Lanczos Method for QRPA Strength Functions in Atomic Nuclei

What the math gives to ML

The paper's transferable asset is a matrix-free spectral-response strategy: one symmetric Lanczos Krylov run approximates a resolvent over an entire frequency or damping range, instead of solving a separate linear system at every query. The same construction can use neural-network Hessian-vector products to estimate curvature spectral density and multi-scale inverse-curvature responses without materializing the Hessian. This is most promising as an optimizer and training-dynamics diagnostic: spectral edges can set learning-rate ceilings, while broadened resolvent responses can determine damping or trust-region scales. The expected benefit is reduced overhead for curvature-aware training and improved stability, rather than replacing ordinary first-order optimization.