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But what is a convolution?

3Blue1Brown
7.34M subscribers
3M views 2 years ago
Discrete convolutions, from probability to image processing and FFTs. Video on the continuous case:    • Convolutions | Why X+Y in probability is a...   Help fund future projects:   / 3blue1brown   Special thanks to these supporters: https://3b1b.co/lessons/convolutions#... An equally valuable form of support is to simply share the videos. Other videos I referenced Live lecture on image convolutions for the MIT Julia lab    • Convolutions in Image Processing | Week 1,...   Lecture on Discrete Fourier Transforms    • What is a Discrete Fourier Transform? | We...   Reducible video on FFTs    • The Fast Fourier Transform (FFT): Most Ing...   Veritasium video on FFTs    • The Most Important Algorithm Of All Time   A small correction for the integer multiplication algorithm mentioned at the end. A “straightforward” application of FFT results in a runtime of O(N * log(n) log(log(n)) ). That log(log(n)) term is tiny, but it is only recently in 20 …...more
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But what is a convolution?
109KLikes
3,082,018Views
2022Nov 18
Discrete convolutions, from probability to image processing and FFTs. Video on the continuous case:    • Convolutions | Why X+Y in probability is a...   Help fund future projects:   / 3blue1brown   Special thanks to these supporters: https://3b1b.co/lessons/convolutions#... An equally valuable form of support is to simply share the videos. Other videos I referenced Live lecture on image convolutions for the MIT Julia lab    • Convolutions in Image Processing | Week 1,...   Lecture on Discrete Fourier Transforms    • What is a Discrete Fourier Transform? | We...   Reducible video on FFTs    • The Fast Fourier Transform (FFT): Most Ing...   Veritasium video on FFTs    • The Most Important Algorithm Of All Time   A small correction for the integer multiplication algorithm mentioned at the end. A “straightforward” application of FFT results in a runtime of O(N * log(n) log(log(n)) ). That log(log(n)) term is tiny, but it is only recently in 2019, Harvey and van der Hoeven found an algorithm that removed that log(log(n)) term. Another small correction at 17:00. I describe O(N^2) as meaning "the number of operations needed scales with N^2". However, this is technically what Theta(N^2) would mean. O(N^2) would mean that the number of operations needed is at most constant times N^2, in particular, it includes algorithms whose runtimes don't actually have any N^2 term, but which are bounded by it. The distinction doesn't matter in this case, since there is an explicit N^2 term. Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Italian: Emanuele Vezzoli Vietnamese: lkhphuc -------- These animations are largely made using a custom python library, manim. See the FAQ comments here: https://www.3blue1brown.com/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: https://github.com/3b1b/videos/ Music by Vincent Rubinetti. https://www.vincentrubinetti.com/ Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw... Timestamps 0:00 - Where do convolutions show up? 2:07 - Add two random variables 6:28 - A simple example 7:25 - Moving averages 8:32 - Image processing 13:42 - Measuring runtime 14:40 - Polynomial multiplication 18:10 - Speeding up with FFTs 21:22 - Concluding thoughts ------------------ 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: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter:   / 3blue1brown   Reddit:   / 3blue1brown   Instagram:   / 3blue1brown   Patreon:   / 3blue1brown   Facebook:   / 3blue1brown  

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3Blue1Brown

7.34M subscribers