curvature-aware-nonconvex-optimization

Detect negative curvature directions and escape saddle points in nonconvex optimization.

2|Updated Feb 12, 2026

Search Tags:#optimization #hessian #curvature #non-convex #saddle-point #crgd #trust-region

Ready to run

npx skills add https://github.com/hiyenwong/ai_collection --skill curvature-aware-nonconvex-optimization

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: curvature-aware-nonconvex-optimization
Source: https://github.com/hiyenwong/ai_collection/tree/main/collection/skills/curvature-aware-nonconvex-optimization
Command: npx skills add https://github.com/hiyenwong/ai_collection --skill curvature-aware-nonconvex-optimization

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

将二阶几何信息（曲率/海森矩阵特征值）显式纳入优化目标或约束，帮助逃逸鞍点、加速收敛。

Core Features & Use Cases

Explicitly leverage Hessian information to detect negative curvature directions and guide escape from saddle points.
Support CRGD, trust-region, and second-order methods for curvature-informed optimization.
Applications include deep learning training, neural network initialization, and curvature-sensitive optimization tasks.

Quick Start

Use curvature-aware optimization to escape saddle points by estimating the Hessian's smallest eigenvalue and perturbing along the corresponding negative curvature direction.

Frequently Asked Questions about curvature-aware-nonconvex-optimization

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I escape saddle points in non-convex 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.

What is curvature-aware optimization and how does it use Hessian information?▼

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.

How to apply trust-region methods for deep learning training?▼

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.

Does curvature-aware optimization work for neural network initialization?▼

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.

Why does my non-convex optimization stagnate and how can CRGD help?▼

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.

Do I need Hessian-vector products to overcome saddle-point stagnation?▼

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.