Gauss-Newton Accuracy and Indefinite Hessians: Uniform Coexistence in Low-Cost Sets

Key points

• Under local regularity and persistence of level-set curvature magnitude along an exact-fit section, we prove uniform coexistence of two curvature regimes.1
• Global minimizers exist, and every global minimizer has relative Hessian error below $(1+\sqrt2)/8$, while the same low-cost set contains a point with an indefinite Hessian and relative error at least $15/8$.1
• A pointwise certificate based on the current prediction level set controls the normal, mixed, and tangent parts of the Hessian correction.1
• We prove a sharp relative-error bound over the stated pointwise class when the prediction map and ridge vary.1

Sources (1)

• [1]Gauss-Newton Accuracy and Indefinite Hessians: Uniform Coexistence in Low-Cost Sets
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 08:38 AM

  We study the accuracy of Gauss-Newton curvature in ridge-regularized nonlinear least squares.

  Under local regularity and persistence of level-set curvature magnitude along an exact-fit section, we prove uniform coexistence of two curvature regimes.

Extractive summary: sentences quoted from the sources.