arxivcs.LG2026-07-04
Directional Curvature from Armijo Backtracking: A Low-Cost Sharpness Probe and a Calibration-Free Learning-Rate Safeguard for Adam
The local sharpness of the loss, the top Hessian eigenvalue $λ_1$, determines the largest stable gradient step, but measuring it normally requires Lanczos or Hessian-vector iterations. We observe that a single Armijo backtracking line search already carries this information at th…