New research explores Gauss-Newton accuracy and indefinite Hessians in low-cost sets

This paper delves into the accuracy of the Gauss-Newton curvature within ridge-regularized nonlinear least squares. It establishes that under specific conditions of local regularity and level-set curvature persistence, two distinct curvature regimes can coexist uniformly. The research proves the existence of global minimizers and provides a bound for their relative Hessian error, while also identifying points within the same low-cost set that exhibit indefinite Hessians with a higher relative error. The findings are supported by analytic examples illustrating the influence of output alignment, curvature orientation, and persistence, alongside a structural result on Jacobian row rank. AI

RANK_REASON This is a research paper published on arXiv detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

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