention mechanisms on youtube right now. I really liked the fact that you explained matrix multplications with linear transformations. It brings a whole new level of understanding with respect to embedding space. Thanks a lot!!

I have watched more than 10 videos trying to wrap my head around the paper, attention is all you need. This video is by far the best video. I have been trying to assess why it is so effective at explaining such a complex concept and why the concept is hard to understand in the first place. Serrano explains the concepts, step by step, without making any assumptions. It helps a great deal. He also used diagrams, showing animations along the way as he explains. As for the architecture, there are so many layers condense in to the architecture. It has obviously evolved over the years with multiple concepts interlaced into the attention mechanism. so it is important to break it down into the various architectures and take each one at a time - positional encoding, tokenization, embedding, feed forward, normalization, neural networks, the math behind it, vectors, query-key -values. etc. Each of these are architectures that need explaining, or perhaps a video of their own, before putting them together. I am not quite there yet but this has improved my understanding a great deal. Serrano, keep up your approach. I would like to see you cover other areas such as Transformer with human feedback, the new Qstar architecture etc. You break it down so well.

this is definitely the best explained video for attention model, the original paper sucks because there is not intuition at all, just simple words and crazy math equations that I don't know what it's doing

This is unequivocally the best introduction to Transformers and Attention Mechanisms on the entire internet. Luis Serrano has guided me all the way from Machine Learning to Deep Learning and onto Large Language Models, maximizing the entropy of my AI thinking, allowing for limitless possibilities.

Best video explaining what the query, key, and value matrices are! You saved my day.

This is the best description of Keys, Query, and Values I have ever seen across the internet. Thank you.

you explain very well Luis. Thank you. It's HARD to explain complicated topics in a way people can easily understand. You do it very well.

Please continue making videos. You're the best teacher on this planet.

The best explanation I've seen so far! Really cool to see how much closer the field is getting to understanding those models instead of being so abstract thanks to people like you, Luis! :)

I really like how you're using these concrete examples and combining them with visuals. These really help build an intuition on what's actually happening. It's definitely a lot easier for people to consume than struggling with reading academic papers, constantly looking things up, and feeling frustrated and unsure. Please keep creating content like this!

Just the Keys and Queries section is worth the watch! I have been scratching my head on this for an entire month!

Amazing video. pushed forward my understanding of attention by quite a few steps and helped me build an intuition for what’s happening under the hood. Eagerly waiting for the next one

This is the best video that I have seen about the concept of attention! (I have seen more than 10 videos but none of them was like this.) Thank you so much! I am waiting for the next videos that you have promised! You are doing a great job!

Honestly you are the best content creator for learning Machine learning and Deep learning in a visual and intuitive way

Great explanation. I was waitinig for this after your first video on attention mechanism! Your are so talented in explaining things in easily understandable ways! Thank you for the effort put into this and keep up the great work!

This video is, without a doubt, the best video on transformers and attention that I have ever seen.

Thanks for sharing your knowledge freely. I have been waiting patiently. You add a different perspective that we appreciate. Looking forward to the 3rd video. Thank you!

La mejor explicación que he visto sobre los Transformers. Gracias!

These are the best videos so far I saw to understand how Transformer / LLM works. Thank you. I really like maths but it is good that you keep math simple that one don't loose the overview. You really have a talent to explain complex things in a simple way. Greets from Switzerland

Absolutely the best set of videos explaining the most discussed topic. Thank you!!

Great video as always ! Thank you so much for this quality content.

Thank you, really good job on the visualization! They make the process really understandable.

very nice and easy explanation, thanks!

The best explanation l've ever seen about the attention mechanism, amazing

Finally! This is the best from the tons of videos/articles I saw/read. Thank you for your work!

This really is one of the best videos explaining the purpose of K, Q, V. The illustrations provide a window into the math behind the concepts.

Amazing explanation. Thanks a lot for your efforts.

One of the Best video on Attention. Such a complex subject been taught in a simple manner.Thank u!

this is absolutely the best video that clearly illustrate and explains why we need v,k,q in attention. Bravo!

Amazing video! Took my intuition to the next level.

Thanks! This is one of the best explanations of Q, K & V I've heard!

This probably is “the best video “ on this topic

Today i have understood attention mechanism better than never before

This is great videos with clarity! on Keys, Query, and Values. Thank you

A professor here - preparing for my couse and tryng to find an easier way to talk about these ideas. I learned a lot! Thank you!

Your explanations are truly great! You have even understood that you sometimes have to ‘lie’ first to be able to explain things better. My sincere compliments! 👊

Simply the best explanation on this subject.Crystal clear .Thank you

The best video I have ever watched about this!

This is one of the best videos on attention and w,k,v so far.Thank you for a detailed explanation

Math is not my strong suit, but you made these mathematical concepts so clear with all the visual animations and your concise descriptions. Thank you so much for the hard work and making this content freely accessible to us!

Amazing explanation of very difficult concepts. The best explanation I have found on the topic so far.

Best Video to get clear understanding of transformers

Excellent explaination

Brilliant Explanation.

Excellent job! Please continue making videos that breakdown the math.

This is one of best video I've come across to understand embeddings, attention. Looking forward to more such explanations which can simplify such complex mechanisms in AI world. Thanks for your efforts

This is truly the best video explaining each stage of a transformer, thanks man

Thank you it was a superb explanation 🤩

MAN! I have no words! Your channel is priceless! thank you for everything!!!

This is the best video I had seen explaining attention mechanism. Keep up the good work!

Amazing explanation. I am a professional pedagogue and this is stellar work

Thank you for the great tutorial. This is the clearest explanation I have found so far.

@SerranoAcademy If you want to come to the same notation as in the mentioned paper, Q times K_transpose, than the orange is the query and the phone is the key here. The you calculate q times Q times K_transpose times key_transpose (as mentioned in the paper) Remark: the paper uses "sequences", described as a "row vectors". However, usually one uses column vectors. Using row vectors, the linear transformation is a left multiplication a times A and the dot product is written as a times b_transpose. Using column vectors, the linear transformation is A times a and the dot product is written as a_transpose times b. This, in my opinion, is the standard notation, e.g. to write Ax = b and not xA=b.

Are these slides available somewhere for reference? It will be a great help. Thanks

Great explanation. I just really needed the third video. Hope you will post it soon.

This is Great ! in next video can you please include why we need sin and cosine functions for posistional encoding ? whats the intution behind it? if we add this vector to embedding vector what happens ?

I'm going to try implement self-attention and multi-head attention myself, thanks so much for doing this guide!

I can't wait the third video any more, when it will appear?

One of the best explanations I have ever watched

I haven't blinked my eyes for a sec. 👏🏼🙏🏼

Thank you for the explantion.

You are a master!

Thanks a lot for this. I always got terrified of the maths that might be there but the way you explained it all made it seem really easy ❤

amazing video. that's what i looking for. I need to know mathematical background to understand what is happening behind. thank you sir!

Great video finally understood all the concepts in their context

I've been watching over 10 of the Transformers architecture tutorial videos, This one is so far the most intuitive way to understand it! really good work! yeah, Natural language processing is a hard topic, This tutorial is kind of revealed the black boxe from the large language model.

HI Luis. Thank you for this video. I'm sure, this is a very good way to explain this complex topic, but I just won't get this into my brain. I'm currently doing the Math for Machine Learning specialization on Coursera and brushing up my algebra and calculus skills that are way to low. In any case, you made me getting involved into this and now I will grind through it till I make it. I'm sure the pain will become less and the fog will lighten up. 😊

Great and intutive explanations! Well done!

I had to read this research paper for my Intro to AI class and it's obviously written for people who already have a lot of background knowledge in this field. so being a newbie I was so lost lol. Thanks for breaking it down and making it easy to understand!

Very well explained. Got a bit closer to understanding attention models.

"This step is called softmax" . 😮😮😮 Today I understood why softmax is used. Such a beautiful function. And such a great way to demonstrate it.

This is the best video for people trying to understand basic knowledge about transformer, thank you so much ^^

Amazing video and explanations, thank you !!

This is powerful yet so simple. Thanks

Best video on this topic so far!

Best video so far on this topic

Great video series! Thanks you! That helped a ton 🙂 One small remark: the concept of the "length" of a vector that you use here confused me. Here, I guess you take the point of view of a programmer: len(vector) outputs the number of dimensions of the vector. However, for a mathematician, the length of a vector is its norm or also called magnitude (square root of x^2 + y^2).

Fast forward watched, seems to be good , thx will watch

Thanks, very useful. I love the way you explain things here and on Coursera.

the scaling factor in scaled dot product can be understood as the ~ dis(points). in higher dimentions the estimate of distance between two points in roughly srqt(dimentions)

so great video

Sir , You are a Blessing to New Learners like me , Thank You , Big Respect.❤

Thank you so much! the image at 24:29 made this whole concept click immediately.

Great Explanation. Thank you so much

Love the simplification you brought !!! super

This video has the best explanations of QKV matrices and linear layers among the other resources i ve come across. I don't know why but people seem not interested in explaining whats really happening with each action we take which results in loads of vague points. Yet, the video could ve been further improved with more concrete examples and numbers. Thank you.

So great content. You really have a gift to distillate complex concepts! Thank you. Slight typo tho on the softmax (from 16:45), is vector-valued, so the numerator must be calculed in each component... in the slides the fractions cancel out to 1...

Super clear ! Great video !!

I studied linear algebra during the day on Coursera and watch RU-vid videos at night on state of the art machine learning. I’m amazed by how fast you learn with Luis. I’ve learned everything I was curious about. Thank you!

This is one of the best resource on attention mechanism. Key, query, value explaination was just awesome. Just one question though how do we know that key matrix is capturing high level concept , query matrix capturing low level concepts and value matrix more focused on predicting next word. Can you share code or playbook which validates this?

@SerranoAcademy At 13:23, you show a matrix-vector multiplication with a column-vector (rows of the table times columns of the vector) by right-multiplication. On the right side, maybe you could use, additionally to "is sent to", the icon "orange' (orange prime). This would show the multiplication in a clearer way Remark: you use a matrix-vector multiplication here (using a row of the matrix and the words as a column on the right of the matrix). If you use row vectors, the the word vector should be placed horizontally on the left of the matrix and in the explanation, a column of the matrix has to be used. The result is then a row vector again (maybe a bit hard to sketch)

Thanks for the first two videos; they are great! Where can we find the third video?

Amazing. Thanks a lot for this!

Yep, a truly terrific video. Congrats!

God sent video. So incredibly well put

Thank you so much !! I watched several video and none could explain the concept so well

As always, great content! Thanks

Hello Dr Serrano . What is the reason when comparing the query of the ith word with the keys of other words rather than comparing with query of the ith word with the queries of other words? I understood that queries extract fine tuned embedded features and keys capture general concepts but still the different weight aspect confuse me . Is it because having two different weights allows more variability when doing linear transformations? Like also the same reason we use multiple gates with their respective weights to capture patterns about remembering and forgetting corect?

It was fascinating to me, I searched a lot for a math explained which didn't find thanks for this Please do more😅 with more complex ones