The spelled-out intro to neural networks and backpropagation: building micrograd
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- Опубліковано 4 тра 2024
- This is the most step-by-step spelled-out explanation of backpropagation and training of neural networks. It only assumes basic knowledge of Python and a vague recollection of calculus from high school.
Links:
- micrograd on github: github.com/karpathy/micrograd
- jupyter notebooks I built in this video: github.com/karpathy/nn-zero-t...
- my website: karpathy.ai
- my twitter: / karpathy
- "discussion forum": nvm, use youtube comments below for now :)
- (new) Neural Networks: Zero to Hero series Discord channel: / discord , for people who'd like to chat more and go beyond youtube comments
Exercises:
you should now be able to complete the following google collab, good luck!:
colab.research.google.com/dri...
Chapters:
00:00:00 intro
00:00:25 micrograd overview
00:08:08 derivative of a simple function with one input
00:14:12 derivative of a function with multiple inputs
00:19:09 starting the core Value object of micrograd and its visualization
00:32:10 manual backpropagation example #1: simple expression
00:51:10 preview of a single optimization step
00:52:52 manual backpropagation example #2: a neuron
01:09:02 implementing the backward function for each operation
01:17:32 implementing the backward function for a whole expression graph
01:22:28 fixing a backprop bug when one node is used multiple times
01:27:05 breaking up a tanh, exercising with more operations
01:39:31 doing the same thing but in PyTorch: comparison
01:43:55 building out a neural net library (multi-layer perceptron) in micrograd
01:51:04 creating a tiny dataset, writing the loss function
01:57:56 collecting all of the parameters of the neural net
02:01:12 doing gradient descent optimization manually, training the network
02:14:03 summary of what we learned, how to go towards modern neural nets
02:16:46 walkthrough of the full code of micrograd on github
02:21:10 real stuff: diving into PyTorch, finding their backward pass for tanh
02:24:39 conclusion
02:25:20 outtakes :) - Наука та технологія
![[1hr Talk] Intro to Large Language Models](http://i.ytimg.com/vi/zjkBMFhNj_g/mqdefault.jpg)
![[1hr Talk] Intro to Large Language Models](/img/tr.png)
When I'm confused about deep learning, I go back to this video and it calms me. It shows that there is a simple explanation waiting for someone like Andrej to show the light.
Yep I watched a 52 hours course on pytorch, I was learning how to build a neural network but not how neural network works, which is a stupid thing from me, and a good lesson, to learn how things works if you want to learn it.
Andrej, the fact that you're making videos like this is AMAZING! Thank you so much for doing this. I will be spending some quality time with this one tonight (and probably tomorrow lol) and can't wait for the next one. Thank you, thank you, thank you!
And thank you for your videos, Dr Know It All. Always appreciate them.
I was stoked to discover Andrej sharing the knowledge on these videos as well!
You made love to the video?
And what happend? Do you now understand DNN?
Simply stunning. I'm a 72 year old fiction writer with rudimentary computer programming skills whose son works professionally in this area. I wanted to gain a better understanding of the technology he's working with, and writes scientific papers about, and now I feel I've made a great start in that direction. Wonderful!
You're a great father never change!!
what an amazing father you are, My dad also tries to keep up with all the technologies just so he can understand and get to bond with his children. I want you to know that we appreciate you guys and love you.
You're awesome!
May I ask, how has it been to work as a fiction writer? Would you recommend it?
All the people fawning over him, you do realize he started with saying he is a "fiction writer".
Granted that it's pretty cool if this isn't fiction.
@@manishj5154 he's likely backpropagating
The fact that this video is free to watch feels illegal. It really speaks volumes about Andrej. What a stunning explanation. It takes incredible skill and expertise to be able to explain such a complex topic this intuitively and simply. All I can say is thank you from the bottom of my heart that you offer videos like this for free. What an amazing man!
This reminds me of my college courses, except it's way better in three ways: 1) Here the speaker really does know what he's talking about. 2) I can stop and rewind, get definitions, and practice myself before moving on to the next step over and over, so I can get the most out of the next step because I actually had the time to understand the last step. 3) I can do this over several days so I can keep coming back when I'm fresh and present. You are a gem and I really, really appreciate you creating this.
Just and FYI for those following at home. If you are getting an error at 1:54:47 you should add __radd__ into your Value class similar to __rmul__. It will allow the order of addition to not matter. I don't think it was shown in the earlier sections.
ty, i needed this at t=6422 in order to sum(wi*xi for wi, xi in zip(self.w, x)) + self.b
@@adamderose9468 Thanks Adam. This had me stumped.
Underrated comment...
OMG, thank you so much. It was driving me nuts.
That’s comforting. I thought I just missed it. Good on you for sharing this
Finally… someone who understands it well enough to explain it to a beginner. This is hands down the best NN video on the Internet. Thanks a ton!
Just wanted to say a big thanks to you Andrej and the team working on this. Truly amazing, the clarity with which you explain these things is impressive and inspiring! Looking forward to see the remaining videos and even more. Thanks again!
"remember back in your calculus class?...." nope. I'm subscribing anyway whenever I need a humble reminder that I don't know anything and there are people way way smarter than I am.
W
O
W
Same realisation 🙌🙌😔😔😔
It's never too late to learn.
The beautiful part of tech is the feeling of constantly being mind blown when realizing how little one knows and how much there is to learn. Studying micrograd has been on my list for a while thanks to George Hotz and this series is making the owning of this context so much easier. Loving it. ❤️
If someone can explain, means its simple
I took through calc3 and aced it twenty years ago. If you put even the most basic calc problem in front of me now I couldn't even tell you how to start.
OMG! This is the first time I've ever TRUELY understood what's actually going on when training a NN. I've tried to learn so many times, but everyone else seems to make it so unnecessarily complex. Thanks for this!
It’s spelled “truly.”
@@ophello giggity
@@ophello Excuse his poor training dataset
@@ophello an example of backpropagation, you have no doubt adjust Greg's waits...lol
@@veganath it's spelled weights ...
Thank you so much for doing a step by step simulation on how gradient descent works. I am grateful for the passion and effort you make in order to teach. These lessons are very essential as we continue to dive deep into learning.
This was an exceptional lecture. Just wanted to say thank you for taking the time to make this.
I have spent time in university courses, reading books, doing assignments and yet, I truly understood more out of this single lecture than from anything else prior.
This is literally gold, you have explained everything so intuitively and made it so much easier to understand!
Thank you so much Andrej for sharing this in-depth knowledge for free!
You literally don’t know what “literally” means.
@@ophello Not necessarily. One can use a word incorrectly while still knowing its true meaning.
love your videos bro
@@ophello I know this is a year old comment, and my reply is pointless, but _technically_ 🤓Merriam Webster lists "used in an exaggerated way to emphasize a statement or description that is not literally true or possible" as one of the definitions. People define the dictionary. Not the other way around. And yes, it *literally* doesn't matter at all, but it annoyed me that you were wrong when trying to _correct_ somebody else's well meaning compliment.
This is the single best explanation of backprop in code that I've seen so far. I've once implemented a neural network from scratch, except autograd, so Micrograd is a good fit and so clear and accessible. Thanks Andrej!
Actually true. And exactly the same, I've once implemented a neural network from scratch, and I broadly understood, but this is the best explanation of backpropagation I've seen. Excellent work.
I was looking for some intuition on backprop and this is it! Thanks Andrej for taking time out of your schedule to share this precious knowledge.
Thank you for making this tutorial! I have always been on a lookout for something like this. Normal videos either discuss super deep details or go on a brief overview. This was a perfect balance between depth and showing the actual usage of what we built. Bingeing your playlist now! :D
I'm really inspired by you as an educator, and I'm very happy to see you sharing your knowledge in a lecture after a long time!
I'm a traditional dev and I have tried a lot of different guides and tutorials on neural networks. This is the first time I have been able to understand it. I'm about 1/3 through the video and it's 2am. Thanks for your excellent breakdown!!!
Did you finish the Video? Do you now understand it? Are you able to read papers in this area and implement them?
@@0GRANATE0 Is this some kind of suggestive question?
Thank you so much for your insights into the field. I try to wrap my head around NN for so long (2001). I am so glad to finaly found a teacher that gets down to the core with the least amount of clutter and teaches me the fundamental basics. Looking foreward to the following videos where it gets more complicated and you show the history of ML with accessible examples.
Awesome Video. I did not only finally understand back propagation in a way that I could explain it to someone else, but also realized again that math can come across super complex when explained poorly, or nearly obvious with a different approach. Thank you so much for putting in the effort to record the videos in that much detail. I loved that you took the time to explain the main topic and also all the math around it.
It takes real talent, dedication and complete mastery of the subject matter to breakdown difficult technical topics so clearly. Its also clear that Andrej is having fun while he elucidates. This is simply the most amazing series of educational videos on the internet on these topics. I hope you continue to put out more material like these.
Thanks for this Andrej! I love the direction you are taking. I’ve been wanting to learn this and now I get to learn from the best
Thank you for implementing backpropagation and automatic differentiation in such an elegant and easy to understand way. This is the most detailed and in-depth beginner's course I have ever seen.
I have been watching educational videos about neural networks for years, but no one had ever taught me like this. I know you since 2016 with your machine learning class videos. Thank you very much for these wonderful tutorials
Great teacher with great background and expertise. We're lucky to have him spending his time to share his knowledge with anyone who wants to learn, for free. Looking forward to more videos.
He's great! He even has an old UA-cam cubing channel (Badmephisto) and his tutorials there are awesome too!
@@notkamara omg i learned how to solve a rbx cube from him decades ago thats crazy, now im learnning neural networks, crazy how the world works
This video is by far the best and most educational I've seen regarding "how NN work", and I have looked very long. For me, even though I thought I knew how NN work and operate, at least to the point that I could use the tools out there to build a simple one. I never fully grasped the details and was always frustrated why I didn't know WHY I had to use a specific setup for my NN, I just "knew" that this is the way to do it. This video explains the basics in such a simple and logical way. Thank you Andrej! And please keep up the good work.
I'm in awe of your rare and great gift for explaining complex things in a way to make them easy to understand. My mind has many possibilities I hadn't considered before this video. I can't thank you enough for doing this.
This is enormously valuable knowledge and I'm grateful for your insight and how exceptionally well you are at teaching the fundamentals.
Thank you Andrej
Amazing tutorial, very cool! I love that you patiently walked through a lot of manual examples - too often educators get self-conscious about showing simple steps more than once and then yada yada yada their way through it, which helps nobody. Love your teaching style and hope to see more.
You are really fun to watch. It's so nice to learn this from someone who really understands how everything works.
Revisiting this again and appreciating how much of your time you put into educating the rest of us. Again, thank you!
Hey Andrej, thanks for the very detailed and understandable explanation. I went through the NNFS book last year and your video was the perfect complement to it. The graph plots were particularly helpful in visualizing the architecture. Looking forward to watching the rest of the series.
This video reminds me of my old numerical analysis professor who forced us to draw every interpolation problem by hand as an assignment. We drew all the tangent lines with a ruler and a protractor like a kid in primary school. We were complaining because that was just a few lines of code in Matlab, but in the end, that really helped us to develop true intuition behind it. Thanks for the intuitive video.
Brilliant. I have a few years of experience in the field and yet this thing did not get boring to me even one second. Awesome, easy-to-understand way to explain it, thanks! My favourite parts were how you dealt with the bugs which you had overlooked and that you did not re-shoot but fixed them on video. Very instructive!
I have carefully listened to lots of explanations about Backpropagation and every time I understood a little more but this was SO clear and easy to visualize. Thanks Andrej!
This is an excellent tutorial not only on neural networks but python and Jupyter notebooks as well. Lost sense of self for 2.5 hours and learned a ton! Thank you.
Our professor highly recommended us to use your video to learn more about back propagation. You explained it so well. Thank you so much for making this video, this video really helped our study and understanding!
Watched this again, and its still blowing my mind how useful this tutorial is. Thank you Andrej!
It's really easy to see people who master stuffs and are actively into it, because they love what they do/talk about and are still excited to talk about it, I feel the same on the subject I'm focused on. Keep up the wonderful job you've done here!
Andrej, Great to see you on UA-cam - you're knowledge is incredible and an asset to the community
By far, the best neuronal networks introduction and tutorial ever made on UA-cam. Thank you Andrej for sharing your valuable knowledge.
No amount of thanks will be enough to show how much I appreciate your lectures. They have inspired me so much!
One day I will make amazing things with it just like you told to show my appreciation for you.
Thank you sooooo much. 🔥
The best ML tutorial video I have watched this year. I really like detailed example, and how these difficult concepts are explained in a simple manner. What a treat for me to watch and learn!
Thanks, really cleared up a few confusions for me... And added new ones. Perfect. I'm looking forward to your future videos.
What an astonishing lecture, the best explanation of backprops, and the whole cycle is so intuitive and easy to understand.
I wish I had a teacher like that. I would know everything 100 times better than I do now.
Somebody is still saying that a child will learn everything on his own,
but I bet everyone will be a genius if Andrej teaches them and all of you are happy you attended his lectures at Stanford.
I wish I had such an explanation skill one day
I'm glad to see you on UA-cam, and I hope you continue this series in the future
I have a lot more to say, but I hope to tell you in person one day
thank you 100 times
Awesome! Finally finished walking through this in my own notebook. Doing it myself and being able to play around with it really solidified my understanding of building a simple neural net with forward pass and back propagation. Thanks so much for the learning opportunity!
This is amazing! You've just simplified the mathematics behind neural networks to an extreme extent. Thank you Andrej.
This was an incredible video. I wish I would have had this when I very first tried to learn about NNs. I would have been able to start my journey with so much more intuition on how things work. Thank you for making this - I will whole heartedly suggest this to anyone who wants to start learning about ML.
Many others have already said it, but thank you so much for making this. I've been trying to learn machine learning for many years now (in several short-lived attempts), and this lesson was a huge missing piece for me. Understanding the calculus behind it all, and how to really grasp how the weights and biases affect the output, really made back propagation and the learning flow click for me
Absolutely the most informative and satisfying explanation and illustration of back-propagation and NN frameworks- and perhaps educational videos in general, that I've seen. Thank you!
Honestly, I have no words. This is an amazing presentation, in terms of code, math, logic. Can't wait to continue with the other videos. Just amazing. Thank you so much for taking the time, and sharing your knowledge
Thank you very much for that lecture Andrej! It really helped to understand and to combine different pieces I learned separately into one structured concept. I especially appreciated that you left the part with the bug on gradient zeroing and made an explanation for it at 2:10:24. Making mistakes and learning from them is so effective and undervalued imo. Thanks a lot!
The weird sense of accomplishment I felt when I visualised (draw_dot) the all the operations in its full glory is unreal 😂. Thank you for this 🙏. I'm a software engineer that has been trying to truly understand neural nets for a year now. I'm not sure you understand how much this means for me.
I really appreciate you 🙏
When I started watching this a big smile grew on my face because it all started to click. Hours of formulas, animations, math symbols, etc. just suddenly began to make sense. Thank you!
I feel a lot of gratitude to you Andrej.
Your teaching skills are exceptional! The way you approach an explanation that considers broad backgrounds and goes into basics and refreshers from the school time is hard work. I very much respect the time and effort you put into this course and made it available for free, for humanity to improve.
Thanks a lot Andrej!
I would like to thank you from the bottom of my heart for making this. I'm a developer myself but this new advent in AI seemed unapproachable. Thanks, for making it clear that no subject is tough if you have a great teacher. I am seriously going to consider this area as a thing I want to do next.
When I took my AI course some 20 years ago, people were pretty depressed because things were too hard to compute and there was very little future in this type of thing. Awesome to see the simplicity in this and how powerful it is. We’ve really come far in the field of AI.
Wow!! I am watching this tutorial half way through and I am so stoked to learn the fundamentals of neural networks with such clear explanations. I don't remember in any of my university studies to have received a learning session as this one for a subject like this. If you are curious to learn the basics of modern ML and inner workings of neural networks, this is definitely the video to watch!!:) Thank again Andrej!
Andrej, can't thank you enough, i have spent fantastic two days brushing my calculus and what I did 25 years ago in school on theoretical basis. Clear, intuitive, well presented. Thanks for sharing to public to help us all get better for better world.!
CS231 was life-changing for me. You are a fantastic educator. I hope this new endeavor works out for you!!
Andrej, I am a huge fan of your previous videos. Thanks for making this investment of your time to bring us closer to these amazing concepts!
It feels good to learn from someone well known in the industry. Thank you for sharing. I have learned a lot from a practical perspective and look forward for more. Really appreciate these videos!
Andrej, thanks for your NN video series! It’s really amazing how you explain in so simple terms how it works under the hood! Wish you all the best on your new position and hope you are going to continue making such great content!
Wow Andrej! Big Fan of your work. Looking to learn more from you about Neural Networks and you being on UA-cam teaching is going to reach billions of people who wants to get into AI and learn from the amazing instructor the world has ever seen. Really loved your Stanford Computer Vision course now looking forward to more awesome content here in UA-cam
Андрей, огромное спасибо! То, что ты делаешь обучающие видео просто невероятно! Спасибо!!!!!👏👏👏
Wooow what an introduction! It is by far the best and the easiest to understand. The way you break up and simplify things in a way that we are not loosing the main focus on the WHY we are doing this, is absolutely impressive ! Thanks for sharing your knowledge.
Thank you for sharing your valuable knowledge and making this complex topic so clear and understandable. Your trainings are much appreciated.
This is probably the simplest, most well-paced explanation of back-propagation I've seen on UA-cam.
I wish everyone would break down information in this way. Thank you.
Its really sad; we don't pay the smartest people enough to be teachers. You think about it and its atrocious; the problem is actually worse - people like Andrej are coopted by big corporations where their expertise and research can be hidden behind a wall of NDAs
I already know this is going to be good. I remember watching and enjoyin your Stanford lessons on UA-cam.
Remarkably effective explanation Andrej; I was able to grasp your explanation due to how you represented the updating of nodes visually and then explained the derivative so intuitively. I was quite impressed by this lecture. I'm still halfway through but I am already subscribed and will go through your entire playlist. You are a brilliant teacher.
Extremely lucid, crisp and a splendid explanation of Neural Nets from ground zero.
@Andrej Karpathy you are a God send, thanks for all your efforts and time from your busy schedule.
I would love to see an extension of the Micrograd featuring forward-forward propagation by Hinton in future.
Thank you for existing, we are blessed to have you.
Thank you so much Andrej. I'm good at coding and bad at maths and this is the first time I've been able to properly understand a lot of this stuff... I just needed someone to explain it in my language :) I went along with the first half in detail, then in the second half I built the same MLP using pytorch tensors just to prove to myself that I understood how this all applies to pytorch, and it all worked great :)
Nice to see Karpathy going back to making some educational content! 🙂This is a must-watch!
Usually, watching long educative videos gives me headaches, but this time I didn't even noticed how time passed. Thank you! Also, direct connection of the loss function to the neural net was a fascinating insight! Looking forward to watch other videos!
I subscribed right after I saw you are creating videos on Neural Network. I have huge respect for Andrej that shares his valuable knowledge with us for free. I am starting today watching this first one and can't wait to watch the other videos and the upcoming ones. You are changing lives Andrej
Goes without saying, but you're going to blow up on UA-cam. Awesome to see you in the UA-cam edu space.
Maybe I'm a little optimistic, but I think the quality could approach that of Wikipedia one day. You joining is a good sign of that.
Not without clickbait titles and the hint that there might be an exposed body part or two. Though he does have a picture of his face making an expression, so maybe there is some hope.
@@2ndfloorsongs Dude... who hurt you?
@@anasdev1553 Haha, I have nine cats so your guess is as good as mine. 😸
I appreciate that you did not edit out your mistakes in the video.
It helped me to understand the common pitfalls in building neural network.
What a beautiful lecture! Absolutely clear, powerful and systematic exposition of a complex topic. Thank you for your work!
This is an amazing tutorial. Seeing all steps of the development and the subsequent loss convergence feels like magic.
That was incredible. Never has anyone been able to simplify Neural Networks in this manner for me. Please keep making such videos, you're doing gods work. By god, I mean the imminent AGI :)
Prescient. ;)
This is fantastic. Thank you Andrej
So educational and very clear to understand. I never expect to understand the whole nn framework/fundamentals in 2.5 hours. Thank you so much!
These are amazing Andrej. Beautifully explained, logical, easy to follow. Thank you so much for generous knowledge sharing and time you put into creating the content.
You’re an amazing teacher. Thank you for the video!!
Wow the op nodes you demonstrated this through made it so damn easy to intuit, its crazy, I have no math recall from school and didn't do any advanced math after school, nor coding
and I had to watch this whole video in 3 or 5 passes to completely grasp what was happening, it was such an amazing journey to be absolute intimidated with the length of the video, the code, the math... I knew neither, I don't even know python to begin with, yet I was able to derive exactly all the concepts necessary to understand this video
thank you so much Andrej!
"Derive", yes, i think that's the word ! haha
Thank you, Andrej! That was just PERFECT!!! I've decided to dive in neural networks yesterday and today I've successfully done it thanks to you! Your explanations are very clear, and the whole fun vibe of the video is awesome!
Hands down, the most concise and easiest-to-understand lecture on backpropagation. Thank you for posting!
As a dev, sometimes I follow along some A.I. course so I'm looking forward to follow this one!
Thanks for sharing your knowledge.
Just watched the last bit.
The python notation got really intense when Pytorch was introduced. As a non-regular Python dev, I'm going to work out some code snippets to fully grasp the example.
But dang, so all the trouble of the gradient descent is "just" to know the direction of the optimization for each node?
Very insightful!
Is the mathematical capability of computing the local derivative the root cause of the local maximum trap?
58:41 "As long as you know how to create the local derivative - then that's all you need". Ok Karpathy. Next paper title "Local derivatives are all you need".
Nice to see you on UA-cam! :))
Thank you for taking the time to do this. I'm a MSc Economics grad hoping to understand how neural networks work to start an AI startup, and your lecture is a perfect balance between depth and simplicity. Not everyone posses a natural talent for teaching and you have it!
Greate lecture - simply and thoroughly explained with neat and clear code. One of the best lectures I have ever heard. Happy to have found this treasure. Thank you, Andrej!
This video is such an unexpected treat! Thank you so much for taking the time to do this. I have followed your Twitter account since a long time but completely missed this repo. I appreciate your approach of starting with the basics, and building up an intuitive understanding from the bottom up. Your class at Stanford took a similar approach (another fantastic resource!), but this is a speedier introduction 😊
I've been working with Python for years and never implemented classes with those operator overrides. Its never too late to go back to the basics. Great video man.
Fluent Python is a good book if you'd like to understand these overrides, otherwise known as dunder (double-underscore) methods.
Just now started looking into ML/AI from scratch. I'm not sure what prerequisite knowledge is expected for this video but I was able to infer quite a lot from context and understand the lecture. Elegant code and a solid video. Cheers.
Amazing how you broke this down into first principles. I understood a lot of these concepts before now but I'm pleasantly surprised at how much clarity I gained by watching this video. Thank.
Amazing how you taught me how to solve rubiks cubes all those years ago when I was 12 and now at 22 I'm back here again learning backpropagation. You're doing God's work!
Same! I learnt F2L all those years ago and now backprop!
Andrej, thank you so much for doing this 🙏. If all the 10X Engineers out there would do stuff like this, I think it would really boost our collective human intelligence by a significant lot. I appreciate your effort, and looking forward for more content 🤞. Also I hope that you do get to return at Tesla so you can contribute to Optimus👍. Looking forward to your future accomplishments 🚀
I'm pausing frequently each time I encounter something I don't understand and using GPT-4 as an assistant to dive deeper. thank you for this and other amazing instructional videos. I (we) truly appreciate your efforts.
This video on neural network creation is truly enlightening!
It brilliantly captures the essence of how neural networks are built, providing a comprehensive understanding of their intricate architecture and function. The way it delves into the creative process behind designing neural networks showcases the immense skill and ingenuity of their creators.
Watching this video is an enlightening and inspiring experience that leaves me with a newfound understanding of the creative process behind these powerful computational models.
It is amazing to see an AI leader sharing knowledge here