curvature-aware-nonconvex-optimization

Curvature-aware optimization helps escape saddle points by explicitly leveraging Hessian information to detect negative curvature directions. It estimates the Hessian's smallest eigenvalue and perturbs parameters along that direction to guide convergence and overcome stagnation.

Curvature-aware optimization is a technique that incorporates second-order geometric information, such as Hessian eigenvalues, into the optimization process. It uses Hessian-vector products or curvature estimates to identify negative curvature directions and accelerate convergence in non-convex problems.

Apply trust-region methods for deep learning training by using curvature-informed optimization to guide parameter updates. This approach supports trust-region algorithms alongside CRGD to navigate non-convex landscapes and avoid saddle-point stagnation during neural network training.

Yes, curvature-aware optimization works for neural network initialization and training. It applies second-order methods and Hessian information to curvature-sensitive optimization tasks, helping to identify and overcome saddle-point stagnation during the initialization and convergence phases.

Non-convex optimization stagnates when parameters get trapped at saddle points where the gradient is near zero. CRGD helps by using curvature information to find negative curvature directions, allowing the optimizer to perturb and escape these saddle points efficiently.

Yes, overcoming saddle-point stagnation with this approach requires Hessian-vector products or curvature estimates. These calculations provide the necessary second-order geometric information to detect negative curvature directions and guide the optimizer away from saddle points.