Spectral-transport stability and benign overfitting for minimum norm interpolation

תקציר מקורי באנגליתarXiv:2604.08625v3 Announce Type: replace-cross Abstract: Benign overfitting describes the ability of minimum norm interpolating estimators to generalize despite fitting noisy data exactly. Existing characterizations depend on delicate spectral functionals of the population covariance operator, namely the effective ranks of its eigenvalue tail. We study the stability of these characterizations when the covariance spectrum is perturbed, and we quantify perturbations with the Wasserstein distance between spectral measures, a viewpoint we call spectral transport. We prove that eigenvalue tail sums, tail second moments, and the two effective ranks that govern benign overfitting are Lipschitz stable with respect to the spectral-transport distance, with explicit constants driven by an eigenvalue