johnhw.github.io/umap_primes/index.md.html
This is the first million integers, represented as binary vectors indicating their prime factors, and laid out using the UMAP dimensionality reduction algorithm by Leland McInnes. Each integer is represented in a high-dimensional space, and gets squished down to 2D so that numbers with similar prime factorisations are closer together than those with dissimilar factorisations.
# What do numbers look like?  ## A view of a million integers This is the first million integers, represented as binary vectors indicating their prime factors, and laid out using the [UMAP dimensionality reduction algorithm](https://github.com/lmcinnes/umap) by Leland McInnes. Each integer is represented in a high-dimensional space, and gets squished down to 2D so that numbers with similar prime factorisations are closer together than those with dissimilar factorisations. A very pretty structure
related reading
- Visualizing Algorithmsbost.ocks.org
- What Is a UMAP — and Why Do Scientists Love It?alleninstitute.org
- [1802.03426] UMAP: Uniform Manifold Approximation and Projection for Dimension Reductionarxiv.org
- Understanding UMAP – Topos Institutetopos.institute
- Math & Engineeringxn--2-umb.com
- Prism: mapping interpretable concepts and features in a latent space of language | thesephist.comthesephist.com
- Transformer Explainer: LLM Transformer Model Visually Explainedpoloclub.github.io
- How to Use t-SNE Effectivelydistill.pub
- Quantization from the ground upngrok.com
- unit-distance-cot.pdfcdn.openai.com
- How might LLMs store facts | Deep Learning Chapter 7youtube.com
- Factoring RSA-260cognition.com