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/neural-networks-and-deep-learning 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://www.youtube.com/watch?v=i8D90DkCLhI https://www.youtube.com/watch?v=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 ----------------- 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" ------------------ 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.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u 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. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com/ Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown