Definition
Plain language
A pyramid with a triangular base and four corners — the simplest possible three-dimensional shape.
As stated in the literature
A four-vertex simplex; the maximally symmetric arrangement of four equidistant points in three dimensions, found as the learned geometry a transformer decision head uses to encode four multiple-choice options in persuasion-circuit analysis.
Why it matters: As the simplest and most symmetric way to place four equal points in space, it turns out to be the geometry a model uses internally to keep four multiple-choice options apart.
For example, a tetrahedron is the shape of a four-sided die, with a triangle on the bottom and a point on top.
Heard on the show
“And not four clusters in arbitrary positions — four clusters at the four vertices of a near-regular tetrahedron.”Episode 038 — How LLMs Get Persuaded: One Attention Head, A Tetrahedron, And A Single Dial