Free public beta until December 4, 2026: every course is open, no card needed. After that, the first chapter of each course stays free and full access is a one-time $39 ($19 for up to 100 founding members chosen for helpful feedback). Your progress is kept. How the beta works

cross-entropy

How surprised you'd be by the true distribution, if you believed a guessed distribution instead.

Examples

For truth $p=(1,0,0)$ and guess $q=(0.7,0.2,0.1)$ , $H(p,q)=-\ln(0.7)\approx0.357$ nats.