[NO MUSIC] Why do Neural Networks use Linear Algebra? || The Visual Intuition of Cat Mathematics

Rather than studying for math class, come watch some furries instead. This is a prequel / supplementary video to the #SoME3 entry, Non-Euclidean Therapy for AI Trauma: https://youtu.be/FQ9l4v7zB3I ----------------------------------- This is a no-music re-upload of the original video: https://www.youtube.com/watch?v=DHjwbleAgPQ&feature=youtu.be The "unclear narration" is due to too much noise reduction to remove background noise. The audio may be re-done in the future if it can be scheduled in with other projects; for now, removing the music, watching with subtitles (with or without audio), and turning the volume up (subjective to the viewer's output audio device) improves the clarity to a degree. §▬▬▬▬▬§ Chapters §▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬§ 00:00 -- 0 |¤| A Dream of Cats 01:59 -- 1 |¤| Introducing Cat People (The Model) 03:38 -- 2 |¤| The Nap Dimension (The Trivial Dot Product) 05:24 -- 3 |¤| The Neural Network in Hiding (The Neuron Function) 08:05 -- 4 |¤| Who is Tom? (The Vector and the Point) 11:13 -- 5 |¤| As Above, So Below (The Projection) 15:07 -- 6 |¤| King to Queen (The Latent Space) 17:05 -- 7 |¤| Blind Men and an Elephant (The Interpretability of Circuits) 19:26 -- 8 |¤| Traveling Between High Dimensions (The Change of Basis) 24:19 -- 9 |¤| The Cat People Reality Revealed (The Analogy) 28:33 -- ? |¤| ??? 30:14 -- 10 |¤| Inverting the World (The Bijective Linear Map) 32:11 -- 11 |¤| Beware of False Friends in the Matrix ‡▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬‡ Recommended watching: Essence of linear algebra: Chapters 1, 2, 3, 9, 13: https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&ab_channel=3Blue1Brown But what is a neural network? | Chapter 1, Deep learning: https://www.youtube.com/watch?v=aircAruvnKk&ab_channel=3Blue1Brown ‡▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬‡ Academic papers referenced: Geometric Deep Learning: Going beyond Euclidean data-: https://ieeexplore.ieee.org/document/7974879 Zoom In: An Introduction to Circuits: https://distill.pub/2020/circuits/zoom-in/ Mass Editing Memory in a Transformer: https://memit.baulab.info/ The Building Blocks of Interpretability: https://distill.pub/2018/building-blocks/ Distillation of Neural Network Into a Soft Decision Tree: https://vgg.fiit.stuba.sk/people/martak/distill-nn-tree Making Decision Trees Accurate Again: https://bair.berkeley.edu/blog/2020/04/23/decisions/ Toy Models of Superposition: https://transformer-circuits.pub/2022/toy_model/index.html