Beyond Negative-Ridge Endpoints: Mixed-Sign Spectral Regularization via Negative-Shifted Gradient Descent

Mixed-sign spectral regularization via negative-shifted gradient descent for overparameterized linear regression

A new arXiv preprint introduces negative-shifted gradient descent as a method for mixed-sign spectral regularization in overparameterized linear regression, escaping structural limitations of the negative-ridge endpoint. The authors identify a Marchenko-Pastur barrier in a Gaussian spike-plus-flat model and prove that early-stopped paths improve on all admissible endpoints by a polynomial factor in risk under explicit conditions. The main theorem handles general high-effective-rank tails and recovers all head scales simultaneously, with technical control via localized Duhamel integrals and a finite-grid hold-out inequality for validation-selected algorithms.