Definition
Plain language
A measure of how much work it would take to reshape one distribution into another — earth-mover's distance.
As stated in the literature
An optimal-transport distance between probability distributions, equal to the minimum cost of transporting mass between them under a chosen cost function.
Why it matters: It captures meaningful differences between distributions even when they don't overlap, which simpler measures like KL divergence handle poorly.
For example, Wasserstein distance can measure how different two image-generator distributions are by computing the minimum cost to morph one set of samples into the other.
Heard on the show
“" They use what's called a Wasserstein distance, which is a fancy name for an intuitive idea.”Episode 015 — The Audit Number Isn't What You Think: Sycophancy and the Case Against Single-Prompt Bias Tests