Negative-Curvature-Informed L-BFGS via Minimal Secant Corrections for Finite Minimax Problems

What the math gives to ML

The paper provides a practical way to make limited-memory quasi-Newton training robust to locally indefinite curvature without eigendecompositions, Krylov searches, or costly isotropic damping. Its key transferable asset is a minimal correction of only those secant pairs whose curvature is genuinely negative, while retaining the standard positive-definite BFGS update and two-loop recursion. This is especially relevant for optimizing finite worst-case objectives such as maxima over tasks, augmentations, experts, or adversarial scenarios, where nonsmoothness and negative curvature are common. The most direct neural-network test is full-batch or large-batch L-BFGS fine-tuning with an adaptive negative-curvature pair correction.