Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates
Nonlinear least-squares objectives form the foundation of scientific machine-learning tasks, yet even curvature-aware optimizers remain geometrically inconsistent at finite step sizes: Levenberg-Marquardt (LM) derives its direction from local Riemannian metrics but realizes it as a straight parameter update. Here we introduce RNC-LM, which carries the LM direction along a locally constructed curved trajectory in Riemann normal coordinates. A recursive reformulation of the geodesic equation generates arbitrary finite-order corrections while reusing the same damped Gauss-Newton matrix factorization, and curve length is controlled separately from damping. On a reaction-diffusion physics-info...
| Authors | Jianing Liu, Dong H. Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 8 July 2026 |
| Last updated at source | 28 September 2026 |
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