Glossary · Phase 2 · Math, when you need it
Johnson-Lindenstrauss lemma
A result saying points can be projected into far fewer random dimensions while keeping their distances nearly the same.
Try it now
The share of a ball's volume in its outer shell: 1 − (1 − thickness)ᵈ. Push the dimensions up and watch the shell swallow the ball.
Learn it properly
Strange geometry in high dimensions · Near-perpendicular random directions, bunched-up distances, and the curse of dimensionality. About 25 minutes.
Other terms from the same lesson
- curse of dimensionality: The ways space misbehaves as dimensions grow: distances bunch together, data gets sparse, and nearest neighbors stop being much nearer than anything else.
Never trained an AI?
Teach a small one to write, right in your browser. It takes about 20 seconds and needs no account.