In the context of optimization, the curvature of an objective function refers to the rate at which its gradient changes, conceptually captured by its second-order derivatives. Geometrically, curvature indicates how rapidly the surface of the objective function bends. Understanding this property provides useful intuition for adjusting optimization step sizes: in regions of high curvature where the gradient changes quickly, smaller step sizes help avoid overshooting the optimal solution or diverging; in regions of low curvature, larger step sizes can safely accelerate progress. While computing curvature directly is often too computationally expensive for deep learning, it forms the theoretical foundation for designing advanced adaptive optimization algorithms that automatically adjust their learning rates.