Accelerating preconditioned Jacobi methods via perturbation-inspired pivoting

What the math gives to ML

The paper develops a constructive pivoting principle for symmetric eigensolvers: prioritize off-diagonal entries by their predicted eigenvalue impact, not by magnitude alone. The transferable asset is the second-order perturbation scaling A_ij^2 divided by the spectral gap between the associated diagonal entries, which identifies small couplings between nearly degenerate modes as more important than large couplings between well-separated modes. This can be used in approximate eigendecomposition modules for covariance whitening, second-order preconditioning, orthogonal layers, or low-precision spectral normalization, where only a limited number of Jacobi rotations can be afforded.