curvature

Definition

How sharply the loss surface bends, captured mathematically by second-order information: the Hessian, or the Fisher information matrix as a stand-in. Knowing curvature lets an optimiser take a long step along flat directions and a short one along steep ones, which is why second-order methods converge in fewer steps. The catch is size — the matrix is quadratic in parameter count — so every practical method approximates it.