But what is a neural network? | Chapter 1, Deep learning 

Most educational videos give viewers the impression that they are learning something, while in reality, they cannot reliably explain any of the important points of the video later, so they haven't really learned anything. But your videos give me the impression that I haven't learned anything, because all the points you make are sort of obvious in isolation, while in reality, after watching them I find myself much better able to explain some of the concepts in simple, accurate terms. I hope more channels follow this pattern of excellent conceptual learning.

I study mathematics, physics and architecture. By definition this man is an ORACLE in the strict meaning of the word. With all honesty I never imagined someone explaining complex topics with the dexterity this man has. He is literally an institution and an outstanding teacher. The computer graphics and the illustrations are simply perplexing. This guy never evades complexity. He never evades complex arguments. He illustrate the complexity and dive into the exhaustive explanation of the details. It's extremely rare to see a professor and a dedicated user to put a lot of effort explaining, animating and describing mathematics the way he does.

No man, we don't get notifications for your videos. We search for 3b1b. That's how powerful your content is.

Your videos are singlehandedly keeping my PhD research on track. Thank you for your time and effort!

Quote: “Any fool can make something complicated. It takes a genius to make it simple.”…..nailed.

I'm currently taking a computer science math course where the professor strongly advised everyone to watch this exact video series to get an intuition about what all the math is actually used for.

I am blown away by the visual clarity of this description of otherwise a complex technology! More please, I am willing to pay!

I can't wait for neural networking to be able to recognize my doctor's prescription.

In schools everyone taught us to practice maths but this man teaches us to imagine maths

Brilliantly explained

AI, neural networks, machine learning... these things are going to be a HUGE part of our future.

It takes 3000-4000 lines of code to make those graphics possible, he's a freakin legend

The fact that I was sent here by my university lecturer is a testament to how good 3Blue1Brown is.

I am Programming for more than ten years and I never saw anyone explain a complex idea by such a clean and clear terms. Well done.

This is how you taught Deep Learning, people. I've seen lectures that either be categorized into 2 groups: too hard or too shallow/general. You have balanced between them. Thanks you so much!

I am currently doing my Master's in Data Science and this 18 minute video is better than any course I have taken so far

I'm studying AI for my masters degree and my professor told everyone to watch this video to understand the concept :D

Around 2 years ago I was a sophomore statistics student and had no idea what deep learning is, until I met this video and 3b1b channel. His clear explanation of neural network and animations blew my mind. Since then I started my journey in machine learning. For a random reason I clicked onto this video again, and realized how long my journey in this field have been. This video really changed my life and I am really grateful about it.

I just love the way the concepts of neural networks are explained in this video. After watching it, you feel like you have an idea about the "building blocks" of a neural network. Since I'm new to the topic, it's hard to judge whether crucial things are left out or over-simplified, but I feel it's a great introduction to the topic. Thanks a lot for sharing this!

Every few years I come back to watch this series. The most intuitive and understandable explanation of neural networks that exists

In class : printf("Hello world"); The exam :

how is it possible that I can lie in my bed on a Sunday and am presented with mind-boggling cutting edge knowledge told by an incredibly soothing voice in a world class manner on a 2K screen of a pocket supercomputer basically for free

This channel and the visualizations it produces to teach subjects like this one is the best advance in the history of communicating mathematical ideas. It's extraordinarily inspiring that one person can have such a large impact on the world today (and for generations to come). Thank you, Grant Sanderson.

3Blue1Brown is the go-to channel that explains complex math concepts with the highest clarity without any loss of complexity of the topic. Simply brilliant!

Our generation is lucky to have mentors like you, thank you so much sir!

This is my very first time commenting on a RU-vid video, and it's just to say: This is the best explanation of anything ever.

This the most comprehensive and understandable explanation of a neural network. Thank you.

The way u guys animate and explain the difficult topics in the most simple visual way is impressive...kudos and thank you for the efforts.

Is anyone else nominating this series for the "Distill Prize for Clarity" in 2019? I really think he deserves it, excellent visualizations.

THE TEACHING ASIDE , THOSE GRAPHICS MAN! TAKES LOT OF EFFORT!

I absolutely love this video, I saw this video a few months ago and couldn't understand it too well until after I went into linear algebra and took a course on deep learning. This explanation is still one of the best ones I've ever seen. I truly respect your work here and please keep it up!

You have been a key element on my Machine Learning education! I am a visual person. So your videos help me so much to understand the concepts behind the math.

PART 1? THERE WILL BE MORE? YAS 3BLUE1BROWN IS DOING NEURAL NETWORKS! TODAY IS A GOOD DAY

Written some notes from the video to read quickly. Hope it helps somebody. l Neural Networks can recognize hand written digits, letters, words ( in general, tokens ) l What are Neurons? ○ Something that holds a number [ 0, 1] ○ The higher the number, the higher the "activation" rate l Consider a 28*28 table in which each unit is represented by a value between 0 to 1 ( activation number ) ○ Let us divide each row into a "layer", such that, if we were to divide all the layers, the last layer would contain 10 "cells" ( units ). ○ Values are passed from the previous cells to the last layer ( 10 unit layer ), again, between 0 and 1. The higher or closer the value is to 1, the more probability exists that the image scanned represents that unit cell. So, a unit cell that contains the highest value is indication that the index of the unit cell is the value of the image scanned. ○ 16 cells in the second and third last cells are arbitrary. ○ Each cell is linked ( causes activation ) to some ( not all ) other cells in the next layer which further cause more activation. ○ Each 'cell' corresponds to some sort of identification about how much a certain region 'lights up', and then sends a value to another node which reacts based on the received value. ○ To find whether a certain cell with light us, like each cell be represented by 'a Cell_Number ', and let each cell be 'assigned' a certain weight 'w'. The sum of all the products of each cells 'a' and 'w' will be: w1*a1 + w2*a2 + w3*a3 + w4*a4 + … + wn*an ○ Let these weighted sums represent some 'grid cell'. Each cell is either 'on' or 'off' with respect to being positive or negative. In this case, 'green' represents on, and 'red' represents off. ○ Let us concern ourselves to a certain region where the cells are mostly on. Ergo, we would be basically summing up the weightages of those grid cells. ○ Then, if you suppose a region where there are brighter grid cells in some part which are surrounded by dark grid cells, then that area is the main edge we're looking for. ○ Of course the sum of weightages gives us very different value. In order to 'squish' that number line into 0 and 1 , we use the function: Sigma(x) = 1/(1 + e^-x) Which is a sigmoid function or a Logistic Curve. Our equation now becomes: Sigmoid(w1*a1 + w2*a2 + w3*a3 + w4*a4 + … + wn*an) ○ But what if you don't always want to light up when it's a positive value, and rather want it to light up when the weighted sum of that grid cell full fills some condition, such as > 10. This is called 'Bias For Inactivity'. Using this example, our equation becomes, Sigmoid(w1*a1 + w2*a2 + w3*a3 + w4*a4 + … + wn*an - 10) Here, 10 is the "bias". ○ The possibilities of the different knobs and dials open us to the term of "Learning", which just means to find the correct relation of values which perform the expected behavior. ○ The complete expression above can be adjusted in the formula: a(1) = Sigma(W*a(0) + b ) ( (1) and (0) are superscript here ) Where W = k*n matrix whose elements are weights corresponding to a cell. a(0) = n*1 matrix whose elements are the 'a' of each cell. b= n*1 matrix whose elements are the biases of each cell ○ NOTE: Sigmoid function is not used very often now, instead it is replaced by ReLU ( Rectified Linear Unity ), which is defined as: ReLU(a) = max(0, a), a linear function where f(a) = a for a>= 0, which for a < 0, f(a) = 0.

Sigmoid squishification function might just be the best thing I've ever heard in maths

Thanks for all the effort you put into the work! Cannot stress enough how glad and inspired I am for having people like you on the planet.

As a person who has self-learned a bit of python and is just trying to learn this stuff, this is exactly the best place to begin.

this is my first introduction to machine learning and I watched this only twice to get it, really goes to show how good of a teacher this guy is, the effort he puts in is nothing short of amazing !

My God! No words to express as to how you made such a complex topic to be understood using visuals so easily! Hats off!!

i have recommended this channel in every single conversation I had in 2022. Thank you!

Bio teacher: what is a neuron? Me: a thing that holds a number between 0 and 1

One of the few teachers that don't make you feel stupid, but actually help you understand the topic. I appreciate the time you spend on this.

Today I came back to the first video of yours which I saw some years ago and which made me appreciate maths much, much more. It is also incredibly well-made and I just watched it again. Thanks for your work, Grant! I am still subscribed and enjoy and learn from each of your videos since.

This is simplest and best way to explain neural networks. This is the best introductory video on Neural networks I watched so far.

This video kickstarted my journey in ML a year back. Trust me, back then I watched this video three times to finally understand. It might be challenging for few to get it but when you get it, it just feels amazing

I work in a company developing just this kind of stuff. I’m still baffled how incredibly intelligent people are and I have no idea how they can repeatedly accept me as worthy enough to be with them.

I saw this video when it first came out, I was amazed at how Deep Neural Networks worked and how he could explain them so clearly. Now I am working as a Machine Learning engineer. Thank you so much for helping me find my passion

neatly explained, never thought machine learning would be this easy to comprehend most of the youtubers out there just throw bunch of concepts out without actually explaining the relation and the logic of the whole design most of the time i thought i was too stupid to understand these things and that i must take a specialized college course or sth but turns out that wasnt the case, its just that youtube needs more people like you who can explain things with sophisticated details in simple language thanks for your contribution bro

This guy: Uses dark screen to illustrate a long concept so that it's easy on the eyes. Everyone: "Carefully, he's a hero."

"Even when it works, dig into why" - 3B1B. Your lessons are pure gold sir. I'm here after watching the entire Essence of Linear Algebra. Thank you.

I wish I had known this channel 4 years earlier when I did my master's degree in analytics. This is so easy to understand!

I just watched Welch labs machine learning playlist a few weeks ago. It was mind-blowing. I'm glad you're getting into machine learning too! : )

@3Blue1Brown - A quick suggestion: Red-green color deficiency is the most common form of colorblindness. When trying to represent information via a color spectrum, could you please choose colors other than red and green for this reason? Red and blue are good choices because they are distinguishable by both red-green color deficient people as well as blue-yellow color deficient people, which is the second-most common form of colorblindness. I was completely unable to tell which pixels have positive weights and which ones had negative weights in your example due to my colorblindness. Thanks, and keep up the fantastic videos :)

it's incredible and inspiring to witness someone teaching a subject where they know all the details, all the whys and hows behind each detail. I can only thank you and say that you inspire me to enjoy learning especially if i can help someone learn with more ease a subject that was hard for me to gasp. I wish you all the best and thank you so so so much

Never see anything similar than this. Unbelievable that such understandable visualization of illustration can be done. Crazily hard and great work!

I am a Data Scientist and I would like to tell you THANKS. I have NEVER met anyone with the ability to teach complex things in this way. A M A Z I N G. Please continue like this, for example with other statistics videos. You can substitute many of the University courses.

Every second of this video is a Pre-requisite to the next second of the video :D

amazingly well-explained. hats off to you, good sir

Explaining something like Deep Learning with so much clarity is very hard to find, hats off to you and thank you for sharing the knowledge!

3Blue1Brown "Sigmoid Squishification Function": 11:23 Most brilliantly named function I have ever heard named. Absolutely brilliant. The merger of the technical with the simple with a double alliteration for easy memory.

What a time to be alive, with such RU-vidrs around!

This is by far the best explanation I have seen to understand how a neural net works. Kudos.

I have to be honest...During school and college I never was a fan of math at all....But this channel is actually changing my mind. I even bought a math book!!! This is a good channel!

Your way of making things simpler, relevant, and uncovering the most complex concepts into meaningful lessons is amazing.

This channel is so damn good. Other channels give some terrible analogies and some other explain it in extreme technical detail. This strikes the perfect balance and provides a foundation to understand the more technical details

I know you read this all the time, but I must say it. You videos are simply incredible! Your work reshapes education. You deserve every cent that this platform puts in your pocket.

This video explains the subject so clearly and makes the topic so accesible where previously it wasnt - thank you. Great communication.

I am just astounded. I spent so much time trying to understand this concept. Everywhere I looked people would show the similar neural network animation, but no one ever really explained and exemplified every single step, layer, term and mathematics behind it. The video is really well structured and with amazing animations. Extremely well done. My mind is so blown I can barely write this comment.

Finally, a video that does more than just present some neurons and layers and say, “here’s an activation function.” Your video describes how the model is developed and why the algorithmic approach is appropriate for the problems neural networks try to solve. Thanks!

Wow, I sort of kind of understood neural networks before, but after watching this video I feel like I understand them SO much better!! Thanks so much for making math videos that are visual, fun, and thorough! :D

The term "squishification function" really drove the point home for me regarding what these functions were meant to do.

📂Documents └📁Videos └📁 3Blue1Brown └📁 Bad Videos └⚠️ This folder is empty

watching this for a second time and i can't believe how illuminating is to come back to the basics and get a renewed understanding -- grant, you're a treasure

damn, this was 6 years ago

Behind this material is an extreme shot of giftedness. Explaining something is not easy. You first need a solid physical model for the topic in your brain and then you need to translate this model into a mental model that can be faithfully exported into others' brains. I congratulate you for this excellent job and I hope that you appreciate what you are and what you are doing. This is much more important than how much money this business brings.

You're the first person to explain bias in an intuitive manner. Thank you.

Too good. Can't imagine how long it'll take for me to understand this concept without your video!

Thank you so much for making this. I just finished a lecture on this and didn't understand it at all. In 5 minutes here I understood so much more.

ML grad student here and hands down Grant covered an entire chapter concisely and very clearly in this video. I don’t think reading any academic books will give you this amount of intuition on this subject within a few minutes. Still mesmerized by the effort!

Wow a lot of things that i've learned on this first year of system engineering are captured on this video, but previously I didn't understand the real essence of it. Thank you for these amazing vids! Greetings from Argentina :)

It is a tradition for me to come watch this series every now and then.

It was magic when this video starts lining up with what I have just learned in a data mining class. Love your videos so much! Also, would be cool to see your take on power laws and self-organized criticality--I'm sure some really interesting connection can be made visually!

Can't believe how well explained and intuitive this is. I aspire to become a teacher like you.

One “like” is not enough for the work that has gone into making one such video. This video should be part of the curriculum and he should get the royalty for this. Awesome work!

I have never seen a more clear and pedagogic way oof explaning neural networks! Thank you! And awesome graphics btw…

I don’t even speak English perfectly but the way that you explain is even better than a person who knows about this in my language, thanks a lot

This is the best intro to neural networks I have ever seen. The presentation is excellent! The animations are very very very helpful especially in understanding the formulas and matrices and how they came to be. Thanks a million. Looking forward for the next one.

It took me one week to understand this when I was reading a university lecture. You explained it to me in 20 mins. You are such a savior. Thanks 3Blue1Brown!

Fantastic visualized learning!

You are a beautiful human being. I've watched you even before college, just out of interest and curiosity. Now I'm in college, and I can't thank you enough. Math is so much more amazing when you have many different eyes to view it in. Also I'm currently taking linear algebra and an intro to neural networks.

This is deep.

Currently doing my capstone on deep learning and this is among the best, and easiest to understand descriptions I have seen.

I hereby solomny swear, that once I finished my Bachelors next summer, I'm gonna donate 50 Euros to this channel. The vids on the Fourier Transformation saved my ass

Wow. This is one of best videos on deep learning I've ever seen.

This will go down as one of the best lectures in history. What an amazing and concise explanation of something I thought I would never understand ...

Neural networks is a topic I've wanted an intuitive understanding of for a while. 3b1b has the most intuitive explanations on RU-vid. This video could not be any better.

Can't believe that I started watching your videos explaining Linear Algebra when I was a first year Electrical and Computer engineering student four years ago

Thanks for helping me understand how NN works :D I started exploring this subject a few days ago and your video helped me a lot to understand some things better.

Awesome video! As someone who's just starting learning neural networks, I don't have much trouble understanding this video and it helped me understand what weight and bias are! Thank you so much!

This is probably the best video that I've seen on the topic of basic artificial neural networks (ANNs). Most of the videos that I've seen on the topic are either overly complex or leave out important information about ANNs, so you're forced to watch many videos on the subject to understand the basics. But this video gives you all the basics without making you feel like there's a lot of information left out. Granted that there's a lot left to learn, but I'm sure chapter two will get into some of that.