Entropic Optimal Transport and Sinkhorn

On the left wall is a distribution p over eight positions, on the back wall a distribution q. A transport plan moves the mass of p onto q: the bar in row i and column j says how much goes from position i to position j.

Moving mass far is expensive: the cost is the squared distance. Optimal transport keeps the bars on a narrow path near the diagonal.

The rest of the narration is in the book's Companion.