Gauss-Newton Accuracy and Indefinite Hessians: Uniform Coexistence in Low-Cost Sets
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. 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 $15/8$. One positive ridge cap works for all independent center and label perturbations in fixed neighborhoods and every positive ridge weight up to the cap. These neighborhoods do not shrink as the ridge weight tends to zero. A pointwise certific...
| Authors | Kihun Rhee, Hanjoon Byun |
|---|---|
| Primary category | cs.LG |
| Published | 7 October 2026 |
| Last updated at source | 7 October 2026 |
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