What are the neurons, why are there layers, and what is the math underlying it?
Help fund future projects: https://www.patreon.com/3blue1brown
Written/interactive form of this series: https://www.3blue1brown.com/topics/neural-networks

Additional funding for this project provided by Amplify Partners

Typo correction: At 14 minutes 45 seconds, the last index on the bias vector is n, when it's supposed to in fact be a k. Thanks for the sharp eyes that caught that!

For those who want to learn more, I highly recommend the book by Michael Nielsen introducing neural networks and deep learning: https://goo.gl/Zmczdy

There are two neat things about this book. First, it's available for free, so consider joining me in making a donation Nielsen's way if you get something out of it. And second, it's centered around walking through some code and data which you can download yourself, and which covers the same example that I introduce in this video. Yay for active learning!
https://github.com/mnielsen/ne....ural-networks-and-de

I also highly recommend Chris Olah's blog: http://colah.github.io/

For more videos, Welch Labs also has some great series on machine learning:
https://youtu.be/i8D90DkCLhI
https://youtu.be/bxe2T-V8XRs

For those of you looking to go *even* deeper, check out the text "Deep Learning" by Goodfellow, Bengio, and Courville.

Also, the publication Distill is just utterly beautiful: https://distill.pub/

Lion photo by Kevin Pluck

Thanks to these viewers for their contributions to translations
German: @fpgro
Hebrew: Omer Tuchfeld
Hungarian: Máté Kaszap
Italian: @teobucci, Teo Bucci

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Timeline:
0:00 - Introduction example
1:07 - Series preview
2:42 - What are neurons?
3:35 - Introducing layers
5:31 - Why layers?
8:38 - Edge detection example
11:34 - Counting weights and biases
12:30 - How learning relates
13:26 - Notation and linear algebra
15:17 - Recap
16:27 - Some final words
17:03 - ReLU vs Sigmoid

Correction 14:45 - The final index on the bias vector should be "k"

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Animations largely made using manim, a scrappy open source python library. https://github.com/3b1b/manim

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:
https://vincerubinetti.bandcam....p.com/album/the-musi

Stream the music on Spotify:
https://open.spotify.com/album..../1dVyjwS8FBqXhRunaG5

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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