Space-filling curves, turning visual information into audio information, and the connection between infinite and finite math (this is a re-upload of an older video which had much worse audio). Supplement with more space-filling curve fun: https://youtu.be/RU0wScIj36o For more information on sight-via sound, this paper involving rewiring a ferret's retinas to its auditory cortex is particularly thought-provoking: http://phy.ucsf.edu/~houde/coleman/sur2.pdf Alternatively, here is the NYT summary: https://goo.gl/qNuc14 Also, check out this excellent podcast on Human echolocation: https://goo.gl/23f4Yh ... https://www.youtube.com/watch?v=3s7h2MHQtxc

Demystifying attention, the key mechanism inside transformers and LLMs. Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. Demystifying self-attention, multiple heads, and cross-attention. Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/support The first pass for the translated subtitles here is machine-generated, and therefore notably imperfect. To contribute edits or fixes, visit https://translate.3blue1brown.com/ ------------------ Here are a few other relevant resources Build a GPT from scratch, by Andrej Karpathy https://youtu.be/kCc8FmEb1nY If you want a conceptual understanding of language models from the ground up, @vcubingx just started a short series of videos on the topic: https://youtu.be/1il-s4mgNdI?si=XaVxj6bsdy3VkgEX If you're interested in the herculean task of interpreting what these large networks might actually be doing, the Transformer Circuits posts by Anthropic are great. In particular, it was only after reading one of these that I started thinking of the combination of the value and output matrices as being a combined low-rank map from the embedding space to itself, which, at least in my mind, made things much clearer than other sources. https://transformer-circuits.pub/2021/framework/index.html Site with exercises related to ML programming and GPTs https://www.gptandchill.ai/codingproblems History of language models by Brit Cruise,  @ArtOfTheProblem  https://youtu.be/OFS90-FX6pg An early paper on how directions in embedding spaces have meaning: https://arxiv.org/pdf/1301.3781.pdf ------------------ Timestamps: 0:00 - Recap on embeddings 1:39 - Motivating examples 4:29 - The attention pattern 11:08 - Masking 12:42 - Context size 13:10 - Values 15:44 - Counting parameters 18:21 - Cross-attention 19:19 - Multiple heads 22:16 - The output matrix 23:19 - Going deeper 24:54 - Ending ------------------ These animations are largely made using a custom Python library, manim. See the FAQ comments here: https://3b1b.co/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ All code for specific videos is visible here: https://github.com/3b1b/videos/ The music is by Vincent Rubinetti. https://www.vincentrubinetti.com https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly. Mailing list: https://3blue1brown.substack.com Twitter: https://twitter.com/3blue1brown Instagram: https://www.instagram.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Facebook: https://www.facebook.com/3blue1brown Patreon: https://patreon.com/3blue1brown Website: https://www.3blue1brown.com ... https://www.youtube.com/watch?v=eMlx5fFNoYc