Hessian Matrix

The Hessian matrix helps us understand not only the slope of a function, but also its curvature. In other words, it reveals whether the surface is sharp, flat, or geometrically complex by using second-order derivatives. It is used in advanced optimization methods, stability analysis, and in studying local minima and maxima. Although it can be computationally expensive in large models, it is theoretically a powerful tool for understanding optimization surfaces. The Hessian exposes the deeper geometric structure of model behavior.