Definition
Plain language
Approximating something complicated by the single most important pattern it contains.
As stated in the literature
A low-rank approximation that represents a matrix or operator as the outer product of two vectors, capturing its dominant mode.
Also called: rank-1 factorization, rank-one
Why it matters: It's the simplest meaningful compression of a matrix and a building block for interpretability and efficient model edits — capturing the main signal while throwing away the rest.
For example, you might summarize a thousand customers' purchasing patterns with one shared trend vector plus a single number per customer indicating how strongly they follow it.
Heard on the show
“The authors approximate that machinery with what's called a rank-1 factorization, and I'm going to skip the math because the result is the only part that matters.”Episode 038 — How LLMs Get Persuaded: One Attention Head, A Tetrahedron, And A Single Dial