✳flâneur — a map of the web's best reading

A short survey on almost orthogonal vectors in a few specific large dimensions

arxiv.org · 12,575 words · saved by 1 readers

This is experimental HTML to improve accessibility. We invite you to report rendering errors. Use Alt+Y to toggle on accessible reporting links and Alt+Shift+Y to toggle off. Learn more about this project and help improve conversions. The concept of almost orthogonal vectors, i.e. vectors whose cosine similarity is close to 0 , relates to topics both in pure mathematics and in coding theory under the guises of spherical packing and spherical codes. In recent years the rise of advanced language models in AI has created new interest in this concept as the models seem to store certain concepts as almost orthogonal directions in high-dimensional spaces. In this survey we represent some ideas regarding almost orthogonal vectors through three approaches: (1) the mathematical theory of almost orthogonality, (2) some observations from the embedding spaces of language models, and (3) generation of large sets of almost orthogonal vectors by simulations. In a given Euclidean space ℝ 𝑛 there

A short survey on almost orthogonal vectors in a few specific large dimensions ℝ \mathbb{R} ami Luisto Faculty of Information Technology, P.O. Box 35 (Mattilanniemi 2), FI-40014 University of Jyväskylä, Finland and Digital Workforce Services Mechelininkatu 1 a, 00180 Helsinki, Finland and Department of Mathematics and Statistics, P.O. Box 68 (Pietari Kalmin katu 5), FI-00014 University of Helsinki, Finland rami.luisto@gmail.com (Date: September 25, 2025) Abstract. The concept of almost orthogonal vectors , i.e. vectors whose cosine similarity is close to 0 , relates to topics both in pure math

Explore this link on the map →

saved by

related reading