Essential Matrix Algebra for Neural Networks, Clearly Explained!!!
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- Опубліковано 31 тра 2024
- Although you don't need to know matrix algebra to understand the ideas behind neural networks, if you want to code them or read the latest manuscripts about the field, then you'll need to understand matrix algebra. This video teaches the essential topics in matrix algebra and shows how a neural network can be written as a matrix equation, and then shows how understand PyTorch documentation, error messages and the equations for Attention, which is the fundamental concept behind ChatGPT.
Note: If you want to learn more about neural networks...
• The Essential Main Ide...
...backpropagation...
• Neural Networks Pt. 2:...
...the ReLU activation function...
• Neural Networks Pt. 3:...
...tensors...
• Tensors for Neural Net...
...SoftMax...
• Neural Networks Part 5...
...Transformers and Attention...
• Transformer Neural Net...
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0:00 Awesome song and introduction
2:35 Introduction to linear transformations
5:57 Linear transformations in matrix notation
7:34 Matrix multiplication
11:03 Matrix multiplication consolidates a sequence of linear transformations
13: 46 Order matters for matrix multiplication
15:18 Transposing a matrix
16:37 Matrix notation and equations
18:51 Using matrix equations to describe a neural network
24:26 nn.Linear() documentation explained
26:38 1-D vs 2-D error messages explained
27:17 The matrix equation for Attention explained
#StatQuest #neuralnetworks #matrixalgebra
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Hi, i would like to buy the book in color. Does someone know if that is posible ? It seems to me that in amazon is in black and white and on Lulu is on color. Is that right ? I am from spain.
@@bigbacktor They are all in color. And there is a version that is translated into spanish if you are interested.
@@statquest Thanks a lot!! BAM you just sold another book :)
@@bigbacktor Hooray!!! Thank you very much for supporting StatQuest! BAM! :)
All visual learners are blessed by the great Josh Starmer!
Thank you! :)
What you do is nothing short of a miracle! Immense gratitude
Thank you!
You have been staying the course for a long, long time. It's not so easy ! Keep up the good work!
Thank you!
this is freaking amazing! Would love to see more math lessons like this
Thank you!
World is a better place with Josh🎉
Thanks!
Could you please make a video about QLORA? ❤ You're our savior when it comes to understanding complex concepts, thank you man
I'll keep that in mind.
that would be lovely, perhaps LORA itself holds a strong glue potential across neural networks, will be looking forward for such amazing video
You will be known and remembered for the next 1000 years ..
bam!
10000000 years
Thank you for explaining it so simply even a novice like me can understand it.
Thanks!
Man u deserve a thousand times more subscribers
Thank you!
i love your videos, it helped me so much.. learned a lot.. i was able to make UNA thanks to your learnings :)
Triple bam! Congratulations!
Wow, just the perfect video I was looking for! Loved all the Taylor references, and music puns.
Hooray!!! You're the first person to mention the Taylor references in a comment. BAM!!! :)
@@statquest I was looking for it, since you mentioned something with Taylor was coming soon, in one of my Linkedin Posts :) Plus, I've been reading a lot of academic papers lately, So needed a better context on matrix transformations to interpret the math better! So, Double BAM, indeed!
Hi Josh... would you please make a video and explain the differences between different statistical tests like t, z, chi... I want to know the differences and when to use each.
I'll keep that in mind.
Baaam this is good :D I have been waiting for this, to be honest, I had the feeling that one day you would make such a tutorial. Your content is great.
Thank you very much!
I found this channel when searching for a clear explanation of central limit theorem on Google (after doing some simulation in R using sample size much less than 30 and being intrigued by the results I got) and I just want to say I love the content so much! (And the ukulele episode ❤) I’ve recently started some machine learning classes on coursera and EdX, and I must say the explanation you have here in these episodes are SO MUCH BETTER AND MORE TO THE POINT/BETTER DEFINED than the multi thousand dollar classes (I’m surely glad I chose to audit them first!) taught by professors from Harvard or Engineers working for Google/IBM. So much better!… ❤❤❤
Just want to say thank you and Merry Christmas! I know I will be going through these videos one by one in the coming months…
Thank you very much!!! I'm so happy you enjoy my videos. BAM! :)
@@statquestI really did and binge watched a bunch… But I must say I now enjoy your songs even more 😂 Just bought all your albums on bandcamp - they are awesome! That going back to Cali song just had me rolling off my chairs at the end of it… I relocated from San Francisco Bay Area to Florida panhandle not long ago so that song really struck a cord with me 😂😂😂
@@arenashawn772 Thank you very much! I'm glad you enjoy the tunes and the videos. I hope the move went well! :)
Really amazing work! This set of videos (neural network playlist) has really helped me in my uni coursework and project! My groupmates and I are planning to get a statquest triple bam hoodie each haha!
That's awesome!!! TRIPLE BAM! :)
I was thinking about taking a course to learn matrix algebra yesterday. Thanks for posting this video. It is really helpful and it is like a wish came true.
BAM! :)
Absolutely fantastic explanation again
Thank you!
Tripple Bam for sure. Amazing explanation.
Thanks!
Thank you for this video. I think I understand what a transformer is now.
Thanks!
Very nice video! Thank you for uploading such helpful material :). It would be great if you made a video on vector and matrix calculus. These are important topics in NNs too :).
I'll keep that in mind.
Thanks for the great video! Also the topic proposed here would also be super interesting, so I hope you could do it someday
Superrrb Awesome Fantastic video
Thanks 🤗
Squatch: So it's all just matrix multiplication?
Josh: Always has been
bam! :)
Please part 2 with more details, and new terms
I'll keep that in mind.
Quadruple bam! (One bam for me finally understanding)
Hooray! :)
Joshua your teaching was fantastic, but I couldn't quite grasp the concept.
What time point (minutes and seconds) was confusing?
Quite good. ❤
Thanks!
Very good video ! You should remake one of the transformer videos with the matrix notation as you done at the end of this vide.
I'm working on it right now. Hopefully it will be ready soon.
@@statquest take your time and thanks you very much, your content is so much valuable !
Your video is just a lifesaver to me and my essay! Could you make a video on the Glove model in NLP?
I'll keep that in mind.
Can you please create a video on multi-modal transformer architecture?
I'll keep that in mind.
I hope he does it, he's our savior when it comes to understanding complex concepts
Hey Josh! I love your channel and I was thinking about buying a study guide. What is the difference between watching one of your playlists and buying a study guide? Do you cover exactly the same in both and buying the study guide is for support/like a donation or is there any difference?
They are the same. The difference is that some people like to have the study guides for offline use or adding their own notes to. In some ways, the study guides are like "cheat sheets" - everything in a video is condensed to about 3 to 5 pages.
Ok, it always annoyed me that when you're doing matrix vector (col) multiplication they always write the matrix first, then the vector. It never occured to me until you said so just now that the cols and rows aren't valid tensor operations if you write them the other way round... Doh! It doesn't look nice though.
Btw, why did you use a row vector and a transverse matrix? I would always use a col vector. Col space transforms are the default for me and you can picture the latent space.
The only times I'd use rows is if I have a system of linear equations.
I agree that the matrix * column looks bad. And I chose to do row * matrix because that is what they used in the PyTorch documentation.
@@statquestGlad it's not just me that thinks it looks backwards! :)) But you're of course right; 2x2 * 2x1 is a valid operation whereas 2x1 * 2x2 is, strictly speaking, undefined.
Oh, a tip you may (or may not!) find a useful teaching tool:
I always look at matrix multiplication in terms of a series of dot product operations. Once the student understands that the dot product outputs a scalar expressing the likeness of two vectors (eg whether two normalised vectors pointing the same way) then rather than just mechanically running an algorithm - the student can see that it's plotting the vector in the new space by comparing its likeness to the space's basis vectors one axis at a time. That's why I think it's always handy to see a square matrix as a series of basis vectors.
So, if you're going from an orthonormal basis to one where, say, y is mirrored - {{1, 0}, {0, -1}} - then it's quite apparent why taking the dot product for each spatial dimension will plot the vector upside-down. You could show an image flipping to drive the point home.
I just think that's intuitive and why we're multiplying and adding across columns and rows.
At least that's how I like to see it.
thanks for ur effort, ur videos helped me so much, but could u plz tell us how lghm works
Do you mean Light Gradient Boost? LightGBM?
I mean LightGBM
@@statquest
hello statquest, what software do you use to create your videos ?
(your answer is really useful to me)
I give away all of my secrets in this video: ua-cam.com/video/crLXJG-EAhk/v-deo.html
great
Thanks!
You are awsome
Thanks!
Could you explain the math behind a basic liquid neuron and show how it differs from other neuron ?
I'll keep that in mind.
Could you do a series on "attention is all you need " paper ? Thank you Sir.
This video walks you through the concepts in that paper: ua-cam.com/video/zxQyTK8quyY/v-deo.html
And this video goes through the math: ua-cam.com/video/KphmOJnLAdI/v-deo.html
@@statquest thank you so much!!
Triple Bam🎉❤
YES! :)
Hi Josh, Could you do video on time series clustering , and time series analysis please?
I'll keep that in mind.
We want yolo series mainly yolov8 from scratch
I'll keep that in mind.
Please Professor, it’s an earnest request. Lots of Love from Bangladesh ❤❤
Do more videos related to GAN etc.
I'll keep that in mind.
Can u please discuss about stochastic gradient boosting for classification?. I'm having trouble understanding that 😢
I have a whole series of videos on Gradient Boosting. You can find them here: statquest.org/video-index/
What about a video on MAMBA architecture ? That would be really BAAAM
I'll keep that in mind.
Thanks Josh. But naughty, naughty, the stage is not just rotating, it is flipping. Which you can also encode in matrices of course ;-)
I'm not sure I understand what you mean by flipping in addition to rotating as stage left and stage right are maintained through out each change.
@@statquest The drawing of the stage is asymmetrical (one edge is slightly erased). When you did the slides you flipped it instead of rotating it. As a result, Statsquatch is sometimes on one side, sometimes on the other. I know it was not on purpose 🙂 Thanks for the excellent vid as usual.
@@Nono-de3zi I'm still confused because statsquach is always on stage left.
But the *stage* is flipped :-)
@@Nono-de3zi If it was flipped, then wouldn't stage left stay on top and stage right stay on the bottom?
Can we book on these concepts as well
I'm writing it right now.
14:05 matrix multiplication cant be rearranged, as matrix multiplication is a sequence of calculations. is this indicated by using X as a multillication symbol and not •? Becaus in school we used • to indicate multiplications.
ah no the x is not signifying order. but I would like that to be visible from writing alone, without the helpful explanation.
i wonder why matrices are turned sideways like that. it would feel easier for me to multiply rows with rows.
This is explained, although I'm guessing not to your satisfaction, at 10:58. It has to do with the ability to combine transformations. For more details, see: math.stackexchange.com/questions/271927/why-historically-do-we-multiply-matrices-as-we-do
BAM!
:)
Woaw
:)
after 10000000 years, scientists found fossil record of statquest, then he said " BAM!"
Ha! You made me laugh.
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The topics again:
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Great video, but i don't quite understand 25:25...
It just means that PyTorch stores the weights differently than we used in the earlier examples and in order to get the same math, we have to transpose the PyTorch weight matrix.
zhina！
?
97 videos finished … small bam 🥲
Wow!